{"Bibliographic":{"Title":"Satellite Doppler positioning : proceedings [of the] International Geodetic Symposium, October 12-14, 1976, hosted by Physical Science Laboratory, New Mexico State University, Las Cruces, N.M. Volume 2.","Authors":"","Publication date":"1976","Publisher":""},"Administrative":{"Date created":"08-17-2023","Language":"English","Rights":"CC 0","Size":"0000669644"},"Pages":["OB\n343\nI53\nSatellite\n1976\nv.2\nDoppler\nPositioning\nVol. 2\nPROCEEDINGS\nINTERNATIONAL\nGEODETIC SYMPOSIUM\nCosponsored by:\nU.S. DEFENSE MAPPING AGENCY\nNATIONAL OCEAN SURVEY, NOAA\nOctober 1976","QB\n343\nSatellite\nI53\n1976\nV. 2\nDoppler\nPositioning\nVOLUME 2\nPROCEEDINGS\nINTERNATIONAL\nGEODETIC SYMPOSIUM\nOctober 12-14,1976\nHosted by:\nMARINE AND EARTH\nSCIENCES LIBRARY\nPhysical Science Laboratory\nNew Mexico State University\nBox 3548\nAUG26 1977\nLas Cruces, N. M. 88003\nN.O.A.A.\nCosponsored by:\nU. S. Dept. of Commerce\nU. S. Defense Mapping Agency\nNational Ocean Survey, NOAA\n77\n3015","i\nTABLE OF CONTENTS - VOLUME II\nPage\nRELATING DOPPLER DATUM TO ORDNANCE SURVEY DATUM\n453\nLt. Col. M.R. Richards RE, Ordnance Survey of Great Britain\nRECOMMENDATIONS OF THE WORKSHOP ON DOPPLER DATA REDUCTION AND\nANALYSIS\n461\nREFERENCE ORBITS FROM RANGE AND DOPPLER OBSERVATIONS\n465\nJ. Berbert, H. Parker, NASA/Goddard Space Flight Center\nA COMPARISON OF SEVERAL DOPPLER-SATELLITE DATA REDUCTION METHODS\n479\nRonald Brunell, JMR Instruments, Inc.\nNEW POSITIONING SOFTWARE FROM MAGNAVOX\n499\nRon Hatch, Magnavox Government and Industrial Electronics\nCompany, Advanced Products Division\nNAVAL SURFACE WEAPONS CENTER REDUCTION AND ANALYSIS OF DOPPLER\nSATELLITE RECEIVERS USING THE CELEST COMPUTER PROGRAM\n519\nJames W. O'Toole, Naval Surface Weapons Center\nVARIATIONS IN DOPPLER POSITIONS RESULTING FROM DIFFERENCES IN\nCOMPUTER PROGRAMS AND TROPOSPHERIC REFRACTION COMPUTATIONS\n551\nHaschal L. White, Defense Mapping Agency, Aerospace Center\nANALYSIS OF GEOCEIVER RECEIVER DELAYS\n577\nFran B. Varnum, Defense Mapping Agency Topographic Center\nWORKSHOP ON POINT POSITIONING AND TERRESTRIAL ADJUSTMENTS\n587\nEFFECT OF GEOCEIVER OBSERVATIONS UPON THE CLASSICAL TRIANGULATION\nNETWORK\n591\nRobert E. Moose, Soren W. Henriksen, National Geodetic Survey,\nNational Ocean Survey, NOAA\nUPDATING SURVEY NETWORKS - A PRACTICAL APPLICATION OF SATELLITE\nDOPPLER POSITIONING\n657\nJoseph F. Dracup, Horizontal Network Branch, National Geodetic\nSurvey, NOS, NOAA\nADJUSTMENT OF TERRESTRIAL NETWORKS USING DOPPLER SATELLITE DATA\n675\nMark G. Tanenbaum, Naval Surface Weapons Center\nAN ORB DOPPLER PROGRAM ANALYSIS AND ITS APPLICATION TO EUROPEAN\nDATA.\n707\nJ. Usandivaras, Université de Tucuman, Conicet, Argentine\nP. Pâquet, R. Verbeiren, Observatoire Royal de Belgique,\nBruxelles, Belgium","ii\nTABLE OF CONTENTS - VOLUME II\n(Continued)\nPage\nCONCEPTS OF THE COMBINATION OF GEODETIC NETWORKS\n727\nD.B. Thomson, E.J. Krakiwsky, Department of Surveying Engineering,\nUniversity of New Brunswick, Fredericton, New Brunswick\n747\nINTRODUCTION TO THE WORKSHOP ON POLAR MOTION\nPaul Melchior, Royal Observatory of Belgium, Uccle-Bruxelles\nMINUTES OF THE WORKSHOP SESSION ON POLAR MOTION\n755\nJ. Popelar, Department of Energy, Mines & Resources,\nOttawa, Canada\nDETERMINATION OF GEOPHYSICAL PARAMETERS FROM LONG TERM ORBIT\nPERTURBATIONS USING NAVIGATION SATELLITE DOPPLER DERIVED EPHEMERIDES\n763\nBruce R. Bowman, Defense Mapping Agency Topographic Center\nAPPLICATION OF DOPPLER SATELLITE TRACKING SYSTEM FOR POLAR MOTION\n783\nSTUDIES IN CANADA\nJ.A. Orosz, J. Popelar, Gravity and Geodynamics Division, Earth\nPhysics Branch, Department of Energy, Mines & Resources,\nOttawa, Canada\nDOPPLER DATA TRANSMISSION AND HANDLING AT THE GEODETIC INSTITUTE\n793\nOF UPPSALA\nMichael O'Shaughnessy, Geod. Inst. Uppsala University,\nUppsala, Sweden\nERRORS OF DOPPLER POSITIONS OBTAINED FROM RESULTS OF TRANSCONTINENTAL\n813\nTRAVERSE SURVEYS\nB.K. Meade, NOAA, National Ocean Survey, National Geodetic Survey\nDETERMINATION OF NORTH AMERICAN DATUM 1983 COORDINATES OF MAP\n831\nCORNERS\nT. Vincenty, National Geodetic Survey, National Ocean Survey, NOAA\nDOPPLR - A POINT POSITIONING PROGRAM USING INTEGRATED DOPPLER\n839\nSATELLITE OBSERVATIONS\nRandall W. Smith, Charles R. Schwarz, William D. Googe, Defense\nMapping Agency Topographic Center\n891\nCLOSING REMARKS\nOwen W. Williams, Defense Mapping Agency\n895\nLIST OF ATTENDEES\nPHOTOGRAPHS TAKEN AT SYMPOSIUM\n899","453\nRELATING DOPPLER DATUM TO ORDNANCE SURVEY DATUM\nLt. Col. M. R. Richards RE\nOrdnance Survey of Great Britain\nSummary\nThe national triangulation network is briefly described and the necessity\nfor the use of satellite-Doppler observations, in the context of an established\nprecise triangulation, is considered. A comparison is made between existing\navailable Doppler observations and co-ordinates derived from the triangulation.\nRefinements of transformation parameters are investigated and discussed.\nFuture plans for derivation of translations with greater precision are noted.\nThe Ordnance Survey of Great Britain has a basic responsibility for\nmapping the country, which carries with it responsibility for all geodetic and\nlower order control networks. We have what may arguably be described as one\nof the best primary triangulation networks in the world.\nThe present network of some 290 stations is a mesh of permanently monumented\ntriangles. It was adjusted as a single figure in 1970, to derive the Ordnance\nSurvey of Great Britain 1970 (Scientific Network) datum, or OSGB 1970 (SN).\nThe adjustment was done on Airy's spheroid which was known to be a reasonably\ngood fit. The observations are all modern; nothing pre-dates 1935 and much\nwas post-1950. The adjustment incorporated 15 Laplace azimuth observations\nand 180 distance measurements among the 900 odd sides; these measurements were\neither invar tape in catenary (with no base extension), laser Geodimeter or\nTellurometer.\nAt the time of the adjustment, the only geodetic information of any sig-\nnificance that was lacking was deviation of the vertical and hence the geoid/\nspheroid separation over the country. Investigation had, however, indicated\nthat corrections for deflection would, in the worst possible case, never\nexceed 1 arc second; subsequent observations have proved this point, and\ndetermined that the separation, on Airy, is nowhere more than 41/2 meters; it is\nthus barely significant. If confirmation is required, it is encouraging to\nnote that the most recent Laplace azimuth observations and distance measurements\nshow remarkably small residuals -- generally less than 1 arc second and 5 ppm\nrespectively -- in comparison with values taken from the adjustment. There is\na suspicion, which we hope to resolve, that the whole network might be 2 or\n3 ppm small in scale, due possibly to a preponderance of microwave measured\nsides, but this does not materially change the high opinion in which we hold\nthe network.\nIt is against this background that the Ordnance Survey has viewed the\nprogress of satellite geodesy over the years. Since the early days we have\nparticipated in optical satellite tracking as we still do -- but this was\nmore with a view to international collaboration than with any thought to\nimprove the domestic triangulation. The various developments have been noted\nand their potentials assessed, but as their application in general has not","454\nbeen seen to be of direct relevance, or has been regarded as not being cost\neffective, they have not been pursued.\nWe are, however, extremely interested in the U.S. Navy Navigation Sate-\nllite System, particularly because of its availability and high potential as\na geodetic tool. This is not in the sense that we need it to establish the\nnetwork. Neither is it only because it has pointed up the possibility of\ntriangulation scale error, already mentioned, nor even because it can help to\nprovide geoidal information.\nThe most important factor is the obvious value in positioning points\ninaccessible to the triangulation network, namely drilling platforms in the\ncontinental shelf areas round the UK, where large hydrocarbon energy reserves\nhave been discovered. In this area, but most particularly where oil and gas\nfields straddle internationally agreed median lines, meters matter. Because\nthose international agreements pre-date the use of Doppler for position fixing\nthey are couched in classical geodetic terms; it is therefore necessary, if\nDoppler is to be used, to be able to translate the satellite datum values\ninto the local system.\nThe local system, as adopted in European waters, is European Datum 1950\n(ED50). There have been numerous assessments of the translation parameters\nfrom satellite datum to ED50. But ED50 is not a very satisfactory datum in\nmodern geodetic terms and translation parameters, together with assessments\nof their precision, vary with the array of stations used in their determina-\ntion, by quantities sometimes very much greater than the claimed precision\nof the Doppler observations. It is because we have a triangulation system\nheld, at least by us, in high regard that we venture, as a first step in our\ninvestigations, to draw comparisons with it to assess for ourselves the value\nwhich we may place on the satellite-Doppler observations, as translated into\na local system. Later, working in close collaboration with our European\nneighbors, we would hope to be able to agree on the relationship with ED50.\nThe epoch of the available Doppler observations varies and, with it, the\ndatum of those observations. It goes without saying that every care has been\ntaken to ensure that all the Doppler values used in this paper have been\ntransposed to a common datum, namely WGS 72, in order to ensure that like is\nbeing compared with like. The first available set of observations for study\nwere those obtained in the Defense Mapping Agency programme, during which\nnine stations were occupied within UK mostly by 512 Specialist Team RE (512\nSTRE). One of these was among the very earliest of observations and exhibits\nresiduals in comparison with the others which give reasonable cause for its\nrejection from the outset. We thus have eight sets of values to consider.\nThey are all precise ephemeris fixations, but the distribution of them in\nthe country, as shown on the map at Annex A, is rather less than ideal, with\nfour groups within about 200 km in the South, the others more widely spread\nbut well to the North. Another disadvantage, although relatively minor, is\nthat only one of the stations is coincident with a triangulation station\nincorporated in the 1970 adjustment.\nAs a \"first look\", the comparison has been effected in the conventional\nway. Utilizing the fact that any two geodetic systems, each satisfying the","455\nLaplace equation at a number of stations, will each have their cartesian axes\nof co-ordinates parallel to each other, the datums can be related by a constant\ndatum shift (dx, dy and dz) obtained by direct comparison of co-ordinate values.\nWe therefore compute three-dimensional cartesian co-ordinates of the Doppler\nstations from their OSGB 1970 (SN) latitude, longitude and spheroidal height\n(which is now everywhere known), taking into account the antenna height. These\nco-ordinates we compare directly with the Doppler cartesians. The resulting\nvalues are given in Table 1 below.\ndx\ndy\ndz\n1. Lasham 106\n-366.542\n+120.291\n-425.943\n2. Barton Stacey\n-368.147\n+121.224\n-428.965\n3. Mangersta\n-367.193\n+122.523\n-430.164\n4. Handgate Farm\n-367.821\n+122.577\n-428.815\n5. Herstmonceux\n-368.651\n+121.638\n-429.055\n6.\nEarly Coast\n-366.331\n+121.625\n-429.026\n7. Wick\n-366.133\n+120.215\n-429.606\n8. Scatsta\n-366.037\n+121.043\n-431.233\nMean\n-367.107\n+121.392\n-429.101\nEstimated Standard Error + 1.166m\nof a single difference\nTable 1\nCo-ordinate differences, OSGB 1970 (SN) - WGS 72, in meters\nThese figures represent a very good start, indicating a good measure of\nconsistency between the two datums, but they deserve some comment. Had we\nbeen considering perfect systems comprising errorless observations, with\nLaplace exactly satisfied, we would have expected the co-ordinate differences,\ni.e., the implied datum shift at each station, to be everywhere the same. The\nfact that this is not so must be attributed to errors in one or other or\nboth systems.\nWe were therefore encouraged to try to find a better fit by introducing\nadditional degrees of freedom into the translation. If we allow the possibility\nto exist that the scale of the two systems is not the same and, further, if we\nallow that the cartesian axes of the two systems are not necessarily exactly\nparallel, a simple seven parameter transformation might well improve the fit.\nWe thus used the available data from the same eight stations in a least squares\nsolution to derive not only a geocentric datum shift but also a scale factor\nand rotations about the three cartesian axes.\nWe acknowledge that the result of this exercise must be treated with some\ncaution. Because two of the stations used are very close to each other\n(within 25 km) they may exert undue weight upon the solution. Secondly, the","456\nsolution is unique to the array of stations used; any other array will produce\na different answer and the parameters derived can be used only when the part-\nicular array is being considered. But the process is reasonable; the trans-\nlation remains linear, with no second order terms introduced and, with the\nabove mentioned reservations, the results proved to be extremely interesting.\nThe parameters are given in Table 2.\nGeocentric datum shift\nRotations\nW1 (X axis) = -0.078 + 0.551\ndx = -350.439 + 0.3 m\nW2 (Y axis) = -0.261 + 0.198\ndy = +116.151 + 0.3 m\nW3 (Z axis) = +0.162 + 0.396\ndz = -419.393 + 0.3 m\nScale correction - 2. 8ppm + 0.8ppm\nTable 2\nTransformation parameters, Eight station fit, with estimated standard errors.\nThe geocentric datum shift differs from that previously determined, as is\nto be expected. The scale factor indicates that a reduction in scale of the\nDoppler of 2.8 ppm is called for, confirming perhaps the suspicion that the\nscale of the triangulation is too small. Let us admit to the possibility of\na small scale error in both, as it would be a very confident man who would\nassert the impossibility of scale error in the Doppler. Finally the rotations;\nthey are small, almost to the point of insignificance, but that which given\nconcern is the size of their standard error which indicates that they have been\nonly weakly determined. In fact the whole solution may justly be described as\nunstable. However, we apply the transformation to the Doppler co-ordinates\nand arrive at the residuals given in Table 3.\nResiduals in\nStation\nX\nY\nZ\n-1.230\n+1.071\n-2.123\n1\n+0.368\n+0.206\n+0.908\n2\n3\n+0.933\n-0.549\n+0.139\n4\n+0.224\n-1.082\n+0.481\n-0.530\n+1.051\n5\n+0.726\n-0.107\n-0.351\n6\n-0.602\n-0.293\n+1.122\n-0.583\n7\n+0.479\n8\n-0.124\n-0.130\nEstimated Standard Error +0.944 m\nTable 3\nResiduals from seven parameter transformation, eight stations. (Station numbering\nas in Table 1.)","457\nThe reduction in estimated standard error from + 1.166m to + 0.944m is\nbarely significant. We have further cause for concern as the residuals at\nLasham 106 are higher than the remainder. We therefore felt justified in\nrepeating the process omitting this station which is, in any case, very close\nto the permanent Tranet station at Barton Stacey. A second set of transla-\ntion parameters were then determined, as given in Table 4.\nGeocentric datum shift\nRotations\ndx = -356.099 + 0.2m\nW1 (X axis) = -0.085 + 0.372\ndy = +114.406 + 0.2m\nW2 (Y axis) = -0.069 + 0.110\ndz = -417.122 + 0.2m\nW3 (Z axis) = +0.260 + 0.268\nScale correction - 2.6ppm + 0.6ppm\nTable 4\nTransformation parameters, Seven Station fit; with estimated standard errors.\nThe geocentric datum shift changes once more, but this is unremarkable;\nthe scale factor remains virtually the same. More change is evident in the\nrotations. Not only have their standard errors reduced -- although they still\nremain disappointingly large -- but also two have almost disappeared. That\nwhich remains is a longitude rotation which is, by coincidence, of the same\nsize and in the same direction as that which should be applied in transforming\nfrom NWL 9D to NWL 10F. This solution can hardly, in fact, be described as\nbeing any more stable than the former, but having applied it, we arrive at\nthe residuals given in Table 5.\nResiduals in\nStation\nX\nY\nZ\n2\n-0.024\n+0.541\n+0.209\n3\n+1.013\n-0.565\n+0.135\n4\n-0.100\n-0.791\n-0.127\n5\n+0.260\n-0.164\n+0.318\n6\n-0.725\n+0.024\n-0.617\n7\n-0.304\n+1.135\n-0.578\n8\n-0.120\n- -0.180\n+0.661\nEstimated Standard Error + 0.635m\nTable 5\nResiduals from seven parameter transformation, seven stations (Lasham omitted). .","458\nThe magnitude of the inevitable improvement in estimated standard error\nto + 0.635m is gratifying. We compare this with the rather cautious state-\nment that accompanies many DMA precise fixations, to the effect that the\npositional accuracy -- which we understand to be the one sigma level -- in each\naxis is 1.5m or sometimes an even larger figure and consider that, perhaps,\ntheir claim may be too modest.\nOne might reasonably conclude from the foregoing that we should have\nevery confidence in the employment of the NNSS in the role earlier described,\nthat is for position fixing in offshore locations. Strictly speaking, however,\nthese results only allow of this conclusion when dealing with precise ephemeris\nfixations within UK and the number of stations used in deriving the transla-\ntions is probably too small. In the normal course of events, as will be the\ncase when observations are taken by commercial organizations, the positions\nwill have been fixed from the broadcast ephemeris only. We need to reassure\nourselves that we can continue to get good results without having to rely on\nprecise ephemeris data obtained after the observations have been made. A\nstudy of broadcast ephemeris data is thus desirable. We would like to improve\nthe number and distribution of precise Doppler fixes in the country; we may\nthus redetermine our transformation parameters with more confidence in their\nprecision. We would also like to consider the possibility of drawing up a\ndatum shift contour map, which would allow a simple three parameter transla-\ntion to be effected between the two systems, but which varies according to\ngeographical location. Again the lack of stations and their poor distribution\nis against us. We were therefore very pleased to accept when Nottingham\nUniversity invited us to cooperate with them in a programme of observations.\nThe University has received a Government grant for an investigation into\nsatellite-Doppler methods, absolute and relative accuracies and contributions\nto surveying networks. Through the grant they have purchased a Marconi CMA-722B\ngeodetic Doppler receiver. The University facilities enable them to conduct\nresearch into computation programmes but it is less easy for them to obtain\nthe basic observational data on which to work, a task for which the Ordnance\nSurvey organization is well suited. A joint programme was prepared, encompassing\nall the practical and technical aspects of field operations and support,\nequipment, software, exchange of data and theoretical applications.\nThe first stage has been a series of observations designed to supplement\nthe data given earlier in this paper, from which we may effect improvement in\nour translation parameters. The original intention was to observe at about\n12 to 15 stations evenly spaced through the country but this plan was modified.\nTo investigate the precision of the broadcast ephemeris, computation on which\nwould be done before the precise ephemeris could be made available, there would\nbe no selectivity in the observation of satellites. We considered it important\nto check the consistency of the broadcast ephemeris positions with localized\ngeographical areas. The programme was therefore changed to the observation\nof groups of contiguous stations, two or three in number and roughly 25 km\napart shown on the map at Annex A. Because resources were not unlimited, we\nrestricted ourselves to 5 locations in the country, giving good overall\ncoverage but not yet saturation.","459\nThe observations have been completed in a concentrated field programme\nwhich ended in September 1976, but at the time of writing insufficient obser-\nvational data has been reduced, so that we cannot yet make any detailed com-\nparisons. We have also welcomed 512 STRE for a brief stay in September, during\nwhich they have observed a further station for us. Results will be reported\nlater.\nThe second phase in the joint programme will be aimed at determining the\naccuracies of the various relative Doppler positioning techniques, including\nthe so-called translocation and simultaneous multi station determination\nFollowing this, effort will be concentrated on the problem of geoidal informa-\ntion and the extent to which satellite Doppler observations can be used to\nreplace expensive and time consuming astro-geodetic observations. Considera-\ntion of these subjects is, however, outside the scope of this paper.\nIn summary we are confident that the Doppler observations, as reduced\nfrom the precise ephemeris and translated into a local system, lose nothing\nof their geodetic accuracy and, as far at least as the area of the United\nKingdom is concerned, the probability is that they are more precise than\ntheir authors would claim. Further observations, necessary before firm\nconclusions can be drawn about broadcast ephemeris reductions, have been\ntaken but not yet computed. These further observations will also be reduced\non the precise ephemeris, where its availability permits, to broaden the\nscope of coverage in the country and allow definitive translation parameters\nto be produced.","5 W\n0\n460\nDisposition of\n60\n60 N\nDoppler Stations\no\nDMA/512 STRE Pre 1976\nX\nOS/Nottingham\n1976\n512 STRE\n1976\nx\n55°N\n55\nAnnex A\n0\n50\n5°W\n50 N","461\nRECOMMENDATIONS OF THE WORKSHOP ON\nDOPPLER DATA REDUCTION AND ANALYSIS\n1. That the following terminology be adopted for various methods of Doppler\nsatellite positioning:\na) \"short arc\" refer to methods in which the a priori ephemeris be given\nat least six degrees of freedom,\nb)\n\"semi-short arc\" refer to methods in which the a priori ephemeris be\ngiven between one and five degrees of freedom,\nc)\n\"rigorous translocation\" refer to methods in which only common data\npoints from passes simultaneously tracked at all stations be used in\nthe data reduction,\n\"translocation\" refer to methods in which receivers are operated\nd)\nsimultaneously, although the data points may not be identical.\n2. That the following preprocessing data analysis procedures be adopted as\nstandard:\na) that tests to monitor the following three receiver characteristics in\nthe field be devised; signal to noise ration, oscillator performance,\ntime recovery circuit performance,\nb) in the field, when a processing facility is not available, to use pass\npredicts of propagation delays to plot clock drift,\nc)\nin the field, when a processing facility is available, to compute\nand maintain records of offset frequency for each satellite tracked,\nand the rms residual noise for each pass,\nd) to minimize the resets of receiver local clocks,\ne) in majority voting, to retain all variable orbit parameters, including\nthose received only once or twice,\nf) in office preprocessing, to compute plots of frequency offset against\ntime with the following performance standards - a scatter about a\nlinear trend for each satellite of 5 parts in 1011 is excellent data,\nand of 5 parts in 1010 is marginal data. The linear trend itself\nshould not exceed the manufacturers specifications,\ng)\nin office processing, to compute plots of estimated receiver noise\n(standard deviation of Doppler residuals) against time with the following\nperformance standards - an rms noise of 5 cm is excellent, and in the\nrange 20-30 cm (depending on which program is used) is marginal,\nh) in office preprocessing, a statistical analysis of least significant\ndigit in the timing and Doppler data be performed to detect equipment\nmalfunctions,\ni) in office preprocessing, to test the timing and Doppler data values\nagainst maximum and minimum values, and to test the normalized Dopplers\nfor monotonic increase.\n3. That studies be encouraged to resolve the following unresolved problems:\na)\nthe stability, variation with elevation angle, orientation, site\nenvironment and signal strength of the antenna phase center location\nfor various antennas, and possible models for these phase center\nvariations,","462\nb) the geometric effect of earth tides on both ephemeris and station\nposition computations,\nc)\nthe effects of orbit error models, including short arc and various\nsemi-short arc techniques, on station position results,\nd)\nmore adequate inonopheric refraction correction models, including\nresidual range error computations from FOF2 data, triggering extended\ncorrections from the observed two-frequency correction (implying that\nthe two frequencies should both be recorded as data rather than being\ncombined by the receiver hardware), and separation of the refraction\nscaling bias into tropospheric and ionospheric terms,\ne) the weighting of observations according to elevation angle, signal\nstrength, antenna pattern, and noise in the corresponding broadcast\nmessage word,\nf) the serial correlation between range difference observations, and\nbetween range observations,\ng)\nthe utility of observed weather data in modelling tropospheric refrac-\ntion, improvements of such modelling and standardization of weather\ndata acquisition (in particular for special applications such as\npolar motion monitoring, etc.),\nh) the magnitude and effect of lags in the phase lock loop as a function\nof equipment and signal strength,\ni)\nabsolute and relative accuracies when using broadcast or precise\nephemerides; factors affecting the relative accuracy, such as range\nof distances between stations, minimum number of passes and minimum\ntime overlap,\nj)\nthe effect of different methods of handling time and frequency biases,\nusing laboratory measured values held fixed in the computation, using\nvalues given in the U.S. Naval Observatory Time Service Publication\nSeries 17, treating them as solution biases or the combination of the\nabove.\n4. That the following standards be adopted:\na) the velocity of light for ephemeris and station position computations\nbe 299792.458 km/sec,\nb)\nin polynomial fits to the precise ephemeris for station position\ncomputations, at least 6th order be used, and both the positions and\nvelocities of the precise ephemeris be used in the fitting.\n5. That test data sets from different receivers be established for processing\non different programs, and be made available to requestors on either 7-track\nor 9-track magnetic tape. These data sets should be in as close to the manu-\nfacturers raw data format as possible, should be from a minimum of 4 simultan-\neously tracking stations, should include a minimum of 100 passes per station\n(permitting several 20-pass solutions for the network), should include both\nbroadcast and precise ephemerides, meteorological data, and documentation of\nties to external standards against which this data may be compared.\n6. That in describing programs and communicating results, authors are encouraged\nto describe the detailed characteristics of their processing including the\nfollowing information:","463\na) simultaneity of receiver operation, of passes used, and of data points\nused,\nb) ephemeris used (precise or broadcast or both), ,\nc)\nephemeris interpolation method used (standard interpolation, polynomial\nfit, fit of functions which model ephemeris shape, fit to positions\nor to both positions and velocities) including order of polynomial\nand weighting used,\nd)\nmodelling of ephemeris errors (assumed perfect, short arc, semi-short\narc with degrees of freedom and a priori constraints described if\napplicable),\ne)\ninput data characteristics (receiver used, range or range difference\nobservations, correlated or uncorrelated observations),\nf) time recovery method,\ng) refraction correction methods (ionospheric model, tropospheric model,\nelevation editing criteria, scaling bias used),\nh)\nerror parameters included in the solution vector, with weights used,\ni) pass rejection criteria (elevation angle, rms residual or chi-square\ntest, etc. ) ,\nj) data point rejection criteria (residuals, etc.), ,\nk) the preprocessing diagnostic methods used and their results,\n1) standard deviations for Doppler residuals and percentage rate of data\npoint rejections (cycle corrections) associated with them,\nm) criteria for termination of the iterations if applicable.\nAttendees\nName\nOrganization\nJim O'Toole\nNSWC/DL Dahlgren, VA 22448\nAttention: DK-11\nAlex Hittel\nShell Canada Ltd.\nP.O. Box 880, Calgary\nDuane Brown\nDBA Systems, Inc.\nP.O. Box 550,\nMelbourne, FL 32901\nW. Blanchard\nDecca Survey Ltd.\nKingston Road,\nLeatherhead,\nSurrey, England\nPaul Paquet\nObservateire de Belgique\nAv. Circulaire 3\n1180 Brussels, Belguim\nGeorge Bynum\nMobil Oil\nP.O. Box 900,\nDallas, TX 75221\nRon Hatch\nMagnavox\n2829 Maricopa\nTorrance, CA 90503","464\nOrganization\nName\nDMAAC/GDGS\nHaschal L. White\nSt. Louis AFS, MO 63118\nRandall W. Smith\nDMA Topographic Center\n6500 Brookes Lane,\nFran Varnum\nATTN: (52000)\nWashington, D.C. 20315\nNational Geodetic Survey C12\nJames R. Lucas\n6001 Executive Blvd., ,\nRockville, MD 20852\nNational Geodetic Survey C133\nLarry D. Hothem\n6001 Executive Blvd., ,\nRockville, MD 20852\nDMATC/Geodetic Survey Squadron\nHarry C. Harris\nF.E. Warren AFB, WY 82001\nRonald Brunell\nJMR Instruments\n20621 Plummer Street,\nChatsworth, CA 92801\nBedford Institute of Oceanography\nD.E. Wells\nP.O. Box 1006,\nDartmouth, N. S.\nJ. Kouba\nGeodetic Survey of Canada\nSurveys and Mapping Br., E.M.R.\n615 Booth Street,\nOttawa, Canada K1A OE9","465\nREFERENCE ORBITS FROM\nRANGE AND DOPPLER OBSERVATIONS\nJ. Berbert\nH. Parker\nNASA/Goddard Space Flight Center\nGreenbelt, Maryland\nAbstract\nReference orbits accurate to better than 2 meters in height are required\nfor the GEOS-3 altimeter evaluation. Our previous study indicated this\naccuracy could be achieved by a network of 4 20-cm lasers simultaneously\ntracking the same pass. Orbits with 3 lasers were almost as good as those\nwith 4 lasers, but the fourth laser was needed to provide a reasonable\nprobability of obtaining data from at least 3 lasers due to weather and other\nproblems. Orbits with less than 3 lasers were not consistently below 2 meters\nin height error. In this paper various alternatives to the laser-only refer-\nence orbits are considered. It is found that when up to 3 of the 4 lasers\nare replaced by Doppler stations (retaining at least one laser), the reference\norbits are still useful for the altimeter evaluation, although height errors\nincrease up to 50% over those from the orbits with 4 lasers. These results\nhave practical significance for the GEOS-3 project since passes containing\nsimultaneous data from 3 or more lasers were not obtained as often as\ndesired and additional suitable reference orbits can be obtained from the\nlaser plus Doppler data.\nIntroduction\nFor in-orbit intercomparison of the GEOS-C radar altimeter with other\nGEOS-C systems using short arc reference orbits, the reference orbit heights\nmust be accurate in the calibration area to better than 2 meters to meet the\ntotal error budget of 5 meters for the altimeter calibration as specified\nin the GEOS-C Project Plan.\nSimulation Studies\nA previous study1 1 using the ORAN multi-arc error analysis program indi-\ncated this accuracy could be achieved by a network of four 20-cm lasers\nsimultaneously tracking the same pass. The laser network for the calibration\narea consists of the fixed laser at Goddard (GSC) chosen as the survey, time,\nand calibration reference laser, Patrick Air Force Base, Florida (PAT),\nBermuda (BER), and Grand Turk (GTK) and is shown in Fig. 1 with 20° elevation\ncoverage circles and the 2 typical GEOS-C passes used in this report. The\nstudy was done in two parts. First, station survey uncertainties were\nrecovered using 20 short arc passes over the networks. Then orbit uncertain-\nties for the 2 typical passes were recovered using the previously recovered\nsurvey uncertainties as part of the input.\n1\nBerbert, J. H. and Carney, D. , \"Laser Network Survey and Orbit Recovery\",\npaper presented at International Symposium on the use of Artificial Satellites\nfor Geodesy and Geodynamics, Athens, Greece, May 14-21, 1973.","466\nReference orbits with 3 lasers are almost as good as those with 4 lasers,\nbut orbits with less than 3 lasers are not consistently below 2 meters in\nheight error. We replaced 3 of the 4 lasers with 3 Doppler stations as an\nalternate to the laser-only reference orbits since passes containing simultan-\neous tracking data from 3 or more lasers were not obtained as often as desired.\nThe orbital height accuracy of the 1 laser, 3 Doppler station network turns\nout to be about the same as the 3 laser station network.\nThe priori errors assumed for the observations, gravity field, and station\nsurveys are summarized in Table 1. These survey uncertainties were obtained\nin the previously referenced study using 4 lasers and 20 short arc passes.\nNote that for the Doppler (geoceiver) stations zero range rate measurement\nbiases and zero time biases were assumed.\nThe GEOS-C short arc orbital elements or state vectors are assumed to be\ninitially unknown, with assumed uncertainties of 101 meters in each of the\n3 position components and 10 meters/second in each of the 3 velocity compo-\nnents. These values are provided as input to the ORAN computer program, where\nthe assumed observation noise values determine the observation relative weights\nand the assumed observation bias, state vector, gravity field, and timing\nuncertainties are propagated through the Bayesian least squares process into\nthe orbit recovery uncertainties.\nThe resulting height uncertainty estimates as a function of time along\nthe pass are given for each network in Table 2 and Fig. 2. The time (in\nminutes) that the height uncertainty is below 2 meters is 20, 16, and 12\nfor the S+N pass and 17, 13 and 14 for the N-S pass, respectively for the 4\nlaser, 3 laser, and 1 laser/3 Doppler networks. Thus, the 4 laser network\ngives the best results, but the 3 laser network and the 1 laser/3 Doppler\nnetworks are both potentially useful for calibrating the altimeter.\nReal Data Results From Lasers and Geoceivers Tracking GEOS-3\nOne to four geoceivers in the altimeter calibration area tracked GEOS-C\n(186 passes) between April 21, 1975 and May 19, 1975. Six of these passes\nwere also tracked by both STALAS (GSC) and the Goddard Mobil Laser #2 (ML2)\nstationed at Grand Turk. The geoceivers were stationed at Grand Turk (GTK),\nBermuda (BER), Mila, Florida (MIL), and Wallops (WFC). These data afford\nan opportunity to test the validity of the simulation results and to possibly\nprovide reference orbits suitable for altimeter calibration. The 6 passes\ntracked by the geoceivers and the 2 lasers were selected for this purpose.\nThese passes are numbered 1, 11, 14, 15, 17, and 18 in Fig. 3. In each of\nthe 6 passes, orbits were formed using data from the GSC laser and from the\nparticipating geoceivers. The number of participating geoceivers varied from\n1 to 4 such that 2 passes had 4 geoceivers, 1 pass had 3, 2 passes had 2, and\n1 pass had only 1 geoceiver. The orbits thus determined were evaluated in a\nseparate set of bias recovery runs in which the orbits were held fixed and pass\nbiases were determined for independent tracking systems which were tracking\nthe same passes but were not used in the orbit determinations. These other\nsystems included the second Goddard laser (ML2) at Grand Turk and, whenever\npossible, the Wallops laser (WFC), the Wallops C-band radar (NWALI8 or W8),\nand the Bermuda C-band radar (NBER05 or B5).","467\nIn passes 1 and 11, in which all 4 geoceivers participated, the orbits\nwere also determined using the ML2 instead of the GSC laser and evaluated\nusing GSC instead of ML2.\nThe a priori error estimates for the observations are summarized in\nTable 3, first for the laser, geoceiver orbit recovery runs, then for the\nbias recovery evaluation runs with the orbit held fixed. After finishing\nthe simulation studies we learned that with real geoceiver data it is essential\nto allow for both measurement and time biases, so these are included in the\norbit recovery runs as indicated in Table 3.\nThe observation statistics derived for the single laser and several\ngeoceivers in the orbit determination runs are summarized in Table 4 and the\nobservation system statistics for the other lasers and radars from the bias\nrecovery evaluation runs are summarized in Table 5. The first row in Tables\n4 and 5 for passes 1 and 11 give results when GSC was the reference laser and\nthe second row gives results when ML2 was the reference laser.\nThe observation statistics in Table 4 show that the laser noise about\nthe combined orbit varies from about 4 to 10 cm. This is better than an\norder of magnitude improvement over the 1 to 2 meter laser data obtained\nduring the GEOS-2 active period 6 or 7 years earlier. 2, , 3 The geoceiver noise\nabout the combined orbit, after removal of the recovered measurement and time\nbias, varies from about 3 to 8 mm/sec, which is also better than the 3 to 6 cm/\nsec obtained with the Tranet data on GEOS-2. However, the geoceiver measure-\nment biases of about 1 to 7 meters/second and time biases of about 0 to +24\nmilliseconds are much larger than the 0 to 20 cm/second and several milliseconds\n2, 3\npreviously seen on the Tranet data. Independent results from intercompari-\nsons of collocated geoceivers and lasers strongly support the validity of\nthe geoceiver measurement biases recovered in these 6 passes and will be\npublished in a later report.\nIn Table 5 we see the observation statistics for those independent lasers\nand C-band radars used to evaluate the orbits, but not allowed to contribute\nto the orbit determinations. Again the RMS or noise values are given after\nremoval of the recovered measurement and time biases. For the 2 Goddard lasers,\nGSC and ML2 all of the RMS values, except that for pass 14, lie between 8 and\n15 cm. The fact that these values are somewhat larger than the 4 to 10 cm\nvalues obtained when either of these lasers helps determine the orbit reflects\nthe somewhat better capability of the short arc orbital elements to adjust to\nthe laser residuals on each pass than for the chosen simple error model coeffi-\ncients to do this. The pass 14 orbit is determined from only 1 laser (GSC)\nand 1 geoceiver (BER) and the computed trajectory is less constrained than\nfor the other 5 orbits when more systems are tracking. Thus the ML2 residuals\n2\nBerbert, John H., Parker, Horace C. \"Comparison of C-Band, Secor, and Tranet\nWith a Collocated Laser on 10 Tracks of Geos-2\", NASA-GSFC X-514-68-458,\nNov. 1968.\n3\nBerbert, John H. \"Geos Observation Systems Intercomparison Investigation\nResults\", NASA-GSFC X-932-74-212, July 1974.","468\nfor the unrealistic pass 14 orbit are large and exhibit a U-shaped pattern\nwhen plotted versus time. This shape cannot be removed from the residuals\nplot with only a measurement bias (offset) and a time bias (slope), leaving\na large RMS value of 2.35 meters for the pass 14 ML2 laser data.\nThe Wallops laser (WFC) RMS values of 1.1 meters, when the GSC laser\nforms the orbit, and 1.6 meters with the same data, when the ML2 laser forms\nthe orbit, are consistent with previous results of 0.9 to 1.9 meters obtained\nduring several collocation passes between WFC and the Goddard laser (ML2)\nprior to GEOS-3 launch. 4 Similarly, the C-band radar RMS values of 1.8 to\n3.3 meters for W8 and 4.0 to 5.9 meters for B5 are consistent with the previous\nresults of 0.8 to 2.1 meters for W8 seen in reference 2, since these larger\nvalues include the effects of all the unmodeled errors, such as survey errors.\nThe biases of the Goddard lasers GSC and ML2 are thought to be no more\nthan 5 to 20 cm, based on a series of collocation tests and other studies at\nGoddard. 5 Furthermore, the clocks on these lasers are thought to be synchro-\nnized to UTC transmitted to within about 5 microseconds, based on the charac-\nteristics of the station clocks, monitoring of Loran-C, and portable clock\ntrips. Therefore, the GSC and ML2 laser system biases in Table 5 should\naccurately represent the average range errors due to orbit and survey errors\nin the vicinity of these check stations.\nThe biases for the Wallops laser (WFC), the Wallops FPS-16 C-band radar\n(W8), and the Bermuda FPQ-6 C-band radar (B5) are also included in Table 5 for\ncomparison. Previous results with these systems gave range biases of from\n1.0 to 13.1 meters for WFC4 and from -1.9 to 7.5 meters for W8. 2 The Bermuda\nradar is generally believed to be a 5 to 15 meter system, based on some Apollo\nnear-earth orbit evaluations.\nThe survey positions which we used for all stations in this report were\nderived from C-band data on GEOS-2. 6\nMore recent survey recoveries now in\nprogress at Goddard using laser data appear to want to change the longitude\nat Bermuda by about 8 meters, and all 3 coordinators at Grand Turk by about\n5 to 7 meters, and the height of Wallops by about 4 meters with respect to\nGoddard. The direction of these changes is such that we ought to expect to\nsee something like a -4 meter bias at ML2 when GSC forms the orbit and perhaps\na several meter bias at GSC when ML2 forms the orbit. If we discount the\nlarge -13.4 meter biases obtained on pass 14 (1 laser/1 geoceiver (BER), average\nE = 55°) and on the low elevation pass 18 (1 laser/3 geoceivers (BER, MIL, WFC,\naverage E = 23°), then the recovered biases for the GSC and GTK lasers are\nfairly consistent with these expectations.\n4 Berbert, J. H., Carney, D. V. \"Geos-C Pre-Flight Laser-Laser C-Band Collo-\ncation Experiment\", Geos-C Principal Investigator Quarterly Progress Report\nNo. 2, April 1976.\n5\nMcGunigal, T., et al, \"Satellite Laser Ranging Work at the Goddard Space\nFlight Center\", NASA-GSFC X-723-75-172, July 1975.\n6\nMarsh, J., Douglas, B., Walls, D. M., \"Catalog of Station Coordinates for\nGEOS-C Orbit Determination\", Bulletin Geodesique No. 117, Sept. 1975.","469\nSimilarly the survey height change of 4 meters at WFC should reduce the\n3 recovered W8 biases to less than 2 meters and the longitude change of 8\nmeters at BER should reduce the 3 recovered B5 biases to about -8 to -17\nmeters.\nIn summary, the real data results given here neither prove nor disprove\nthe validity of the simulation study result that short arc orbits from 1\nlaser and 3 Dopplers should provide satellite heights accurate to better than\n2 meters. If the survey values we used were correct to within less than 1\nmeter, as assumed in the simulation, then our real data results would indicate\nthat we cannot quite obtain orbits accurate in height to 2 meters using a\nsingle laser and geoceiver Doppler data, for which we must allow a measure-\nment and time bias, unlike the zero bias assumptions for Doppler data in our\nsimulations. However, since the survey values we used are probably incorrect\nas indicated above, it appears likely that using the better survey values,\nwhen they become available, will change our real data results so as to\nsupport the simulation results.","470\nGEOS-0\nHEIGHT = 843 KM\nLASER OBS. MIN. ELEV. = 20°\n60\nis\n50\n40\nGSC\nBER\n30\nPAT\nGTK\n20\n10\nO\nb\n-10\n-40\n-30\n-70\n-60\n-50\n-100\n-90\n-80\n-\nLONGITUDE (DEGREES)\nFIGURE 1. GEOS-C PASSES USED FOR SATELLITE HEIGHT\nRECOVERY WITH 3 OR 4 LASERS AND I LASER\nWITH 3 GEOCEIVERS","471\nTABLE I. A PRIORI ERROR ESTIMATES FOR\nORBIT HEIGHT RECOVERIES\nLASER OBSERVATIONS (1 PER 10 SEC), BOTH 4 AND 3 LASER NETWORKS\nRANGE BIAS\nAR\n20 cm.\nRANGE NOISE\noR\n20 cm\nAZIMUTH NOISE\nof A\n30 arc sec\nELEVATION NOISE\nE\n30 arc sec\nTIME BIAS AT REFERENCE SITE (GSC)\nAt\no H sec\nTIME BIAS AT OTHER SITES\n50 usec\nAt\nLASER 3 GEOCEIVER OBSERVATIONS ( l PER 10 SEC )\nRANGE RATE NOISE\noR\n1.5 cm/sec\nRANGE RATE TIME BIAS\nAt\no usec\nREFERENCE GSC LASER (AR, oR, OA, oE, At )\nSAME AS ABOVE\nGRAVITY FIELD\n25% (APL 3.5-SAO - MI)\nSPHERICAL HARMONIC COEFFICIENTS\n1 x 10-6\nGM\nSURVEY\nLOCAL (X,Y,Z) meters\nREFERENCE SITE\n(0,0,0)\n(GSC)\n(0.7,0.4,0.6)\n(PAT)\n(1.3,0.4,0.9)\n(GTK)\n(0.9,0.6,0.9)\n(BER)","472\n4 LASER NETWORK\nGSC PAT GTK BER\n3 LASER NETWORK\nGSC PAT GTK\nGSC PAT GTK BER\nLASER 3 GEOCEIVER\nNETWORK\n3\no\nX\n2\nI\nx\nS\nN\no\n5\n10\n15\n20\n25\n30\n35\nx\nHELOTH\n3\n2\nN\nS\no\n25\n30\n35\no\n5\n10\n15\n20\nPASS DURATION (MINUTES)\nFIGURE 2. GEOS-C HEIGHT UNCERTAINTIES BASED ON SELECTED\nTRACKING NETWORKS FOR TYPICAL\nS ARCS\nN AND N\nS","473\nTABLE 2. GEOS-C HEIGHT UNCERTAINTIES BASED ON SELECTED\nTRACKING NETWORKS FOR 2 TYPICAL ARCS\n*\nI LASER\n3 GEOCEIVERS\n3 LASERS\n4 LASERS\n*\nGSC\nGSC\nTIME\nGSC\nPAT\nPAT\nPAT\nMINS\nGTK\nGTK\nGTK\nFROM\nBER\nBER\nEPOCH\nS\nN\n3.0\n2.7\no\n-\n2.2\n2.3\n1.9\n2\n1.7\n1.2\n1.6\n4\n1.3\n1.3\n0.9\n6\n1.2\n1.0\n0.7\n8\n1.2\n0.8\n0,6\n10\n1.4\n0.9\n0.8\n12\n1.8\n1.3\n1.1\n14\n2.0\n1.6\n1.4\n16\n2.2\n1.8\n1.6\n18\n2.3\n2.1\n1,8\n20\n2.5\n2.4\n2.0\n22\n2.8\n2.6\n3.3\n24\nN\nS\n3.3\n3.4\n3.1\n4\n2,3\n2.4\n2.1\n6\n1.5\n1.6\n1.2\n8\n0.9\n1.1\n0.7\n10\n0,7\n0,9\n0.6\n12\n0.8\n0.8\n0.6\n14\n1.0\n1.0\n0.7\n16\n1.3\n1.4\n0.9\n18\n1.7\n1.9\n1.3\n20\n2.1\n2.5\n1.7\n22\n2.6\n3.1\n2.1\n24\n3.0\n3.6\n2.5\n26\n3.4\n4.2\n2,9\n28","474\n(SEC)\nBIAS\n0.5\n0.5\n0.5\n0.5\nGEOCEIVERS (GTKG, MIL, BER, WFC)\n-\n0,5\nT\nNETWORKS FOR SIMULTANEOUS LASER, GEOCEIVER ORBIT RECOVERY\n(M/SEC)\nBIAS\n-\n10\n10\nR\n.\nTABLE 3. A PRIORI ERROR ESTIMATES FOR I LASER AND 1-4 GEOCEIVER\n(CM/SEC)\nNOISE\nBIAS RECOVERY WITH THE ORBITS HELD FIXED\n-\n0.5\n30\nR\n.\n(ARC SEC)\nNOISE\n-\n30\n30\n30\nE\nLASERS (ML0204 OR STALAS)\n(ARC SEC)\nNOISE\n30\n30\n30\nA\nBIAS\n(M)\n10\n10\n10\nR\n2.00\nNOISE\n2.00\n0.15\n0.15\n-\n(M)\nR\nLASER (WFCLAS)\nLASER (GTKG)\nGEOCEIVERS\nGEOCEIVERS\nC-BANDS\nLASERS","475\nNORTH\n0° AZIMUTH\nSTALAS (s)\nG\nMLO 204(G)\n3\nG\n7\nS\nS\n16\n17\nS\nG\nS\n14\n19\n15\nS\n10\nS\nS\n18\n90° AZIMUTH\nSTATION\nS\n70° 80°\n90° 80°\n20°\n60°\n50°\n40°\n30°\n20°\n30°\n40°\n50°\n60°\n70°\n270°\nELEVATION-\nAZIMUTH\nG\n20\nG\nS\n21\n22\nS\n5\nG\n180°\n12\nAZIMUTH\nFIGURE 3. NETWORK ARCS AZIMUTH VERSUS ELEVATION","3.4\nT - BIAS (MILLISEC)\n-\nGTK BER MIL WFC\n2.3\n-1.4 -23.6 -2.3-1.1\n0.1\n-0.1\n-20.3 -3.4\n-0.5\n-21.2 - 1.8\n0.6\n8.1 -15.1 6.6\n7.7\nTABLE 4. OBSERVATION STATISTICS DERIVED IN ORBIT DETERMINATION RUN\n-14.0\n19.6\n-23.8\n-21.1\n+0.2\n9.3\n1703 4010 5889\n2334 1904 2604 5043\n3722 2400 4590 6452\n3722 2401 4590 6453\n2345 1924 2618 5061\nGTK BER MIL WFC\n-BIAS(MM/SEC)\nGEOCEIVER\n1791 2560\n2166 4346\n1343\nGTK BER MIL WFC\n5.4\n4.7\n4.3\n4.9\nR- - RMS(MM/SEC)\n4.8\n4.4\n5.0\n3.6\n4.7 7.2\n5.9 4.5\n3.7\n3.1\n3.2\n7.6\n3.0\n3.0\n2.9\n5.7\n5.4\n-\n3.8\n3.8\n4.3\nR-RMS(CM) -\nGSC ML2\n7.6\n8.2\n-\nLASER\n6.4\n6.0\n6.9\n9.9\n4.7\n4.1\nDIRECTION YYMM-DD HHMM\n7504-25 0906\nTIME\n7505-14 1108\n7504-22 0810\n7504-27 0842\n7505-14 1108\n7505-15 1054\n7504-22 0810\n7504-23 0726\nDATE\nPASS NO.\nAND\nSR14\nSRII\nSR15\nSR17\nS 18\nS","-0.2\n1.8\n1..9\nB5\nC-BAND\nRADARS\n-0.03\n-BIAS (MILLISEC)\n-0.4\n-0.3\nW8\n-0.3\n0.7\nWFC\nLASERS\n1.0\n-0.4\n-2.6\n-1.3\n-1.8\n-1.3\nGTK\nGSC\n1.0\n0.6\nTABLE 5. OBSERVATION SYSTEMS STATISTICS DERIVED\n-24.12\n-3.85 - 15.63\n-17.71\nB5\nC-BAND\nRADARS\n-5.18\n-4.68\nR -BIAS (METERS)\nW8\nIN BIAS RUN WITH FIXED ORBIT\n0.5\n-2.5\nWFC\n-13.43\n-4.02\n-4.26\nLASERS\n3.87\n-13.42\n2.76\nGTK\n-8,74\n-3.66\nGSC\n2.54 4.24\n4.03\n3.29 5.87\nB5\nC-BAND\nRADARS\nR-RMS (METERS)\n1.81\nW8\nGTK WFC\n1.6\nLASERS\n2.35\n0.09\n0.10\n0.10\n0.14\n0.15\n0,08\n0.09\nGSC\n-\n1108\n15 7505-15 1054\nHHMM\n0810\n0810\n0726\n0906\n0842\n1108\nTIME\n7504-22\n7505-14\n7504-22\n7504-23\n7504-25\n7504-27\n7505 -14\nYYMM-DD\nDATE\nDIRECTION\nPASS NO.\n14\n17\n18\n11\n11\nI\nAND\nS\nS\nG\nS\nS\nG\nS\nS","478","479\nA COMPARISON OF SEVERAL DOPPLER-SATELLITE\nDATA REDUCTION METHODS\nRonald Brunell\nJMR Instruments, Inc.\nChatsworth, California 91311\nIntroduction\nFor an individual or organization contemplating the purchase of\nany positioning system many questions arise, the most obvious\nbeing what accuracies can be achieved with this system. The\nanswer to this question, when considering satellite positioning\nsystems, is derived from a study of the results of processing by\nthe computer program associated with the positioning system. The\npurpose of this paper is to provide an answer to this question for\nthe available JMR software. There are 5 JMR programs used in\nthis study, these programs are the SP-2, SP-6 and SP-7 along\nwith the translocation versions of the SP-2 and SP-7, designated\nSP-2T and SP. 7T.\nDescription of Programs\nThe SP-2 Program is a fixed station program and is written in\nthe FORTRAN IV language making it adaptable to a wide variety\nof machines. This Program provides a phase adjusted solution\nin X, Y and Z which is converted and printed as latitude, longitude\nand height in any datum for which a center offset from WGS-72 and\nellipsoid definition are known. This program provides great ver-\nsatility in the acceptance of a wide variety of doppler accumulation\nintervals, pass and data point editing criteria and output formats\nas requested by the user. However, these values may be defaulted\nto choices proven to provide excellent results and therefore not\nburden the user with unwanted detail.\nThe SP-7 Program is written in assembly language for the Hewlett\nPackard 2100 or 21 MX computers. This Program provides a three-\ndimensional solution, latitude, longitude and height, for fixed sta-\ntions and a two-dimensional solution in latitude and longitude for\nmoving stations. In both cases the primary pass solution results in\nlatitude and longitude but for fixed stations a centroid of the indivi-\ndual passes is computed along with pass editing features. Height is\ncomputed using multiple passes and a minimum variance technique.\nThe SP-6 Program is written in FORTRAN IV using the same basic\nalgorithms as the SP-7 but with the same versatility as the SP-2.\nThe SP-6 Program is for fixed stations only.\nIn order to verify the results of the JMR Programs three outside\nsources were contacted and graciously agreed to process this test\ndata with their programs. This has provided an excellent independent","480\ncheck against the JMR results. The three outside sources are,\nin alphabetic order, Defense Mapping Agency in Cheyenne,\nWyoming, using the Navy Long Arc Program (NLAP) with pre-\ncise ephemeris, DBA System, Inc., of Melbourne, Florida, using\nthe SAGA Program with broadcast ephemeris and Shell Oil of\nCanada, using the GEODOP Program with broadcast ephemeris.\nI would like to thank the above organizations and the individuals\ninvolved for their efforts and contributions to this paper.\nDescription of Test\nThe data gathering effort for this test began in May 1976. Five\nCalifornia sites were chosen, three of these sites lie on the U.\nHigh Precision Geodimeter Traverse (HPGT), or on well surveyed\noffsets from points on the HPGT. Two sites of unknown location\nwere also included. The first HPGT position was at Edwards Air\nForce Base. This site was previously occupied by a Geoceiver and\nis designated as Station 10032. The second HPGT position is at the\nGoldstone Tracking Station. This position was occupied with the\ngeoceiver on several occasions and is designated Station 10031.\nBecause this position is located under a large dish antenna, JMR\noccupied a site called Aries Eccentric which is at a well surveyed\noffset from the Primary station. The third station chosen is at\nWrightwood and is named Satellite Triangulation Station 111. However,\nbecause the primary location marker was destroyed during cons-\ntruction of a building, we occupied instead Satellite Triangulation\nStation 134.\nThe two unknown stations are designated JMR-A and JMR-B. Sta-\ntion JMR-A is situated on the roof of the JMR building in Chatsworth,\nCalifornia and JMR-B is located north of JMR-A and was used as a\nbackup to the JMR-A site. The geometry of these 5 stations provides\na north/south line of about 130km and an east/west line of appro-\nximately 155km.\nThe Pass Programmer feature of the JMR-1 was put to good use in\ntracking and recording of only the pre-selected passes. The criteria\nused in pass selection included using only passes achieving maximum\nelevation angles in the interval 20° to 70°, satellite 30180 was not\nused at all, passes having conflicting satellites were not used and\nan attempt was made to balance the passes in the quadrants (i. e.\nnorth going east of the station with south going west of the station\netc. ). This pass selection technique resulted in the recording of\nabout 11 or 12 passes per day. The test was set up to record 6\ncassettes of data with 40 to 45 passes per cassette. The stations were\nset up and maintained by personnel unfamiliar with the equipment\nwho received only several hours of training in the operation of the\nJMR-1.","481\nThe maintenance indicated above consisted of returning\nto the sites every 3 to 4 days to insert new cassettes and\nset up the JMR-1 pass programmer for the next set of data.\nAt all other times the receivers were left unattended. The\nactual man hours involved in the data gathering operation\nwas quite small, with the greatest amount of time spent in\ntravel to and from the sites. The maximum time on site was\nless than one hour and with well trained operators the time\nrequired would be much less.\nDescription of Results of Point Positioning\nThe results of processing the test data are presented below\nin two sections, the first section provides independent point\npositions compared with absolute positions, and the second\nsection provides interstation vectors achieved through trans-\nlocation solutions and compared with known or computed\nstandards. At this point, some discussion of the standards\nagainst which these comparisons are made is in order. The\nHPGT values shown here are provided in the NAD-27 datum\nand as the reference datum chosen for this report was WGS-\n72 a transformation was required. The center offsets between\nWGS-72 and NAD-27 vary across the United States with a\nstandard deviation in the 4 meter range. Because of this varia-\ntion the offsets used in this transformation were taken from the\ncontour graphs provided in the document titled \"The Depart-\nment of Defense World Geodetic System 1972\" as presented\nby Mr. Thomas O. Seppelin in May 1974. The use of the\ncontour charts greatly increased the accuracy of the trans-\nformation but still the offset values were only chosen to the\nnearest meter.\nFor some comparisons no HPGT value existed. In these cases\nthe NLAP results were used as the standard.\nTables 1 through 5 below show the independent point positions\nas computed by the programs involved. Each table is labeled\nwith the station name and the degree and minute portions of\nthe station latitude and longitude. In the column labeled Program,\nHPGT means the High Precision Geodimeter Traverse position\nor the HPGT position with the necessary offset applied to give\nthe actual station position, Results for all stations are not avai-\nlable from all programs but all results received are shown.\nThe SP-2, SP-7 and SP-6 Programs did not process all available\ndata to produce one result but rather each cassette was proces-\nsed to gain an independent result, the average number of good\npasses per cassette was 35. The location result as shown in","482\nthe tables is a mean value of these independent results with\na number in brackets which gives the standard deviation,in\nmeters, of the individual results from the mean. This approach\nto the processing was taken in the belief that many surveys\nwill be conducted on the basis of one cassette full of data and\nthis provides a measure of the effectiveness of such a survey\nas well as providing a measure of the consistency and repea-\ntability of the results.\nAt the sites Edwards, Goldstone and Wrightwood Geoceiver data\nwas available at the same site as occupied by JMR or a nearby\nsite with a known offset. At the time DMA processed the JMR\ndata the existing Geoceiver data was reprocessed with the JMR\ndata as well as the processing of the JMR and Geoceiver data\nindependently. The results of this comparison generated differ-\nences between the JMR and Geoceiver positions which were\nconsistent with the differences achievable by independent runs\nof several sets of Geoceiver data. This was true for all posi-\ntions with the exception of the height component at Edwards\nwhich indicated a possible difference of 1. 0 to 1. 5 meters.\nThis discrepancy could have been due to a measurement error\nbetween the electrical center of the JMR antenna and the marker.\nThe antenna at Edwards was raised on a pole to clear the roof\nof a camera building situated several meters from the marker.\nThere is a remarkable agreement among all the programs using\nthe broadcast ephemeris that a northward and westward bias\nexists between the results using the broadcast ephemeris and\nthe HPGT and/or program using the precise ephemeris. The\nnumber in parenthesis is the offset in meters from the compa-\nrison standard. It would have been significant to have been able\nto add SAGA results to the point positioning aspect of this studybut\nat the writing of this document sufficient data had been processed\nby SAGA only to provide good interstation results. However, the\ntrend in the processing did seem to bear out that an offset in\nthe same direction would finally result.\nFigure 1 through 5 provide the individual results for the five\nstations and Figure 6 contains a summary of the pertinent statis-\ntics resulting from the point positioning study. This summary\nshows that the results from Wrightwood are not consistent with\nthe other sites and there is good reason for the weakness of the\nsolution.\nThe site occupied at Wrightwood is severly shaded on one side by\na hill 100 meters high with a slope of about 20° to the north of the","483\n754.77 (0.77) [1.43]\n756.60 (2.60) [0.80]\n753.80 (0.20) [0.81]\n752.25 (-1.75)\n755.22 (1.22)\nMEAN OFFSET IN LATITUDE IS 5. 12 METERS WITH A STANDARD DEVIATION OF 0.51m\nMEAN OFFSET IN LONGITUDE IS 5.47 METERS WITH A STD. DEV. OF 0. 79 METERS\nHEIGHT\nMEAN HEIGHT SOLUTION IS 755.1 METERS WITH A STD. DEV. OF 1.01 METERS\n754m\nPOINT POSITIONING RESULTS FOR STATION EDWARDS\nTOTAL DISTANCE SPANNED BY LONGITUDE SOLUTIONS IS 2. 03 METERS\nPOSITION: LATITUDE= 34° 57'N LONGITUDE= 117° 54'W\nTOTAL DISTANCE SPANNED BY LATITUDE SOLUTIONS IS 1.49 METERS\n52.925\" (4.94) [1.25]\n52.946\" (5.47) [2.05]\n52.916\" (4.71) [1.07]\nTOTAL DISTANCE SPANNED BY HEIGHT RESULTS IS 2.80 METERS\n52.996\" (6.74)\n52.751\" (0.53)\nLONGITUDE\n52.730\"\nFIGURE 1\n50.647\" (4.48) [1.75]\n50.695\" (5.97) [3.50]\n50.663\" (4.98) [0.98]\n50.665\" (5.04)\n50.519\" (0.53)\nLATITUDE\n50.502\"\nPROGRAM\nGEODOP\nHPGT\nNLAP\nSP-2\nSP-7\nSP-6","965.54 (1.51) [1.15]\n[1.11]\n[1.17]\n967.01 (2.98)\n(4.64)\n(0.01)\n964.0 (0.03)\n964.03m\nMEAN OFFSET IN LONGITUDE IS 4.31 METERS WITH A STD. DEV. OF 0.75 METERS\nHEIGHT\nMEAN OFFSET IN LATITUDE IS 4.49 METERS WITH A STD. DEV. OF 0.70 METERS\n968.67\n964.04\nMEAN HEIGHT SOLUTION IS 966. 32 METERS WITH A STD. DEV. OF 1.72 METERS\nPOINT POSITIONING RESULTS FOR STATION GOLDSTONE\n[1.43]\nTOTAL DISTANCE SPANNED BY LONGITUDE SOLUTIONS IS 2.07 METERS\n12.104\" (4.53) [0.95]\n[2.53]\nPOSITION: LATITUDE= 35° 25'N LONGITUDE=116° 53 W\nTOTAL DISTANCE SPANNED BY LATITUDE SOLUTIONS IS 1.67 METERS\nTOTAL DISTANCE SPANNED BY HEIGHT SOLUTIONS IS 4. 63 METERS\n11.911\" (0.35)\n(5.19)\n(3.12)\n(4.38)\nLONGITUDE\n11.925\"\n12.130\"\n12.048\n12.098\nFIGURE 2\n29.014\" (5.26) [1.88]\n29.008\" (5.07) [2.08]\n28.960\" (3.59) (1.65)\n28.974\" (4.02)\n28.844\" (0.0)\nLATITUDE\n28.844\"\nPROGRAM\nGEODOP\nHPGT\nNLAP\nSP-2\nSP-7\nSP-6","485\n[1.63]\n58.979\" (4.91) [2.12] 245.29 (2.79) [1.65]\n59.042\" (6.51) [2.10] 244.54 (2.04) [3.10]\n245.13 (2.63)\n(5.90)\nMEAN OFFSET IN LONGITUDE IS 5.88 METERS WITH A STD. DEV. OF 0.62 METERS\nHEIGHT\n242.5m\nMEAN OFFSET IN LATITUDE IS 2.77 METERS WITH A STD. DEV. OF 0.80 METERS\n248.40\nLONGITUDE= 118° 34'W\n[1.87]\nTOTAL DISTANCE SPANNED BY LONGITUDE SOLUTIONS IS 1.60 METERS\nMEAN HEIGHT SOLUTION IS 245. 84 WITH A STD. DEV. OF 1.50 METERS\nPOINT POSITIONING RESULTS FOR STATION JMR-A\nTOTAL DISTANCE SPANNED BY LATITUDE SOLUTIONS IS 1.67 METERS\nTOTAL DISTANCE SPANNED BY HEIGHT SOLUTIONS IS 3. .86 METERS\n(5.80)\n(6.31)\nLONGITUDE\n58.785\"\n59.014\"\n59.034\"\nFIGURE 3\n35.422\" (2.01) [2.01]\n35.473\" (3.59) [3.59]\n35.419\" (1.92) [1.92]\nPOSITION: LATITUDE= 34° 14'N\n35.472\" (3.56)\nLATITUDE\n35.357\"\nPROGRAM\nGEODOP\nNLAP\nSP-2\nSP-7\nSP-6","367.53 (1.5) [1.83]\n373.00 (6.97) [1.22]\n368.22 (2.19) [1.99]\nMEAN OFFSET IN LONGITUDE IS 5.11 METERS WITH A STD. DEV. OF 0.73 METERS\n366.03m\nHEIGHT\nTOTAL DISTANCED SPANNED BY LONGITUDE SOLUTIONS IS 1.75 METERS\nMEAN OFFSET IN LATITUDE IS 4.44 WITH A STD. DEV. OF 0.54 METERS\n17.188\" (5.88) [1.65]\n17.119\" (4.13) [1.81]\nTOTAL DISTANCED SPANNED BY LATITUDE SOLUTIONS IS 1.30 METERS\n17.166\" (5.32) [3.13]\nMEAN HEIGHT SOLUTION IS 369. 58 WITH A STD. DEV. OF 2.43 METERS\nPOINT POSITIONING RESULTS FOR STATION JMR-B\nPOSITION: LATITUDE 34° 22'N LONGITUDE= 118° 32'W\nTOTAL DISTANCE SPANNED BY HEIGHT SOLUTIONS IS 5.47 METERS\nLONGITUDE\n16.956\"\nFIGURE 4\n25.706\" (5.01) [1.53]\n25.693\" (4.61) [6.53]\n25.664\" (3.71) [0.85]\nLATITUDE\n\"\n25.544\"\nPROGRAM\nNLAP\nSP-2\nSP-7\nSP-6","2164.27 (-1.13) [2.37]\n[2.75]\n2168.98 (3.58) [4.24]\n2163.86 (-1.54)\n(-2.13)\nMEAN OFFSET IN LONGITUDE IS 6. 76 METERS WITH A STD. DEV. OF 0.81 METERS\n2165.4m\nHEIGHT\n2163.27\nMEAN OFFSET IN LATITUDE IS 4.46 METERS WITH A STD. DEV. OF 1.69 METERS\nPOINT POSITIONING RESULTS FOR STATION WRIGHTWOOD\nMEAN HEIGHT SOLUTION IS 2165. 51 WITH A STD. DEV. OF 2.49 METERS\n54.703\" (5.65) [3.23]\n[4.92]\nTOTAL DISTANCED SPANNED BY LATITUDE SOLUTIONS IS 1.90 METERS\nLATITUDE= 117° 40'W\n[0.78\nTOTAL DISTANCE SPANNED BY LATITUDE SOLUTIONS IS 4.09 METERS\nTOTAL DISTANCED SPANNED BY HEIGHT SOLUTIONS IS 5. 71 METERS\n54.543\" (1.60)\n(7.55)\n(7.09)\nLONGITUDE\n54.480\"\n54.778\"\n54.760\"\nFIGURE 5\nPOSITION: LATITUDE= 34° 22'N\n44.424\" (4.92) [1.58]\n44.336\" (2.20) [2.31]\n44.467\" (6.25) [1.20]\n44.313\" (1.48)\nLATITUDE\n44.265\"\nPROGRAM\nHPGT\nNLAP\nSP-2\nSP-7\nSP-6","488\nantenna. This resulted in the average observations per pass\nbeing limited to 16 thirty second intervals. This poor antenna\nsiting resulted because it was not known that the primary marker\nhad been destroyed until the test was almost in execution. Also\na considerable amount of data was lost due to a tractor severing\nthe antenna cable and unauthorized personnel playing with the\nreceiver. The results from Wrightwood are presented as a\nmatter of interest but in the summary of results this station is\nexcluded. This is done because it is our belief that the results\nare not indicative of what could be expected from a well executed\nsurvey.\nIt was the original intent of this paper to provide an absolute frame\nof reference, or as close to one as could be provided, for the\npurpose of judging the accuracy of the JMR Programs. This frame\nof reference was to be provided by the HPGT positions, the NLAP\nprogram using precise ephemeris and the SAGA and GEODOP\nprograms using the broadcast ephemeris. As it turned out, how-\never, this well thought out frame of reference fell apart with the\ndiscovery of the offsets. That part of the reference depending\nupon the broadcast ephemeris held up very well indeed. The most\ngraphic representation of how well it held up is the fact that all\nthe solutions of the various programs at each site lie in an ellipse\nwith a semiminor axis of 0. 84 meters and a semimajor axis of\n.04 meters. The other part of the frame of reference held up\nexcellently as well (i. e. the NLAP results corresponded with the\nHPGT positions). But the two parts do not fit together. I have\ndiscussed this discrepancy with a number of people and agencies\nbut no magic explanation to make it disappear has as yet been\nfound.\nIn an attempt to recover the original intent of this paper a mean\noffset in latitude, longitude and height was computed and applied\nto the results at each site. The offsets chosen appear to be quite\nreasonable in the sense that the resulting RMS values for each\nprogram correspond well with the RMS values attained in the trans-\nlocation results. The offsets in latitude and longitude are quite\nwell defined by the processing results but a height offset is some-\nwhat obscured by the relatively large standard deviations in the\nheight solutions. However, the GEODOP and SP-2 Programs com-\npute in X, Y and Z where as the SP-7 and SP-6 Programs compute\nin latitude and longitude and the height result is achieved through\na nonrigorous method. With this in mind, another look at the\nresults show the height solutions of GEODOP and SP-2 agree bet-\nween themselves much better than they do with the SP-7 or SP-6\nresults and also better than the SP-6 and SP-7 results agree with\neach other. Because of this the height offset was computed using\nonly the GEODOP and SP-2 values. The resultant height offset is\na positive 1. 91 meters.","489\n*TOTAL\n2.03m\n2.07\n1.90\n1.60\n1.75\nDIST.\n0.79m\nDEV.\n0.75\n0.62\n0.73\nSTD.\n0.81\nWITH A SEMIMINOR AXIS OF 0.84 METERS AND A SEMIMAJOR AXIS OF 1. 04 METERS\nTHE LATITUDE AND LONGITUDE SOLUTIONS AT ALL SITES RESIDE IN AN ELLIPSE\nMEAN OFFSET\nLONGITUDE\n(THIS OFFSET WAS COMPUTED USING ONLY GEODOP AND SP-2 RESULTS)\n* THIS IS THE DISTANCE BETWEEN THE HIGHEST AND LOWEST RESULT\n5.47m\n4.31\n6.76\n5.88\n5.11\nTOTAL MEAN OFFSET FOR ALL SITES IN LONGITUDE IS 5.19 METERS\nTOTAL MEAN OFFSET FOR ALL SITES IN LATITUDE IS 4. .21 METERS\nTOTAL MEAN OFFSET FOR ALL SITES IN HEIGHT IS 1.91 METERS\nSUMMARY OF OFFSETS\n*TOTAL\n1.49m\n1.67\n4.09\n1.67\n1.30\nDIST.\nFIGURE 6\n0.51m\nDEV.\nSTD.\n0.70\n1.69\n0.80\n0.54\n** ALL SITES EXCLUDES WRIGHTWOOD\nMEAN OFFSET\nLATITUDE\n5.12m\n4.49\n4.46\n2.77\n4.44\nWRIGHTWOOD\nGOLDSTONE\nEDWARDS\nJMR-A\nJMR-B\nSITE","490\n0.82m\nTOTAL\n0.87\n2.26\n1.16\nTHE FOLLOWING VALUES ARE BASED ON THE PROCESSING OF ONE CASSETTE,\nRMS\nRMS VALUES AFTER REMOVAL MEAN OFFSETS\nHEIGHT\n0.84m\n0.72\n3.52\n1.29\nRMS\nFIGURE 7\nLONGITUDE\nTOTAL RMS FOR SP-2 PROGRAM 2.45 METERS\nTOTAL RMS FOR SP-7 PROGRAM 4.64 METERS\nTOTAL RMS FOR SP-6 PROGRAM 2.85 METERS\n0.96m\n1.30\n0.51\n0.81\nRMS\nLATITUDE\n0.62m\nABOUT 35 GOOD PASSES.\n1.22\n1.10\n1.31\nRMS\nPROGRAM\nGEODOP\nSP-2\nSP-7\nSP-6","491\nFigure 7 provides the RMS values for each program as computed\nafter removal of the offsets. As stated before the SP-2, SP-7\nand SP-6 results were actually mean values obtained from indi-\nvidual one cassette solutions. To compute RMS values for the\none cassette solutions the offsets were applied back to the indivi-\ndual cassette solutions resulting in the values shown on the\nbottom of Figure 2. In addition to these single quality numbers,\nit is of interest to look at the standard deviations associated with\nthe mean values. For the SP-2 these standard deviations ranged\nfrom 0.95 meters to 12 meters, for the SP-7 the range was\nfrom 0.80 meters to 6.53 meters, and for the SP-6 the range\nwas from 0.81 meters to 3.13 meters.\nDescription Translocation Processing\nFor the translocation aspect of this test four programs are used,\nall of which use the broadcast ephemeris. The four programs\nare GEODOP, SAGA, SP-2T and SP-7T. Three sites were used,\nwhich provided three interstation vectors for comparison. The\nthree sites chosen were Goldstone, Edwards and JMR-A. The\nreference interstation vector for Edwards to Goldstone was com-\nputed from the HPGT positions of the two sites. There is no\nHPGT position for JMR-A so the reference for the Goldstone to\nJMR-A and the Edwards to JMR-A was chosen as the NLAP\ncomputed positions at each site. The use of NLAP positions for\nall solutions involving JMR-A should result in a more consistent\nstandard than could be achieved by mixing NLAP `results with\nHPGT positions.\nDescription of Translocation Results\nThe translocation results are presented as vectors rather than\npositions because translocation is concerned with relative rather\nthan absolute locations. Figures 8, 9 and 10 show the results for\nthe three vectors. The presentation of the information is the same\nas with the point positioning. The degrees and minutes portion of\nthe solution is in the header and the body of the Figure only shows\nthe seconds portion of the vector. The number in parenthesis is\nthe deviation, in meters, of the result from the standard of com-\nparison. As in the previous section, the SP-2T and SP-7T did\nnot process all of the data for one solution but rather generated\nindividual solutions from one cassette with the mean solution\nshown in the Figures. The number in brackets is the standard","492\ndeviation, in meters, of the individual solutions from the\nmean.\nFigure 11 shows the RMS value for each program in each\ndimension as well as a total RMS value for each program.","493\n38.309 11 (-1.02) [0.94] 40.819\" (0.36) [1.33] 211.30 (-1.70) [2.11]\n38.339\" (-0.09) [1.58] 40.877\" (1.82) [1.17] 212.80 (-0.20) [0.75]\n211.79 (-1.21)\n212.95 (-0.5)\nINTERSTATION RESULTS FOR TRANSLOCATION OF EDWARDS AND GOLDSTONE\n213.00m\nHEIGHT\nINTERSTATION VECTOR: LATITUDE 27\" LONGITUDE 1° 1'\n40.796\" (-0.23)\n40.866\" (1.54)\nLONGITUDE\n40.805\"\nFIGURE 8\n38.309\" (-1.02)\n38.330\" (-0.37)\nLATITUDE\n38.342\"\nPROGRAM\nGEODOP\nSP-2T\nSP-7T\nHPGT\nSAGA","494\n511.25 (2.00) [2.00]\n510.25 (1.00) [2.79]\n(0.84)\n(0.67)\n509.25 m\nHEIGHT\n510.09\n509.92\nINTERSTATION RESULTS FOR TRANSLOCATION OF EDWARDS AND JMR-A\n15.241\" (2.44) [2.03] 6.055\" (0.33) [2.38]\n15.209\" (1.76) [2.75] 5.894\" (-3.75) [5.35]\nINTERSTATION VECTOR: LATITUDE 43' LONGITUDE 40'\n(-0.61)\n(-0.40)\nLONGITUDE\n6.042\"\n6.018\"\n6.026\"\nFIGURE 9\n15.161\" (-0.03)\n15.193\" (0.96)\nLATITUDE\n15.162\"\nPROGRAM\nGEODOP\nSP-2T\nSP-7T\nNALP\nSAGA","(0.85) [1.67]\n723.30 (2.30) [0.98]\n495\n(0.88)\n(1.87)\n721.00 m\nHEIGHT\n721.88\n722.87\n721.85\nINTERSTATION RESULTS FOR TRANSLOCATION OF GOLDSTONE AND JMR- - A\nINTERSTATION VECTOR: LATITUDE= 1° 10' LONGITUDE= 1° 41'\n46.923\" (1.24) [2.97]\n46.955\" (2.05) [3.64]\n46.822\" (-1.31)\n46.884\" (0.25)\nLONGITUDE\n46.874\"\nFIGURE 10\n53.497\" (0.31) [1.25]\n53.508\" (0.65) [1.31]\n53.502\" (0.46)\n(0.12)\nLATITUDE\n53.487\"\n53.491\"\nPROGRAM\nGEODOP\nSP-2T\nSP-7T\nNLAP\nSAGA","496\nTOTAL\n0.94m\n0.83\n1.35\n1.87\nRMS\nTHE SAGA RESULTS ARE BASED UPON THE REDUCTION OF 25 PASSES\nRMS VALUES FROM TRANSLOCATION RESULTS\nHEIGHT\n0.99m\n1.18\n1.59\n1.45\nRMS\nFIGURE 11\nLONGITUDE\n0.97m\n0.80\n0.77\n2.68\nRMS\nLATITUDE\n0.85m\n0.23\n1.53\n1.08\nRMS\nPROGRAM\nGEODOP\n* SAGA\nSP-2T\nSP-7T\n*","Residuals\nRESIDUALS OF DOPPLER* DERIVED STATION COORDINATES\n60\n.69\n1.02\n.65\nRMS\nWere Scaled By -1 ppm\nFROM JOINT DOPPLER* - GEODIMETER ADJUSTMENT\n5\nNWL 9D Coordinates\nEXCERPT FROM NWL TECHNICAL REPORT TR-3129; October 1974; R. J. Anderle\nSCALE OF METERS\nMETERS\n4\nAssumed\nStd. Day.\n65\n3\nLatitude (m) 1.2\nLongituda (m) 1.5\nHeight (m) 1.6\n2\nI\n70\no\n75\n*\nS-U\n1.1\n9\na -.5\nO -3\n80\n2.7@\n1.0\nCXO\n85\nO\n-6\n5\no\no\n7\n-1.5\n1.4\n- 1.2 (C)\no\nOF\nCASE 5\n1.76\n90\n.2\n-5\nHeight Residuals\nc 4\n95\n-1.0\nO\n(meters)\no\nO\n100\n-.4\n105\n(o)\n- 1.3\n- 9\n1.\no\n.3\no\n5\n1.2\nO\n-\n110\nO\n-0\no\n115\n10031\n8\no\n20\no\n(o)\n120\n4\nO\n10032\n-1.2\n125\n130\n45\n50\n40\n35\n30\n25\n20","498","499\nNEW POSITIONING SOFTWARE FROM MAGNAVOX\nRon Hatch\nMagnavox Government and Industrial Electronics Company\nAdvanced Products Division\n2829 Maricopa Street\nTorrance, California 90503\nAbstract\nMagnavox, as a part of our continuing software development, has recently completed\nnew point positioning and translocation software to be used in conjunction with the\nnewly developed GEOCEIVER II satellite receiver. The intent of the development was\nto provide a program that would: (1) supply a new level of accuracy to the user; (2) be\neasy to use; and (3) be portable from one machine to another.\nTo meet the accuracy objective a number of new features were incorporated into the\nprogram. The most significant of these are:\nImproved orbit recovery\nRemoval of time recovery jitter effects\nTropospheric strength solution\nEditing in the plane of least movement\nPseudorange processing\nEach of these new features will be considered in detail and sample results presented to\nshow that indeed a new level of accuracy was attained.\nIntroduction\nMore than five years ago (Stansell, 1971) Magnavox introduced the first multi-pass\npoint positioning program resident in a minicomputer. This program incorporated a\nnumber of processing techniques only recently described in readily available literature.\nThe technique of obtaining multiple pass solutions by simply cumulating the individual\npass contributions (Hatch, 1965 and Wells, 1974) is an example.\nThough a number of improvements have been made to this program over the past five\nyears, the increased computing power of available minicomputers and a number of\nimproved computational techniques dictated that a completely new program be developed.\nThis task was commenced in late 1975 and completed in early 1976.\nThe increasing power of the minicomputer allowed us to write the program in FORTRAN\nwhich not only significantly decreased the development time but also made the program\neasily portable from one machine to another. This in turn kept the development cost\nat a minimum.\nAs with previous assembly language programs a major objective was to make the\nprogram easy to use. We believe that this was accomplished.","500\nMost significant, however, are the new computational techniques employed. Five\nof these have been selected for detailed consideration. In each case, the technique\ndescribed represents either a significant improvement over previously described\nalgorithms or a significantly simplified method of implementing the algorithms.\nIn the final section some sample results are presented to verify that these techniques\ncan indeed result in significant accuracy improvements.\nImproved Orbit Recovery\nThe predicted orbital information transmitted by the satellite consists of a group of\nfixed parameters which define an approximate precessing ellipse and a set of variable\nparameters which define three corrections to the nominal ellipso at even minute\n(universal time) marks. These three corrections are:\n1) A correction to the semi-major axis of the ellipse.\n2) A correction to the eccentric anomaly of the ellipse.\n3) An out of plane correction to the nominal planc of the ellipse.\nEach correction is given to a precision of approximately ten (10) meters.\nWith the first \"Short Doppler'' programs pioneered by Magnavox in 1969 it became\nnecessary to obtain orbital positions at times other than the even minute mark. The\nsimplest and most straightforward method is to use interpolation techniques to obtain\ncorrections at intervening times. These corrections are then added to the mean\nellipse to obtain the desired satellite positions.\nA slightly better approach used at Magnavox for seven years, is to solve for the four\ncoefficients of a cubic equation which pass through the two-minute corrections in a\nleast squares sense. This results in a set of parametric equations describing the\namount of correction to apply as a function of time. This technique has the added\nvirtue of removing some of the +5 meters of round-off noise present in each of the\ntransmitted corrections.\nVisual inspection of the transmitted corrections indicated that an even better curve-\nfit could be obtained by fitting the corrections of both eccentric anomaly and semi-\nmajor axis to a biased sine/cosine curve at twice orbital frequency.\nFor the cross-plane correction a sine/cosine curve of orbital frequency appeared\nbetter. This curve-fitting process yielded a consistently excellent fit for the cross-\nplane corrections. The in-plane corrections were disappointing, however, with a\nmixture of both good and poor fits from one pass to the next. These tantalizing\nresults were first obtained in 1971.\nWells (1974) by adding a time dependent trend to the biased, twice orbital frequency,\nsine/cosine curve (four coefficients) was able to obtain excellent fits to the trans-\nmitted corrections. His analysis, however, indicated that the periodic nature of the\ncross-plane correction was not well defined. By contrast our initial results with\nthe cross-plane correction were very good and clearly indicate a once per orbit\ndependency which can be modeled with only three coefficients.","501\nRather than following the Wells approach and adding a fourth coefficient to the approxi-\nmating curve, we found that the two major phenomena contributing to the twice orbital\nfrequency behavior of the in-plane corrections could be computed and removed. Thus,\nwe compute expected corrections to the eccentric anomaly and semi-major axis which\narise from the gravitational oblateness (earth flattening). Though this is not a simple\ncomputation, neither is it overly complex. Similarly, we compute corrections to\neccentric anomaly and semi-major axis which arise from the approximations employed\nin the fixed parameter representation of the elliptical orbit. Specifically, in the\ndefining equations of the Transit system (1) the eccentric anomaly was approximated\nto avoid its transcendental nature and (2) the in-plane cartesian component orthogonal\nto the semi-major axis of the satellite orbit was simplified by removing the 1-e2\nmultiplicative factor. These approximations required the addition of corrective terms\nin eccentric anomaly and semi-major axis to adjust for the simplification.\nWhen these expected corrections are removed from the transmitted corrections the\nunknown residual corrections were found to be typically less than 100 meters and\nwere clearly of a sine/cosine nature with frequency equal to the orbital frequency\nrather than twice orbital frequency.\nThese residual corrections were then curve-fit to a sine/cosine curve with bias (three\ncoefficients) and extremely good results were obtained. The residuals following this\nfinal curve-fitting process are almost always less than the five meter round-off in\nthe transmitted parameters, lending a high degree of confidence in the results, while\nusing only three coefficients to describe the magnitude of the residual correction.\nReviewing this new method for recovery of satellite orbital data: first, corrections\nto the eccentric anomoly and semi-major axis are computed at every even minute\ntime mark based upon both the gravitational oblateness and the fixed parameter\napproximations employed. These corrections are then subtracted from the trans-\nmitted values to obtain residual corrections to eccentric anomoly and semi-major\naxis. These residuals as well as the transmitted values of cross-plane corrections\nare fitted to a sine/cosine curve with bias at the orbital frequency to obtain a\nparametric equation with three coefficients for each of the three correction components.\nSatellite positions can now be obtained at any time simply by evaluating the parametric\nequations at the appropriate time, adding on computed corrections and adding the total\ncorrections into the equations of the nominal ellipse.\nTime Recovery Jitter Effects\nThe jitter in the time recovery process within the satellite receiver contributes to\npositioning errors in two ways: First, the measured doppler counts are distorted by\nthe product of the frequency being counted (difference between receiver frequency\nand local oscillator frequency) and the time recovery error. Second, the position of\nthe satellite at the start and stop of the doppler count, if not adjusted, will be in error\nby the product of its velocity and the time recovery error.\nBoth of these errors can be removed if the satellite receiver is instrumented to\nmeasure the time recovery jitter. The first is the larger effect and it is relatively\neasy to remove. For translocation applications even the second effect of satellite\nmotion becomes non-negligible.","502\nAnother technique of eliminating time recover jitter is to modify the satellite receivers\nsuch that the doppler integration time is controlled by the local oscillator. This\ntechnique works very well if one counts a large multiple of the doppler frequency to\npreserve precision in the count.\nThe most serious disadvantage of this approach is that with integration times dependent\non the local oscillator frequency one needs to compute positions of the satellite at\ntimes which are also dependent on the local oscillator frequency. This added com-\nplexity in the computation of satellite position more than negates the gain obtained by\neliminating the need for the time jitter adjustment described above.\nIn at least the Geoceiver, the option of using the local oscillator to control the doppler\nintegration time also disables the recovery of message data from the satellite. This\nis a severe limitation. Even if the data is to be used for later tracked orbit process-\ning, the predicted orbits can be used to: (1) identify which satellite is the source of\nthe data; (2) recover the day and time of the satellite pass from a rough estimate of\nreceiver position; (3) compute an on site fix to verify proper equipment operation;\nand (4) be used in a high accuracy translocation mode.\nThe new Geoceiver II is identical to the MX 702A receiver except for one plug-in card\nwhich measures the amount of time recovery jitter. The software then computes the\nrequired adjustments to doppler count and satellite position to yield high precision\nresults.\nSolution of Tropospheric Strength\nMany different techniques exist for modeling and minimizing the effect of ionospheric\nrefraction. In most cases they include eliminating data taken below some threshold\nelevation angle. In some cases where high quality results are desired the tracking\nsites are instrumented to measure the temperature, pressure, and humidity.\nThese are then used in complex tropospheric models to remove the tropospheric\nrefraction effects on the measured doppler count.\nAt Magnavox we have historically used a simple model of the form:\nAR K/(Sin(E) K2)\nwhere K1 is selected to yield the desired range correction when the satellite is directly\noverhead, and K2 is selected to match the horizon or near horizon magnitude of\ncorrection desired. This simple equation has yielded very good results particularly\nwhen a cutoff elevation angle of .50 has been used.\nIn the new point-positioning program, we found that by eliminating the 7. 50 editing\nlimit a significant amount of data sensitive to the troposphere was added into the\nsolution. This allowed the addition of the overhead scale factor, K1, to the solution\nvector. This results in an improved tropospheric model which in turn improves the\nresultant latitude, longitude and height solutions.\nRecent evaluation of the algorithm has lead to a slightly more complex but still simple\nimplementation equation of the form:\nAR = /(Sin(E) + K2 + (Sin(E)","503\nThis equation allows an exact match to a nominal refraction effect curve at four points.\nAt Magnavox we selected the 10° and 5° points for matching along with the overhead\nand horizon points. The overhead value is then freed and determined from the\ndoppler data.\nEditing in the Plane of Least Movement\nAshkenazi and Gough (1975) and Wells (1974) give very good discussions of the use of\nthe Guier plane as a means of editing doppler data and even complete passes. A\nbrief summary is given here.\nThe Guier plane is defined as the plane which passes through the receiver coordinates\n(estimated) and contains the velocity vector of the satellite at closest approach. The\ntechnique depends upon the fact that the doppler curve is essentially two-dimensional\n(ignoring frequency offset). The prominent features of the doppler curve are: (1) the\ntwo relatively flat tails which are a measure of the average frequency offset; (2) the\nintercept of the average frequency offset with the curve which is a measure of the point\nof closest approach or along track position; and (3) the slope or rate of change of\nfrequency at the intercept point which is a measure of cross-track range from satellite\nto observer.\nFrom the above discussion it follows that an observer at the same along-track and\ncross-track range as a second observer will obtain almost identical doppler curves\neven though the two are at physically different locations. This is illustrated in figure 1.\nStated in another way, the doppler measurements are only slightly affected by and\nare very insensitive to both receiver and satellite position errors which are perpen-\ndicular to the Guier plane.\nAlong-track and cross-track errors are observable but are mapped directly into the\nestimated receiver position. Therefore, the doppler measurement residuals after\nadjustment of receiver position are a very good indication of the measurement noise.\nThese residuals, therefore, provide an excellent tool for editing individual doppler\ncount measurements and for editing entire passes from the multipass solutions when\nthe RMS residuals for the pass are large.\nIn our new point-positioning and translocation software, an almost equivalent, but\nmuch easier to implement technique has been employed. We have labeled it \"Editing\nin the plane of least movement\".\nWhen forming the set of normal equations each equation corresponds to a particular\nparameter for which we are solving. Thus, the equation which results from the\nderivative of the sum of the residuals squared with respect to frequency, we have\nlabeled the frequency equation. We have labeled in the same fashion those equations\nformed by taking the latitude, longitude and height derivatives respectively.\nIn our edit pass computation we first proceed to form the normal equations just as if\nwe were to add them into a multipass solution with solution coordinates of offset fre-\nquency, latitude, longitude, and ellipsoid height corrections. Next, we proceed via\nthe Gauss elimination technique to eliminate offset frequency and latitude corrections\nfrom the longitude and height equations. An inspection of these two equations reveals\nthat they are almost identical. (Another evidence of insensitivity to out of Guier plane\norbit or receiver position errors.) An exaggerated plot of these equations is given\nin figure 2.","-------------------\nZ\nFIG. 1 Two-Dimensional Nature of Position Fix\nDISPLACEMENT\nLONGITUDE\nY\nGUIER PLANE\nX\nALTITUDE 2\nALTITUDE 1","505\nPLANE OF LEAST\nMOVEMENT\nGUIER PLANE\nLONGITUDE\nEQUATION\n\"AVERAGE EQUATION\"\nGEOIDAL HEIGHT EQUATION\nLONGITUDE CORRECTION\n1076-5020\nFIG. 2 Example of Guier Plane and Plane of\nLeast Movement Solution\nIf the Guier plane were intersected with this longitude, height plane it would result in\na line through the origin (receiver position) almost perpendicular to the two equations\nalready plotted.\nThis exercise reveals a technique by which we can let the data itself tell which plane\nis least sensitive to out-of-plane orbit or receiver position errors. First, we simply\naverage the two equations we have obtained for minimizing the corrections to longitude\nand height. Next, we construct (an easy task) the equation of a line passing through\nthe origin (receiver position) perpendicular to the 'average equation'. If we now\nsolve these two equations for longitude correction and height correction, we obtain\ncorrections to longitude and height which minimize the total correction and are least\nsensitive to out-of-plane position errors.","506\nUsing this procedure we form the derivatives and obtain the solution corrections in\nthe same natural coordinates that are used in the multipass point-positioning and\ntranslocation solutions. The only expense is a little extra logic at the time the\nnormal equations are inverted.\nThis special single pass solution provides the natural tool for residual editing of\nboth individual doppler measurements and entire passes.\nPseudorange Processing\nOver six years ago a drawback in the typical processing algorithms used to obtain\nposition fixes was discovered. Specifically, the old Magnavox 702CA satellite\nreceiver accumulated doppler counts for two minutes but shorter interval readings\ncould be strobed out and differenced to obtain shorter interval doppler counts.\nThe disturbing paradox was that as more and more readings were strobed out\n(which is equivalent to adding more and more information about the doppler curve)\nthe solution obtained first improved as the doppler counting interval approached\nthe 10- to 30-second period and then degraded rapidly as the counting interval\ncontinued to descrease. This result either disagrees with the laws of entropy or\nindicates a processing problem.\nA search for possible sources of processing errors quickly revealed that the culprit\nwas the statistical correlation between adjacent doppler counts. To test this concept,\na nonoptimum, but easily implemented technique was added to our position fixing\nalgorithm. Specifically, we implemented a \"moving interval\" doppler count whereby\nfrom five to ten short doppler counts were added together. The next doppler count\nwas then generated by removing one short doppler count from the front of the combined\ncount and a new short doppler count was added on at the end of the interval. This\ndecreased the cross correlation between counts but the number of counts and statistical\nredundancy remained high. As expected, significantly better results were obtained.\nSince early 1971 this technique has been employed in all Magnavox navigation programs.\nBecause the above approach was sub-optimal, we derived what appeared to be an\noptimal method, implemented it and found that the results were inferior to the sub-\noptimal approach described above! Much later the source of this problem became\napparent. Specifically, the solution was strengthened to the point that it became\nmuch more sensitive to systematic sources of error. In particular, better results\nare obtained using the optimum technique only after adding to the algorithm the solu-\ntion for tropospheric refraction magnitude and thus decreasing the systematic errors\npresent in the data.\nBefore describing our technique and its advantages, let us point out two alternate\nmethods which others have employed to overcome the statistical correlation problem.\nThe Brown Technique\nThe first to recognize and deal with the problem was Duane C. Brown of DBA Systems\nIncorporated (Reference 5). His technique of Continuously Integrated Doppler (C.I.D.)\nwas to simply add each doppler count obtained to the previous doppler counts. Com-\nbined doppler counts are measures of the range change since lock on. The range at\nlock time was then added to the solution process as a nuisance variable similar to the","507\noffset frequency. There is, however, one serious drawback to this approach. For\nevery loss of lock or doppler count edited, an additional nuisance range at time of\nrelock must be added to the solution process. This can negate the use of this\ntechnique for all but a very few satellite passes.\nThe Kirkham Technique\nA second direct approach has been described by Perry Kirkham in 1972. In his\napproach the statistical cross correlation matrix of the doppler counts is generated\nand inverted to obtain a weight matrix to be used in the formation of the normal\nequations.\nThis technique works well and is mathematically equivalent to the Brown technique.\nHowever, it too, suffers from some serious implementation problems. Specifically,\nthere is no problem when two-minute doppler counts are used and generation of the\nweight matrix requires inverting only an 8 X 8 matrix. However, when 30 to 40 short\ndoppler counts are considered and a square matrix of that size must be inverted (and\nreinverted whenever a doppler count is edited out) the technique clearly becomes\nunworkable.\nThe Magnavox Technique\nThe basic concept of the technique we have employed is very similar to that used by\nDuane Brown. However, instead of adding sequential doppler counts together we\ndefine a linear mapping of N sequential doppler counts (range difference measurements)\ninto N + 1) range minus range average measurements. Having performed this opera-\ntion we need not add another nuisance variable into the solution processes, yet we\nhave minimized the residuals in ranges and the individual pseudo-measurements are\nstatistically uncorrelated. This technique is equivalent to the previous two approaches\nbut does not suffer from any significant implementation problems.\nTo illustrate the technique, we have chosen two applications which are not as complica-\nted as doppler position fixing. In addition, they illustrate that the technique has\ngeneral applicability to many positioning problems:\nA one-dimensional example\nFirst, let us consider a simple problem which occurs in the formation of clocked\ndoppler measurements. It is not hard to use the clock readings to generate measures\nof time recovery error differences of the form:\nCi","508\nHowever, in order to correct the doppler counts for satellite movement which occurred\nduring the time errors it is necessary to form the value:\nwhere r is the range rate of the satellite with respect to the observer.\nThe Defense Mapping Agency employs a very clever technique of separating this\nexpression into two terms:\nwhere:\nea\nThe first of these two terms is then combined with another term and evaluated directly\nfrom the doppler count itself. The second term can be further separated into a term\ndue to the average receiver time delay and an additional noise term.\n+\nThe first of these two terms can be minimized by including the average time delay e\ninto the solution vector. The second term is such a small term (not ever larger than\none or two centimeters) that it is completely ignored.\nNow let us see how we can evaluate the above expression using our mapping technique.\nIn order to write specific, easily understood expressions, let us limit ourselves to\nfour measurements:\nC4 = (e5 - e4\nFirst, let's perform the Brown type mapping:\nC1\n(e2-e1)\nC1+C2+C3C4(e5-e1","509\nThen let us include a new pseudo-measurement\nO (e1-e1)\nIf we average these last five equations we get:\n4+3C+2C4-e1\nSubtracting this average from each of the five individual equations (after moving the\npseudo-measurement to the top to display the symmetry):\n1C12C2-2-4\nP3\n(C1+2C23C\nP4\n=\nNote at this point, that although the expressions we obtain are fairly complicated the\nprocedure (which is easily implemented in the computer) is very simple.\nTo finish our illustration, using these new pseudo-measurements P we can evaluate\nthe expression which adjusts the doppler for satellite motion directly\nV11 = -\nThe last term is the same average time delay term obtained in the previous method.\nThe first two terms can be evaluated directly and there are now no (admittedly small)\nerror terms remaining.\nA two-dimensional example\nA second application of the technique which we have used at Magnavox is in a hyperbolic\nLoran C implementation. The raw Loran C measurements are fed into a software\nmodule where the coded time delays are removed. The measured time differences\nafter removal of coding delays are:\nTDA - TA - TM\nTDB = TB -- TM\nTDC = TC - TM","510\nwhere:\nTM is the transit time from the master station\nTA is the transit time from Station A\nTB is the transit time from Station B\nTC is the transit time from Station C\nThese three measurements can be combined to form\nTM - T\n-1/4 (TDA + TDB + TDC)\n- T = 1/4 (3TDA - TDB - TDC)\nTA\nTB - T = 1/4 (3TDB - TDA - TDC)\nTC - T = 1/4 (3TDC - TDA - TDB)\nwhere:\nT = 1/4 (TM + TA + TB + TC)\nA simple numerical example serves to illustrate the improved results. If we assume\nthe receiver measures each of the pulse receipt times to an rms accuracy of 10 nano-\nseconds, then (assuming normally distributed errors) the three time difference\nmeasurements will be accurate to 14.1 nanoseconds rms. On the other hand, the\naverage time of receipt, T, will be accurate to 5 nanoseconds rms, and the combined\nmeasurements of equation (2) will be accurate to 11. nanoseconds rms. Thus,\ninstead of obtaining a position based on a least squares curve fit to three LOP's each\naccurate to approximately 14 feet, we obtain a position based on a least squares\ncurve fit to four LOP's each accurate to approximately 11 feet. This is clearly an\nimproved processing technique.\nIt is not difficult to show that this technique is equivalent to (but simpler to implement)\nthan the result obtained by forming all possible lines of position. Figure 3 shows\nthe\nstandard 3-LOP position fix obtained with large LOP errors for illustrative purposes.\nWith four time-of-receipt measurements, a total of the three additional LOP's are\nadded with dashed lines (figure 4). It is apparent that the position obtained from the\nleast squares curve fit of the three LOP solution (designated 3 ) has shifted sub-\nstantially to the more accurate position (designated\nApplication to Doppler Positioning\nThe applicability of this two-dimensional example to the three dimension case of\ndoppler positioning is obvious and need not be detailed. However, let us review the\nprocedural algorithm necessary to implement it. First, form the individual measure-\nments and their derivatives. Then cumulate each of the measurements and their\nderivatives in the C.I.D. approach used by Brown until either the end of pass or loss\nof lock or an edited doppler is encountered. If the sum of these cumulated values is\nalso formed in a running fashion it is now a simple process to form the averages and\nsubtract them from the individual measurements. This process is repeated for all\nnoncontiguous groups of doppler measurements and then the normal equations are\nformed and inverted in the standard fashion.\nWe feel this method has significantly improved the positioning accuracy without any\nunreasonable expense in either computer memory or time requirements.","511\nC STATION\nC-M\nB-M\nM\nB STATION\nSTATION\n3\n3\nTHREE LOP SOLUTION\nA STATION\nA-M\nFIG. 3 Standard LOP Position Fix","512\nI\nB-M\nB-C\nA-M\nC-M\nA-C\nO\n6\n3\nA-M\nB-A\nTHREE LOP SOLUTION\n3\nSIX LOP SOLUTION\n6\nB-C\nC-M\nB-M\nFIG. 4 LOP Position Fix - Expanded Scale","513\nSample Results\nWhen the results of the single pass \"plane of least movement\" position fixes are\nanalyzed they reveal RSS radial position errors of around 20 meters. These results\nare consistent with the expectation that the errors are dominated by satellite orbit\nbiases. Further supporting this expectation are RMS residuals, which, except in\nunusual situations are always less than 20 centimeters.\nThe point-positioning results (figure 5) are also limited by the orbital errors when\nthe predicted orbits are used and hence are not particularly useful for judging the\noverall processing accuracy of the program.\nThe translocation results are, however, relatively insensitive to orbital errors,\nand are hence, a good means of evaluating the processing accuracy. To this end we\nhave included figure 6 showing a scatter plot of 4 pass translocation results and figure 7\nof 8 pass translocation results which indicate that translocation results to better than\n1 meter accuracy can be attained in as little as twelve hours on site.\nIn addition to these results we have obtained many reports from users who have\nreported accuracies near the one-foot level for translocation distances approaching\n100 kilometers separation. These results are significantly better than what was\nenvisioned as short as five years ago (Stansell, 1971).\nAdditional testing to isolate sources of error is planned. Testing of a live transloca-\ntion using a single receiver for both sites has indicated errors of less than four\ncentimeters with two passes due to the computational process. Even this can be\nreduced simply by tightening the convergence limit. Testing of live translocation\nwith common oscillator and common antenna has indicated two pass accuracies of\nless than 50 centimeters. Additional testing is needed to allocate the source of error\nsuch as differential time delay in the two receivers. In addition, our initial testing\nindicated no need to insist on common doppler between the two sites now that orbital\nerrors are minimized. All of the results sited above have been computed without any\ncommon doppler constraint. This reduces the potential biasing effect of nonsymmetric\ncommon data obtained over long north-south distances.\nOur initial studies also indicate a slight decrease in consistent accuracy if one adds\noffset frequency drift to the solution vector. On the other hand, we have found that\nwith a cold oscillator the solution for frequency drift substantially improves the\naccuracy and the resultant position is only slightly worse than the stable oscillator\nsolution obtained without the frequency drift solution.\nConclusions\nWe believe that we have accomplished our objective of attaining a new level of accuracy\nin a practical easy-to-operate package. In addition, we believe that some of the\ntechniques we have employed should become standard features of the best point-\npositioning and translocation programs. Some additional testing is desirable to find\nwhich error sources are most significant in the high accuracy translocation mode.","0 METERS\n-4\n9\n8\n7\n6\n5\n4\n3\n2\n-2\n-3\n-5\n-6\n-7\n-8\n-9\n1\n-1\n12\nNO. PASSES METERS RSS\n1) THE NUMBER OF PASSES\n11\n= APL-4.5 GEODESY\nIS INDICATED BESIDE\n2) . = WGS-72 GEODESY\n10\nTHREE DIMENSIONAL\n7\n5\nFIX RESULTS (4/76)\n9\n3) APPROXIMATE\nEACH RESULT\nHORIZONTAL\n8\nACCURACY:\nFIG. 5 Three-D Point Positioning Results\n7\n22\n10\n25\nNOTES:\n6\n27\n5\n4\n3\n10\n2\nMETERS\n10\n1\n0\n25\n10\n-1\n10\n51\n-2\n10\n-3\n25\n93\n77\n50\n26\n-4\n-5\n10\n.\n-6\n-7\n10\ne\n-8\n-9\n10\n-\n11\n-\n-12\n2\n9\n8\n7\n6\n5\n4\n3\n2\n3\n5\n-6\ni\nMETERS 0\n4\n.7\n-8\n-9\n1","515\nMETERS\n2.0\n1.5\n1.0\n-1.0\n-1.5\n-2.0\n.5\n-.5\n0\nTRANSLOCATION BETWEEN\nA= 53-PASS SOLUTION\n. = 16-PASS SOLUTION\nMETERS RSS\n.44\n1.00\n1.09\n.76\nSTATISTICS\n(4-PASS SOLUTIONS)\nFIG. 6 Four-Pass Three-D Translocation Results\n2.0\n=\nBUILDINGS\nHORIZ\n1.5\nLAT.\nLON.\nALT\n1.0\n.5\nMETERS\n0\n-.5\n-1.0\n-1.5\n-2.0","METERS\n1.0\n1.5\n-2.0\n1.5\n1.0\n2.0\n-.5\n.5\n0\nTRANSLOCATION BETWEEN\nA = 53-PASS SOLUTION\nO = 16-PASS SOLUTION\nMETERS RSS\n.73\n.76\n.47\n.21\n(8-PASS SOLUTIONS)\nFIG. 7 Eight-Pass Three-D Translocation Results\nSTATISTICS\n2.0\nBUILDINGS\nLAT. =\nLON. =\nHORIT =\nALT =\n1.5\n1.0\n.5\nMETERS\n0\n-.5\n-1.0\n-1.5\n-2.0","517\nReferences\n1.\nAshkenazi, V. and Gough, R.J. (1975). \"Determination of Position by Satellite-\nDoppler Techniques\" First Seminar on Satellite-Doppler Methods, Department\nof Civil Engineering, University of Nottingham, United Kingdom.\n2.\nBrown, Duane C. (1970). \"Near Term Prospects for Positional Accuracies of\n0.1 to 1.0 meters from Satellite Geodesy\". Air Force Cambridge Research\nLaboratories Report AFCRL-70-0501.\n3.\nHatch, R. R. (1965). \"Normal Equations for Multiple Pass Integrated Doppler\nData: A Method of Construction and Solution\". Johns Hopkins University/\nApplied Physics Laboratory internal memo S3R-65-071.\n4.\nKirkham, B. Perry (1972). \"An Improved Weighting Scheme For Satellite\nDoppler Observations\". B. Sc. Report, Department of Surveying Engineering,\nUniversity of New Brunswick, Canada.\n5.\nKrakiwsky, E.J., Wells, D.E., and Kirkham, P. (1972). \"Geodetic Control\nFrom Doppler Satellite Observations\". Technical Report No. 11, Department\nof Surveying Engineering, University of New Brunswick, Canada.\n6.\nStansell, T.A. (1971). \"Extended Applications of the Transit Navigation Satellite\nSystem\". Report OTC 1397, Offshore Technology Conference, April 1971.\n7.\nWells, David E (1974). \"Doppler Satellite Control\". Technical Report No. 29,\nDepartment of Surveying Engineering, University of New Brunswick, Canada.\n8.\nWells, D. E. and Kouba J. (1975). \"Semi-Dynamical Doppler Satellite Positioning\".\nPresented at Special General Assembly of the International Association of\nGeodesy, August 18-23, Grenoble, France.","518","519\nNAVAL SURFACE WEAPONS CENTER\nREDUCTION AND ANALYSIS OF DOPPLER SATELLITE\nRECEIVERS USING THE CELEST COMPUTER PROGRAM\nJames W. 0' Toole\nNaval Surface Weapons Center\nDahlgren Laboratory\nDahlgren, Virginia 22448\nAbstract\nThe Celest computer program uses raw Doppler data to determine\nsatellite orbits. It provides diagnostic information on the quality\nof the orbits. The basic technique employed is one of weighted least\nsquares where the data is edited and weighted within the program. An\niterative capability exists for nonlinear problems. Trajectories are\nformed by directly integrating the equations of motion in an inertial\nframe. The force equation has components due to Earth, Sun and Moon\ngravity, solar radiation, thrust, atmospheric drag, solar and lunar\ntidal distortion. A satellite frequency offset error can be determined\nand the program has the facility for determining unknown receiver\nlocations. The computer program occupies 130K octal units of memory,\nis structured as nine major overlays and is completely written in\nfortran. The program is primarily operated on a sixty bit CDC 6700\ncomputer.\nIntroduction\nDoppler data is widely used to position both satellites and surface\nbased Doppler receivers. The Doppler system has been in use since 1962\nby the U.S. Navy and has been used at the Naval Surface Weapons Center,\nDahlgren, Virginia primarily for Defense Department related geodetic\nstudies. A primary tool in these studies is the Celest Computer program\nfor satellite orbit determination. It is a weighted least squares\nprogram designed agresearch tool and especially configured for the needs\nof short-arc processing.\nThe Celest program is presently operating on a CDC 6700 computer at\nDahlgren, two IBM 1108 computers at the Defense Mapping Agency\nAerospace Center and Topographic Center, on a CDC 6700 at Cambridge\nResearch Laboratory and an SEL 86 located at Naval Space Surveillance\nCenter, Dahlgren, Virginia.","520\nMeasurements\nThe majority of Doppler measurements today are taken by Geoceiver\nor Geoceiver type equipment. This equipment integrates the Doppler\neffect on the transmitted frequency fs over approximately 30 seconds\nto obtain a measurement equivalent to range difference. Letting fr\nbe the receiver generated frequency, slightly offset from fs, and p\nindicate range from the receiver to the satellite we have\nDoppler = Nc = fr - fs(1 - p/c)\n1)\nIntegrating fives\nP2 - p1 = c/fs [Nc - (fr - fs) (t2 - tj)]\n2)\nt2 - t1 112 30 sec.\nwhere\nC = velocity of light\nI r (emission time) - r (reception time)\np =\nsatellite\nreceiver\nOlder Doppler equipment which integrates over a time period less than\na second treats the data as instantaneous range rate. This is done\nby solving equation (1) for P and assigning the midpoint of the\nintegration interval as the time of observation.\nStructural Overview\nThe basic program modules are indicated in Diagram 1. Coordinates\nof the sun and moon are retained at one day and one half day intervals\nrespectively on the Sun-Moon file. They are in the Mean Inertial System\nof 1950.0 and ephemeris time. In addition values for the inertial to\nearth fixed coordinate transformation are retained on this file. These\nvalues are the nutation in longitude and obliquity of the ecliptic of\nthe sun, Besselian day numbers and the equation of the equinoxes. The\nSatellite Table contains offset frequency values to the broadcast\nfrequency of individual satellites. The Gravity file contains\nspherical harmonic coefficients.","521\nSun-Moon\nSatellite Table\nThese files must always be attached to the program.\nGravity\nRaw Data\nStation Table\nInitial Conditions\nPre-Processor\nIntegrator\nData Prep file\nPerturbed Trajectory\nFilter\nPass Matrix file\nCombiner-Solver\nB Inverse file\nV\nPropagator\nImproved Trajectory\nDiagram 1","522\nThe program utilizes various pre-processors as each one is designed\nto process a specific type of data. Pre-processors perform the\nfunction of preliminary data editing, time correcting and placing the\ndata in a specific format on the Data Prep file.\nFinal data point editing and the assignment of weights take place\nin the filter module. This function is performed by fitting a\nsatellite trajectory to one pass of data at a time. Points are re-\nmoved which have a residual, from the fitted orbit, greater than twice\nthe computed standard deviation. This procedure is iterated until no\nfurther outlying points are identified. At this point the RMS of\nresiduals, from the fitted orbit, is assigned as the standard deviation\nof an observation. The reciprocal of this value is assigned as a weight.\nLeast square normal equations are made up using the untagged points and\ntheir weights.\nThe normal equations contain a subset of six osculating orbital\nelements, one drag scaling constant, three thrust parameters, a\nradiation parameter, three receiver station coordinate parameters, a\nrefraction correction parameter, frequency bias and frequency drift\nparameters. The subset is determined by the nature of the problem\nbeing solved. The normal equation, the time of closest approach and\nthe RWS of residuals are written to a file (Pass Matrix file).\nOrdinarily the Pass Matrix file would be the only thing required\nto complete processing as the remaining task is that of summing matrices\nand performing an inversion. The solution area is designed however,\nto determine solutions over various time domains with an option for drag\nsegmentation. This process requires access to partial derivatives\nfrom the trajectory. Segmentation is a process whereby the effect of\nperturbing X number of drag segments independently is desired as part\nof the solution. The program accomplishes this by storing the effect\nof perturbing any number of drag segments an equal amount in the pass\nnormal matrix via\na Data\n= aD\na Drag Parameter\nICD\nand using the trajectory partials in the solution area to transform the\npass matrix value\naD\naCD\ninto its associated values aD\nEach aD\nrepresents the\naCD\nacDi","523\nperturbation in data due to independently perturbing the drag\ncoefficient in the ith segment of the drag force. This permits a\nflexible treatment of drag and is especially designed for short arc\nprocessing.\nThe final step in the orbit determination process is generating a\nrefined ephemeris. This is done by using trajectory partials to\ncompute the effect on the reference orbit due to parameter changes\nindicated in the solution. Trajectory values beyond the reference\ntrajectory time span must of course be generated via integration.\nThe central theme on which both the Celest program and an\nindependent Celest Station Position program operates is the data\nbank concept of Diagram 2.\nIt is pass normal matrices which are saved in the data bank. The\nmatrices become the data for most work although raw data is saved for\nmore fundamental studies. By a continued use of matrices, trajectories\nand the principle of first order matrix adjustment, due to a change in\nthe reference parameter values, orbit refinement and station positioning\ncan be carried on with a minimum of data reprocessing.\nData Filtering\nPoint filtering proceeds with the philosophy that model error\nduring a single pass can be removed by adjusting the orbit in the\nalong track and radial directions together with removing frequency and\ntropospheric refraction error. The ionospheric error has been re-\nmoved at the receiving station by gathering dual frequency data and\neliminating the first order ionospheric effect.\nThe filter process is implemented by forming a pass normal matrix\non a reference orbit.\nBorbit, orbit\nBorbit, bias\nsorbit\nEorbit\n*\nBbias, bias\nAbias\n=bias\nThe orbit section always contains six osculating orbital elements\nat some epoch time. The bias section contains receiver station\ncoordinates, a frequency bias parameter which measures the deviation\nof the satellite frequency offset from an assumed value and a re-\nfraction correction giving the percent deviation from the Hopfield\ntropospheric model. A transformation is formed which takes normal","524\nPass Matrix Data Bank Concept\nRaw Data\nTrajectory for some\nFilter\nreference time span\nExisting Pass Matrix file\nPass Matrix file of new data\nMerge\nUpdated Pass Matrix file\nDiagram 2","525\nequations presented in osculating orbital elements and reforms them\nin position velocity components resolved in a special local frame at\nTCA. The local frame is defined by the station-satellite range (p)\nand along track (p) vectors at the satellites time of closest\napproach.\nR = [0, P, pxp]\nwhere the A indicates unit vectors.\nThe epoch transformation going from the osculating orbital element\ntime to TCA is\n(TCA) = x) (TCA)\naeo (epoch elements)\nThe transformation is then\nR = CRO -0 R-\n= Ry\nA solution is determined and the RWS of residuals computed on the\nadjusted orbit. Data point weights are recomputed by dividing their\npresent value by the adjusted RWS of residuals. Individual data\npoints are tagged if the product of their weight and associated\nadjusted residual is greater than two (2 sigma filtering). . The\nprocess iterates reforming the normal equation at each iteration with\nthe untagged points and improved weights. All points are examined at\neach iteration and the process terminates when the same points are\ntagged on successive iterations. The final normal equation and the RWS\nof unadjusted residuals using untagged points is stored on the Pass\nMatrix file. Basic technical procedures used in this work are given\nbelow.\nStation Coordinate Conversion\n1\nS1\nCOS Qs cos 10\n0\n3)\n- Ae2\n= (A + hs)\ncos Qs\nsin 10\nrso =\nS2\n0\nsin Qs\nS3\nsin Qs","526\nwhere\nrso = earth fixed station coordinates\nhs = Station geodetic height above a reference ellipsoid\n= eccentricity of the reference ellipsoid\ne\n1/2\n= [(2 - f)f] = EL\nf\nflattening\n=\nEL = oblateness\n= 298.25\nae = semi-major axis of the reference ellipsoid\n= 6378.145 km\nQs = station geodetic latitude\n10 = longitude from Greenwich meridian\nA = ae/(1-e2sin20s)\nRange and Range Computation\n(4)\nRange = p(tr)r(te)- rs(tr)\nwhere te = tr- - (p*p)*/c tr= = reception time and te is determined by\niteration starting with te = tr.\n=r(te) - rs(tr) = - p*[r(te) -\n(5)\nc(p*p)1/2\nrs=\nwhere\nrs = inertial station location\n=\n= (ABCD)* rso\n=\n=","527\nCD = Precession Nutation transformation\n13 = Earths mean sideral rotation rate determined by the time\nlapse between successive transits of the mean equinox.\n= .7292115855 E(-04) radians/sec.\nComputation of Time of Closest Approach (TCA)\nDefine\np*p)t.\nSet t1 = value from the observation file and iterate until\n|tj+1 - til < .05 sec. or maximum iteration count is reached.\nComputation of Zenith Angle\nZv= = tan-1 [[1-(p*üs)2: /p*Üs)\n(6)\nUs = (ABCD)*\nS2 S3 S1\n(1-e2)\nRefraction Model (Hopfield)\nNTI = dry term\nE = water vapor pressure\nH = humidity (percent)\nNT2 = wet term\nP = pressure (millibars)\nRO = rso\nTk= Temperature (Kelvin)\nR1 = RO + 40.1 + .149T\n= T + 273 (deg centigrade)\nR2 = RO + 12.0\nN7 = [(776) E-04]P/TK\nH = 50% (default value)\nN2 = [(.373) E-02]E/Tk2\nP=980 (default value)\nT = 15 (default value)","528\nE = H exp(-37.2465 +\nn = index of refraction\nn-1 = NT1 + NT2\nNTj = Nj r2-R\n4\nIf r is in [Ro, Rj]\nIf r is not in [Ro, Rj]\nNTj = 0\nLet Us be the unit normal to the ellipsoid at the station\ns\n60\nZv\nk\nrso\nS1\nUs = (ABCD)*\n(7)\nS2\n=\n53/(1-e2)\n(8)\nk = Irso sin zy = Rosinz\n(9)\nCOS =\nThe refraction model is (1+CR) AfR\n(10)\nAfR===s AR\nrange rate\nAfR== AR\nrange\nAfR= range difference\nAR and AR are obtained by evaluating the integrals","529\n(11) AR rsatellite rstation (n-1) (r*r-k2) (12) AR = kk francophic (n-1) r*dr\n=\nrstation (r*r-k2) 3/2\nwhere\nkk = =R2 cos\n/p/\nLetting RO = rstation and Rj = rsatellite we can compute range and\nrange rate corrections by\nR\n4\n(13) (r*r-k2)1/2\nRO\nF\nR\n2\n4\nF\nNj\nr*dr\n(14)\nRO\nData Type Formulation\nLetting D9 denote range difference and D7 denote range rate we have\nD9e1)( = -\n(15)\ntj-1\nwhere foo is an input quantity usually taken to be E +(06) so that the\nbias solution will be in ppm.\nPartial derivatives are given by\n(16)\nq = orbit set (p),\n(rso),\nstation set fb.\nCR, fb or","530\n(17) a[] = * ax\nap\nap\n(18) a[] = -* (ABCD)*\na rso\na[] = Afr\n(19)\nICR\na[]__c_(t-TCA)\n(20)\nafterfoo\n(21) a[]___c_ (t-TCA)2\nafter 2foo\nThe vacuum received frequency using a transmitted frequency of fs is\ngiven by\n1 + * rs (tr)\n(22)\nfR= fs\nC\n1 + * r(te)\nC\npltn) = -\nwhere\n(te) = tr-(p*p) = = emitted time\nC\ntr = received time\ncomputing 8 from the expression for p and taking into account the\nchange in te as a function of tr gives\n(23) := r(te) rs(tr) + (6*/c) rs(tr)r(te) - (p*/c)r(te)rs(tr)\n(1+6*r(te)\nC\n1- p*p C 1+p*r(te) - - p*rs(te)\nC\nC\nC\n1 + p*r(te)\nc","531\n= rs(tp)/c\n(te)/c\n= fr\nfs\nThus if P is computed to first order in 1/c fr/fs will be given to\nsecond order in 1/c.\nP= order 1st i(te) rs(tr) - (6*/c) (r(te) - is(tr))r(te)\n(24)\nAdding in the contribution of frequency bias and refraction gives the\nformulation for range rate as\n(25) D7 = = s(1+fb/footfood fb (t-TCA)) (1-6*p/c) + (1+CR)AFR\nThis formula is accurate to second order in 1/c where as the corresponding\nformula (15) for range difference is accurate to all orders in 1/c.\n(26) ar oxar ]\npTTapap\np*\nfs\n(ABCD)*\n(27)\n/p/\narso\nC\naD7\n(28)\nAFR\n=\nacr\nD7 = fs_ (1-p*p/c)\n(29)\nafterfoo\n307 = fs (1-p*p/c) (t-TCA)\n(30)\nThe primary output statistics from the filtering process are filtered\nnoise and the RWS of residuals.\nNobs\n1/2\n(31) RWS\n=","532\nwhere D is computed on the reference ephemeris and wf is the computed\nweight.\nNobs\n(32) Filtered Noise [1/(Nobsu?) 1/2\n=\n= standard deviation for an observation\nfrom the pass.\nAs the RWS of adjusted residuals converges to one during the\nfiltering process and the weights are approximately constant we have\nNobs\nEND\n(Dobs - Dadjusted)? /Nobs] = 1\nw [\nor RMS of adjusted residuals = 11 = standard deviation\nw\nFiltered Noise\n=\nSolution of Normal Equations\nThe solution area solves an equation containing from six to thirty\nnine dynamic parameters, several hundred bias parameters and several\nsets of station coordinates. To accomplish this the program performs\nbias and station parameter elimination in order to keep the matrix\nrequiring inversion under dimension of forty. Letting \"o\" stand for\nthe orbit (dynamic) parameters and \"b\" for bias we have the normal\nequation\nE0\nBoo\nBob\nAPO\n=\nEb\nBbb\nApb\nThe bias terms are eliminated from the above equation and the elimination\nequations are saved in order to recover bias solutions.\nApb = BLE (Eb-BboApo)\n(33)\n(Boo-Bobbbb\n(34)\nor Eliminated 00 Apo = Eo Eliminated","533.\nJust prior to bias elimination pass matrices are expanded from\ntheir basic set of parameters to the desired solution set. This\nis\na major task in the solution area. The solution set may consist\nof orbital elements at a different epoch, multiple drag parameters\ndue to drag segmentation, multiple thrust, polar motion parameters,\nup to twenty gravity parameters, bias parameters and station coordinates.\nSubsequent to bias elimination pass matrices are summed to form\nan arc normal matrix. Station coordinate sections of the matrix are\nsummed over each station and eliminated just prior to matrix inversion.\nStation solutions are obtained by backsubstitution Direct observattion\nof all parameters is permitted in the form of apriori sigma input for\neach parameter. The inverse square of the input sigma is added to the\ndiagonal term of the normal matrix prior to inversion. This corresponds\nto an observation of the present value of a parameter with the input\nsigma as the standard error of observation.\nNavigation Solutions\nThe primary diagnostic output is a set of navigation solutions.\nA navigation solution is carried out for each pass of data and consists\nof determining the receiver motion, in the along track and radial\ndirections, which minimizes residuals for the refined ephemeris. The\nreceiver motion is interpreted as satellite ephemeris error as the\nreceiver location is actually well known. The radial and along track\ndirections used are the range and range rate vectors at TCA discussed\nearlier under filtering. The procedure is implemented by saving parts\nof the bias elimination equations (33)\nBbb, , Eb\nand adjusting for the orbit solution Apo obtained at the time of arc\nmatrix inversion.\nBbb sb = Eb - Bbo Apo\nThe Bbb section contains earth fixed receiver coordinates which are\ntransformed to the local TCA frame. Solutions are generated for radial,\nalong track, frequency and refraction error. Diagnostic cards con-\ntaining this information and filter statistics are generated at this\ntime.","534\nStation Analysis Diagnostic Cards\nStation Analysis cards can be punched on option and contain\ndiagnostic informaion useful to the satellite tracking stations.\nThe card values are as follows:\n1. STA - Station number extracted from the header message of the\nraw data.\n2. Time (hr, min) - Time of the first data point.\n3. TCA (sec) - Time of closest appraoch of the satellite obtained\nfrom the satellite orbit by searching for the point in time where the\nrange (p) and range rate (p) vectors are perpendicular to each other.\nP\nsatellite (TCA)\np\n@\nstation\n4. FREQ( (mc) - The Q number from the raw data header message is\nused to determine a base frequency. The frequency given is this base\nfrequency rounded to the nearest MHz.\n5. EL (deg) - The satellite elevation at TCA computed from the\nsatellite orbit.\n6. PTS. Good - Total number of points left after passing\nthrough the Celest point filtering process.\na. Points are filtered out in the Celest Pre-Processor if\ninformation is missing, values are to large or the data fails a\nmonotone test.\nb. Points are filtered out in the Celest Filter by removing\norbit error from the residuals and testing against 2.0 sigma.","535\n7. Filt. Noise (cps/MHz or m) - Filtered noise is the standard\ndeviation on the data after modeling error has been removed. In the\ncase of range rate this value is given in units of cps/MHz. In the\ncases of range difference the value is given in units of meters.\nBefore modeling\nerror removed\nAfter modeling\nerror removed\nFiltered Noise = RMS of residuals after modeling error is removed.\nThis value is scaled to 1 MHz for Doppler data.\n8. ELT. (m) - This is the along track navigation error determined\nfrom the refined orbit. Holding the orbit fixed the station is\nallowed to move in the along track (p) and slant range (p) directions,\nin order to best fit the data from the pass. Since this movement is\nfrom a known position the result is tabulated as along track (ELT)\nand slant range (ELR) errors. The values represent a measurement of\nhow well the final refined orbit fits the data of a given pass. (see\ndiagram for #3)\n9. ELR. (m) - Slant range error.","536\n10. DLT. F. (ppm) (1) - Delta frequency is the value of the\nfrequency bias determined in the above navigation solution. Assuming\nthat the satellite frequency has a constant bias during a given pass,\nthen this number represents that bias in parts per million.\n11. ACT - Action taken in the course of point filtering. Action\nlabel described below.\nA - No TCA\nB - Rejected in filter because to many points were filter out.\nD - Rejected on TCA zenith angle test.\nE - Pass not balanced, i.e. the difference between the number\nof points on one side of TCA and the number of points on\nthe other is greater than the balanced pass tolerance.\nPasses are rejected for reasons other than the above, in the Pre-\nProcessor. These reasons are listed in Pre-Processor under Reject Codes\nbut no indication is given on the Station Analysis cards.\nIntegration\nFor ephemeris computation a variable order routine is used on a\n14 digit machine. Usually the order is set to ten and navigation\ntype satellites use a 60 sec step size. The ephemeris can be computed\nto a one meter accuracy and perturbations of orbit constants to one part\nin 106.\nThe integration routine is a Gauss Jackson technique using backward\ndifferences and follows the basic pattern of first initializing a\nbackward difference table to the order (N) of the process\n(1) A nominal value of oscillator frequency offset (in parts per\nmillion) is associated with each satellite. On the basis of\nthe Doppler data from a given pass, a correction, DLT. F. is\ncalculated. The corrected absolute offset, in parts per\nmillion, for the pass is the algebraic sum of the nominal\noffset and DLT. F.\nAbsolute offset = Nominal offset + DLT. F.\n= AVS + DLT. F.\nThe nominal offset is always negative. For example, if the\nnominal offset for a satellite is -80 ppm, a DLT. F. of +.04\nwould indicate an absolute offset of -80+.04 = -79.96 ppm.","537\nthen\n1. Extrapolates the difference table from line n to n+1.\nx(n) = v-1 X(n-1)+v°X(n)\nv-1\nv-2 X(n) = v-2 x(n-1)\nVN\nk\nX(n) + (n+1) K=N-1\nx (n+1)= vk\n....0\nV\n2. Computes position and velocity by\nN\nK\nXn+1=h2v-2xx+h2\n*n+1\nCK\nK=0\n+\nwhere\n1+a1=1/2 ao=1 a1=-1/2\naeak+2-e\n=\nak-j\nak=\n1+j\n1\nJ\n=\n3. Uses the force function, , G, from X = G(x,x, t) to compute X(n+1)\nand determine the difference between the computed and extrapolated\nvalues of acceleration. The backward difference table is adjusted due\nto this difference.\n4. The process described in 2 and 3 is continued until the desired\nnumber of iterations is reached. The final result from 2 is written\non the trajectory file and the process terminates by carrying out step 3.\nCoordinate and Time Systems\nThe reference frame used for integration is an inertial frame defined\nby the mean equator and equinox of 1950.0 the sun and moon coordinates\nin the 1950.0 system using Ephemeris Time (ET). The time system\nare for Doppler observations is Universal Time Coordinates (UTC) and thus\nthe integration time is UTC. The difference between UTC and ET is\npresently 46.15 sec and is not presently adjusted for when using the","538\nand moon coordinates in the force model. The gravity force is computed\nby rotating the satellite inertial position to the earth fixed frame\naligned with the Greenwich meridian and using the instantaneous earth\nspin axis. The difference between UTC and UT1 is taken into account\nwhen computing the rotation. The calculation of residuals is made by\nbringing station coordinates, referenced to the CIO pole, into the\ninertial system. The transformation between the earth fixed system\nusing the conventional International Origin (CIO) and the inertial system\nis given by\n(35)\nXEF = ABCDX Inertial\nD = general precession\nwhere\nC = nutation\nB = rotation from true inertial equator and equinox of a\ngiven time to Greenwich at that time\nA = polar motion to the CIO pole using polar motion values\nroutinely solved for in Defense Mapping Agency Navigation\nSatellite processing.\nForce Equation\nThe force equation is represented as\n(36) X = G(x,x, t) = Ae + As + Am + Ad + Ar + Ats + Atm + At\nwhere the accelerations are due to earth, sun and moon gravity,\natmospheric drag, radiation pressure, solar and lunar tidal distortion,\nand vehicle thrust.\nAe (Earth Gravity)\nThe earth's potential in an earth fixed frame is\n]\nN n\n(37) V = \"E [ n=0 m=0 and Cnml pm n (12) cos(mx)\npm n (12)\nsin(mx)\nan\nSnm\n+\nn+1\nr n+T\nIr\nI\ne\n(earth fixed coordinates)\nwhere\nr =\nae = Semi-major axis of the earth\n= 6378.145 km\n= Legendre polynomial\npm\nn\n= Earth's gravity constant\nH\n= 398601.0\nl = Longitude with respect to Greenwich\nCnm, Snm = Gravity constants","539\nSince the coordinate system has its center at the earth's center of\ngravity we have C10=C11=S11=0. The earth's gravitational acceleration\ncan now be given by\naV\nax\naV\n(38)\nAe = VIV = =\nay\nav\naz\nwhere VI is the inertial gradient. For the purpose of calculation we\nrewrite (37) as\nn\n(39)\nn=0\nm=0\nnoting the\nDefine the transformation E by\n(40) E = Be\nIntroduce the longitude by\n3\n(41)\nc(2) = sin (e) cos (2) =\nE1j\nXi\ns(2) = sin (e) sin (2) =\nE2i\nwhere\n0 = cos- (12)\nX1\nX\n= inertial components of r.\nX2\n=\ny\n.\nX3\nZ\nUsing the recurrence relations for Legendre polynomials we have\nrecurrence relations for U and V given by\n(42)","540\nun+1= =\n(43)\nVn+1 = n+1)\nwhere and\nEquation (42) is called Horizontal stepping and (43) is called Diagonal\nstepping.\nUsing the values\nUO = H/1/1/\no\nVo = 0\nVO = 0\nwe start at n=1, m=0 in the horizontal stepping equation and compute\nfor i=2,3...N. We then utilize diagonal stepping and calculate UT,V1.\nUi,\nReturning to horizontal stepping enables the calculation of\n, V1\nfor 1=2,3,...N. This process is repeated until m = M, where\nM < N.\nNote that\n= um\n(n+m)!\n(n+m)!\nWe can now compute (38) by\nN\nn\n(44)\nm=0\nwhere V is the earth fixed gradient.\nThe recurrence relations for U and V can be given by","541\nm-1\nm+1\naevum\nVn+1\n(45)\n-(n-m+1) um\n1/Am vm-1\nvm+1\naevvn\n+1 / Um+1\n-(n-m+1)V\nwhere Am = = (n-m+1) (n-m+2)\nAs, Am' (Sun and Moon Gravity)\nCoordinates of the sun and moon are stored on the Sun-Moon file\nat one day and one half day intervals respectively. A sixth order\nLagrangian interpolation procedure is used to obtain the values at\nany time. The sun's acceleration on the satellite is given by\n(46)\nus = .1330614 E(12) =\nThe expression for the moon is similar with Hm= .490074 E(04).\nAts, Atm (Tidal Distortion)\nThe gravitational (tidal) attraction of the sun and moon causes the\nearth to become elongated on an axis pointing toward the disturbing body.\nThe redistribution of mass results in a perturbation of the earth's own\ngravitational field, which is represented by the potentials\n(47) =\nP2(r*rm)\nwhere KL is Love's constant and P2 is the Legendre polynomial.\nThe associated acceleration on the satellite is given by","542\n(48) Ats = k = KL rs|3 HS r|5 ae5 [(-1 (r*rs) 2+3/2)r+3(r*Fg)Fs)\nwith a similar expression for Atm.\nA (Radiation Pressure)\nr\nA shadow test is performed to determine if the satellite is in\nsunlight or shadow. If r.rs>0 then the satellite is in sunlight. If\nr.rs<0 then we compute rrrs If rxrs is less than ae the satellite\nis in shadow and if not then it is in sunlight. When the satellite\nis in sunlight we compute the radiation pressure acceleration by\nAr=krm = 1014 (r-rs)\n(49)\nTr-rs/3\nwhere S is the satellite cross-sectional area and m is satellite mass.\nAr is set to zero in the shadow.\nAd (Atmospheric Drag)\nThe relative velocity of the satellite with respect to the\natmosphere is\nVr= r-wxr\n(r.r) is the inertial satellite position, velocity and w is\nwhere\n(CD)*\nThe acceleration of the satellite due to drag is\n(50) Vr\nwhere m is the satellite mass, S is the cross-sectional area and p the\natmospheric density function defined by\np = Exp [Ah-B-(Ch2+Dh-E) 1\nThe height h is the satellites geocentric altitude above its subpoint\ngiven by","543\nae\n| r/\nh =\n1-\n-\ne2\nz2\n1/2\n+\n1-e2\n-R\n=\nwhere R is the distance from the earth's center to the satellites sub-\npoint.\nae\nR =\n1 + e2 sin20)\n1-e2\n0 = geocentric latitude\n(51)\nAt = RA =\nwhere\nR = [r,r,rxr]\nA = ( Arxr Air Ar\nThe values for A are given by input as constants in the radial,\ntangential and out of plane directions.\nPartial derivatives are computed by the same integration procedure\nsimultaneously with the orbit integration. The variational equations\nare\naG\nh = ax h + ax G h + ap G\n(52)\nwhere\n0 p = osculating orbital element\naG\na Model\np=CD, A or kr\n=\na Model Parameter\nap","544\nEarth Gravity Variation\n[Cnma? v2um + Snma2v2vm]E\nAAe\nv2v\nE*\n(53)\n=\n=\nm=0\nax\n1/2\nwhere\n2V2\nun =\naevvm+1\n-1/2\n-1/2\n=\n-(n-m+1)aevumt-\n(54)\nn+1\nn+1\nazv2vm=\n+1 Am aevum\n=\nn+1\n-(n-m+1)aevvm.\nThe partials for Cnm and Snm are\nVIV\nE*aevum\n(n,m)/(0,0)\n=\n2Cnm\n(55)\n=\n25nm\ndu","545\nSun and Moon Gravity Variation\n|r-rs\nSetting Ps =\nthe derivatives are\n-3(x-xs)2 + p2\n-us\n-3(x-x5) (y-ys)\n-3(x-xs) (z-zs)\n-3(x-xs) (y-ys)\n(56) =\n-3(y-ys)2 p?\n-3(y-ys) (z-zs)\n-3(x-xs) (z-zs)\n-3(y-ys) (z-zs)\n-us\n-3(z-zs)2+p2\nwith similar results for the moon.\nSun and Moon Tidal Variation\nus ae 5 {[3-15(F*Fs)2]\n(57)\n+ 6 rs rs* + [105(r*rs)-15] r*\n-\nwith similar results for the moon.","546\nRadiation Pressure Variation\nSetting Ps = = |r-rsl the derivatives are\n-3(x-xs)2+p\n10 14\n)\n-3(x-xs) (y-ys)\n-3(x-xs) (z-zs)\n(\n-3(y-ys) (x-xs)\nVAr,y krs 1014\n-3(y-ys 2 +ps\n(58)\np 5\n-3(y-ys) (z-zs)\n(\n1014\n-3(z-zs) (x-xs)\nkps\nVAr,z\n-3(z-zs)\npar\n-3(z-zs)2+ pg\nm\naAr= = S 1014 (r-rs)\nDrag Variation\na(rr) aAd= -CDS 2m [Alvrl arry avr + pVr a(rr) alvrl +\n(59)\n2020\nSince Vr = r - wxr=r-\nSo =(CD)* 0 0 (CD)\naVr =-s\nar\navr==\ndr\navr==[-s,I]\na(rr)","547\na/Vrl = V* avr\nr\n(rr)\na(rr)\ndp\nap\n, 0\n=\n(rr)\na\ndr\nap dp ah\n=\nar an ar\ndp\n=p [A- (ch + D/2) (ch2+Dh-E)-]\nah\nah = 1\n(1r/- h)3 e2 (0,0,7)\nar /r/ 2 [h + (rr-h)3 a2 ]r* + (1-e2)\nThrust Variation\n(60)\naAt\naR\nA\n=\na(rr) 2(ri)\naAt\nR\n=\naA\nX1\nSetting r = x2 X3\naR\nar\nar\narxr\na(rr)\n(rr)\n'a\n(rr)\n'd(rr)\nar\no]\nar\nar\nar/\n=\na(rr)\n=\n,\n,\nar ar = r 1 [I - r r*]\nar\na(rr) = [0, an","548\n-\narxr\n=\narxr ar = st*: sir)\narxr ar = Sir rxr I - sr]\nwhere = =\nSup = 0 -x3 0 -x1 x2 0\nx2\nx1\nx}\n-x1x3\n-x1x2\nst\nSup\n=\nx2+x3\n-x2x3\n-X1X2\nx2+x2\n-X2X3\n-X1X3\n-x1x3\nPolar Motion\ndenote the earth fixed station position and ABCD the\nLetting\nrso\ninertial to earth fixed coordinate transformation\nS1\nrs= (ABCD)*rso\n= (BCD)*Atso","549\n1\n-w3\nw2\nA =\nw3\nw7 = Aq w2 = Ap\n-w1\n1\n-w2\nw7\nw3 = 13 (st + tst)\nt = time in sec. from the beginning of the year.\nars = (BCD)* 030 0 S1 -s3 0 51 -WS7 ws2 0 -wts1 wts2 0 =(BCD)*Q\nap\nwhere p = (Aq, AP, , At, , st) is the polar motion set.\naD\naD\nars\nt\n=\nap\nars\nap\naDt\n(BCD)*A*AQ\n=\nars\nDD\nars\nAQ\nars\narso\naDt\naD+\nt\n(61)\nAQ\n=\nap\narso\nThus\naDt\naD\naD*\naD\nt\nt\nt\nQ*(t)\nA*(t)\nA(t) Q(t)\nBpp\n=\n=\nap\nap\narso\narso\n= q(t)A*(t)Bss (t) A(t) Q(t)\nEvaluating AQ at TCA of a pass gives\n(62) Bpp Epass Bpp(t) : = Q*(TCA) A*(TCA) Bss A(TCA) Q (TCA)\nEquation (62) and other similar relations are now used to convert the\nstation coordinate section of the pass normal equations into a polar\nmotion section. This technique is used to incorporate polar motion\nparameters into Celest.","550\nReferences\n1. Brouwer, D. and Clemence, G.M., \"Methods of Celestial Mechanics,\nAcademic Press, 1961.\n2. 0'Toole, James W., \"The Celest Computer Program for Computing Satellite\nOrbits\", NSWC/DL TR-3565, October 1976.","551\nVARIATIONS IN DOPPLER POSITIONS\nRESULTING FROM DIFFERENCES IN\nCOMPUTER PROGRAMS AND\nTROPOSPHERIC REFRACTION\nCOMPUTATIONS\nHaschal L. White\nDefense Mapping Agency\nAerospace Center\nSt. Louis Air Force Station, Missouri 63118\nAbstract\nThe computer program used for Doppler point positioning applications\nat\nthe Defense Mapping Agency Aerospace Center (DMAAC) is an adaptation\nof the computer program developed for this purpose by the Naval Surface\nWeapons Center (NSWC). Within this program, an a priori sigma or\nstandard error can be input for the tropospheric refraction correction\nas well as a sigma limit for the mean clock correction, Computations\nwere made to show the effect on GEOCEIVER derived positions of varying\nthese constraints for data elevation angle cutoffs of five and ten degrees.\nComparisons are also made for two positions derived independently by DMAAC\nand by the National Geodetic Survey (NGS) using different data sets and\ncomputer programs. In addition, tests were made to evaluate the feasi-\nbility of using a Standard Tropospheric Model (STM) in lieu of observed\nweather data.","552\nVARIATIONS IN DOPPLER POSITIONS\nRESULTING FROM DIFFERENCES\nIN COMPUTER PROGRAMS AND\nTROPOSPHERIC REFRACTION COMPUTATIONS\nIntroduction\nDifferences normally result in Doppler derived point position\nsolutions when either different data sets or different computer programs\nare used in data reduction. Differences also occur when different\nassumptions are made regarding constraints to be applied in data pro-\ncessing. Often these constraints are necessarily different due to\ncomputer program concept and design differences or because of analyst\npreferences even when the same computer program is used. Computations\nhave been made at the Defense Mapping Agency Aerospace Center (DMAAC),\nusing an adaptation of the Naval Surface Weapon Center (NSWC) developed\nlong arc point positioning program, to study the differences in Doppler\npositions that result because of variations in the constraints used for\ntropospheric refraction uncertainty, sigma limits on clock error, and\ndata elevation angle cutoff as well as to investigate the possibility of\nsubstituting a Standard Tropospheric Model for observed weather data.\nTwo of the six stations studied were also positioned by the National\nGeodetic Survey (NGS) using the Defense Mapping Agency Topographic Center\n(DMATC) developed DOPPLR computer program which, along with the DMAAC\nLARC computer program, uses the precise Navy Navigation Satellite (NNS)\nephemerides as basic input. The NGS DOPPLR solutions used for comparison\nwere published in a paper by Larry D. Hothem entitled, \"Evaluation of\nPrecision and Error Sources Associated with Doppler Positioning.\" This\npaper was presented to the XVI General Assembly of the International\nUnion of Geodesy and Geophysics, International Association of Geodesy,\nheld in Grenoble, France, in August 1975.\nGEOCEIVER data collected during station occupations in June 1975\nserved as the basic data used in this study. The six stations studied\nare located in Olympia, Washington (10070), Hawaii (30188), Bolivia\n(30120), Thailand (10073), Zaire (30126), and Kenya (30203). In\naddition, some data collected during a 1973 occupation of station 30120\nwas processed so that a comparison could be made regarding repeatability\nwhen identical reduction procedures are used with different data sets.\nDiscussion\nStation 10070 and 30188\nThe clock corrections computed for the Washington and Hawaii stations\nshow uniformly drifting clocks (Figures 1 and 2) with a drift rate of","553\nabout 0.5 msec/day. The frequency bias plots (Figures 3 and 4) also\nshow a uniform drift rate and a low noise level, These plots indicate\nthat quality data was collected at both of these stations, Therefore,\nmost of the differences between the solutions given in Tables 1 and 2\nmust be attributed to the elevation angle cutoff and tropospheric\nrefraction differences rather than to the absorbtion of data errors into\nmodeling parameters. The use of a 100 microsecond (usec) sigma limit\nfor clock error is not a factor in these solutions since data was not\neliminated because of this constraint.\nTable 1, Solution 1, gives the NGS solution for station 10070.\nSolution 2 is a DMAAC solution using the same data elevation angle\ncutoff, refraction uncertainty, and sigma limit on clock error that was\nused by NGS but with a different data set. Solutions 3 through 6 are\nDMAAC solutions using the same data set as Solution 2 with the constraints\nas shown. Solution 7 represents the standard DMAAC solution (STD) and\nSolution 8 assumes a Standard Tropospheric Model (STM) in which an esti-\nmated value for the wet component of the refractivity index (Nw) is\nsubstituted for the one computed using observed weather data, The\nfollowing equations are used to obtain Nw W for a humid climate and for\nan average climate, respectively:\nNw = 99.9[h - hs)/hw.,44\nNw=81.5[h - hs)/hw.,4.4\nwhere hw is the effective height of the wet component of the refractivity\nindex (nominally 12 km) and hs is the station height above mean sea level.\nThe decision regarding whether or not the climate at a station is humid\nor average was based on average recorded humidity during the occupation.\nThe latitude, longitude, and geodetic height differences between the\nstandard DMAAC and the DOPPLR solutions in Table 1 are -0,018, -0,066,\nand -0.36 meter, respectively. However, there appears to be a small\nsystematic difference in that all latitudes, longitudes, and geodetic\nheights, with the exception of Solution 4, are less for the LARC solutions\nthan for the DOPPLR solution. Latitude and longitude variations between\nthe standard DMAAC solution and the other LARC solutions are slightly\nsmaller than similar variations between the standard DMAAC and the NGS\nsolutions.\nTable 2 shows solutions for station 30188 with constraints identical\nto those previously discussed for station 10070, For this station, the\nlatitude, longitude, and geodetic height differences between the standard\nDMAAC and the DOPPLR solutions are 0,022, 0,013, and -0,42 meter,\nrespectively. For this station, all of the LARC derived latitudes are\nslightly above the DOPPLR derived latitude, The reverse was true for\nlatitude differences at station 10070, A comparison of geodetic height\ndifferences at both stations shows that the LARC derived heights are\nconsistently below those derived with the DOPPLR program, It should\nalso be noted that the excellent agreement between Solutions 7 and 8 for","554\nboth stations indicates that a STM can be substituted for observed\nweather data. Similarly, the large height difference between\nSolutions 5 and 7 indicates that the modeling of a tropospheric\nrefraction uncertainty is significant when a five degree elevation\ncutoff is used.\nStation 30120\nTwo different data sets were processed for station 30120. One of\nthese was collected in March 1973 and the other in June 1975. The clock\ndrift rate for the 1973 data is about four times (2 msec/day) the drift\nrate of the 1975 data (0.5 msec/day). Figure 5 is a plot of the clock\ncorrection for the 1973 data which also shows two clock restarts along\nwith approximately a two day gap in data collection. Figure 6 is the\nfrequency bias plot for this same data set. It indicates a relatively\nhigh noise level for the last four days of the station occupation.\nCorresponding clock correction and frequency drift plots for the\nJune 1975 data collection are shown in Figures 7 and 8. Both of these\nplots indicate excellent stability and good quality for the data\ncollected.\nTable 3 shows the various DMAAC solutions for station 30120.\nSolution 1 is the standard solution using the 1973 data. This solution\ndiffers by 0.045 in latitude, 0.'038 in longitude, and 0.58 meter in\ngeodetic height from Solution 7 which was derived from a much better\nquality data set. Although all of the latitude and longitude differences\nbetween the various 1975 solutions are 0.012 or less, the -1,95 meters\nheight difference between Solutions 5 and 7 further emphasizes the need\nfor the refraction uncertainty when five degree elevation data is used.\nComparison of Solutions 7 and 8 shows the agreement between observed\nand modeled weather data for a station at an altitude of about four\nkilometers above mean sea level.\nStation 10073\nThe clock correction plot in Figure 9 shows a clock drift rate of\nabout 4 msec/day. This relatively high drift rate along with the two\ncycles/sec noise level shown in the frequency bias plot in Figure 10\nindicates that this data is not as good as some of the preceding data.\nThis is verified to a certain extent by the rather large geodetic height\ndifferences between the standard DMAAC solution and Solutions 1, 3, 4,\nand 5 in Table 4. It appears from the comparison of Solutons 4 and 6\nthat some of the data noise was absorbed into the refraction uncertainty\nwhich produced a lower RMS and thus improved the editing capabilities\nin Solution 6. Therefore, the actual difference in the geodetic height\nbetween these two solutions is a combination of the refraction uncer-\ntainty and the resulting data edit.","555\nThe geodetic height obtained in Solution 3 with a 10 degree elevation\ncutoff and a 10 percent refraction uncertainty is 1,29 meters below the\nstandard Solution 6. Solution 5 with the same elevation angle cutoff\nand no refraction uncertainty is 1,52 meters above the standard solution,\nThese variations indicate that, although a refraction uncertainty is pre-\nferred in combination with a 10 degree elevation cutoff, a 10 percent\nuncertainty is probably larger than required, A comparison of Solutions\n1 and 5 and 2 and 6 indicates that the sigma limit on clock error was not\na factor in these solutions. The small difference between Solutions 6\nand 7 show once more that the Standard Troposphere Model is acceptable.\nSolutions 30126 and 30203\nThese two stations provide good quality data as indicated by the\nclock correction plots shown in Figures 11 and 12 and the frequency bias\nplots in Figures 13 and 14. They also provide stations with geodetic\nheights that are intermediate between mean sea level and the high\naltitude Bolivian station.\nThe solutions shown in Table 5 for station 30126 have maximum dif-\nferences of 0.028 in latitude, 0.018 in longitude, and 0.15 meter in\ngeodetic height from the standard solution. As in some of the previous\nsolutions, the sigma limit on the clock error is insignificant, The\nsmall and somewhat inconsistent differences between these solutions are\ninconclusive regarding constraint preferences. However, one notable\ndifference is the rejection of two additional passes in Solution 7 in\ncomparison to Solution 6. This is due to the slightly different residual\npatterns between these two solutions and the subsequent rejection of\ntwo borderline passes in Solution 7.\nThe solutions shown in Table 6 for station 30203 also show small\nmaximum coordinate differences of -0,019, -0,013, and 0,27 meter in\nlatitude, longitude, and geodetic height, respectively, These results,\nas well as those in Table 5, lead one to conclude that the elevation\nangle cutoff and the a priori tropospheric refraction constraint used in\nDoppler positioning becomes less significant as tracking data quality\nincreases.\nSummary and Conclusion\nThe results of this study show that variations do occur between\nDoppler positions when data sets are varied, when different computer\nprograms are used, or when different constraints are applied in data\nreduction. However, the variations are usually small enough to make\nit difficult to determine if the coordinate differences are the result\nof the constraint variations or because of the slight change these\nconstraints often produce in the data set through the pass edit pro-\ncedure. Different computer programs also produce small differences as\nindicated by the comparison between the LARC and DOPPLR solutions,\nHowever, these differences were the result of different data sets as\nwell as program differences.","556\nThe most important factor in Doppler positioning is data quality\nprovided a sufficient number of passes are available to assure adequate\ngeometry. Once this criteria is met, the constraints used become less\nsignificant. However, the following general conclusions appear to be\nvalid:\n1. A Standard Tropospheric Model can be used in lieu of observed\nweather data.\n2. A 100 usec sigma limit on clock error appears reasonable and\ncan be used without experiencing a significant data loss when data\nquality is adequate.\n3. When a five degree data elevation angle cutoff is used, a 10\npercent uncertainty in the tropospheric refraction correction is\npreferred.\n4. When a 10 degree elevation angle cutoff is used, a 10 percent\nuncertainty in the tropospheric refraction correction appears to be\nexcessive.\n5. Some data noise is absorbed into the tropospheric refraction\ncorrection when a 10 percent uncertainty is used with moderately noisy\ndata.","162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181\n#\n#\n#\nt+\nt+\n#\n+\n#\n+\nSTATION 10070\nDAY NUMBER\n1975)\n+\nClock Corrections for Olympia, Washington.\n#\n{\n#\n+\n+\nFIG. 1\n-15\n-16\n-17\n-8\n-12\n-13\n-14\n9\n-10\n-11","164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181\n#\n#\n+\n+\n+\n#\n#\n+\nSTATION 30188\n+\nDAY NUMBER\n(1975)\n#\n+\n#\n+\nFIG. 2 Clock Corrections for Hawaii.\n#\n+\n+\n#\n#\n+\n+\n163\n#\n162\n-22\n-23\n-21\n-24\n-25\n-26\n-27\n-23\n-29\n-30\n-32\n-31","162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181\n+\n#\n+\n+\n+ # +\n+\n++ +\n+\n+\n+\n+\n+\n+\nSTATION 10070\nDAY NUMBER\n(1975)\nFIG. 3 Frequency Biases for Olympia, Washington,\n+\n+\n+\n+\n+\n25\n24\n26","162 163 164 165 166 167 168 169 DAY 170 171 172 173 174 175 176 177 178 179 180 181\n+\n+\n+\n+\n+\n+\n++\n+\n+\n+\n+\n+\n+\n+\n+\nSTATION 30188\n+\nNUMBER\n(1975)\n+ + + +\n+\n+\n+\nFIG. 4 Frequency Biases for Hawaii.\n+\n+\n+\n+\n+\n25\n24","83\n4\n82\n+\n+\n81\n80\n++\n79\n78\nSTATION 30120\n77\nDAY NUMBER\n(1973)\n+\n76\n#\n75\nFIG. 5 Clock Corrections for Bolivia (1973).\n74\n#\n7\n73\n+\n#\n72\n++\n#\n71\n+\n70\n+\n+\n69\n-7\n-8\n-9\n-10\n12\n-13\n-11\n-14\n-15\n-16\n-17\n-18\n-19\n-20\n-22\n-23\n-21\n(335).\nMATERIAL\nCLUB","","163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181\n#\n+\n#\n.................\n+\n#\n+\n+\n+\n#\nSTATION 30120\n#\nDAY NUMBER\n+\n(1975)\n+\n#\n#\n+\n+\n+\n#\nFIG. 7 Clock Corrections for Bolivia.\n#\n+\n#\n#\n#\n+\n+\n#\n+\n+\n162\n-22\n-23\n-24\n-25\n-26\n-14\n-15\n--16\n-17\n-18\n-19\n.20\n-21","179\n+\nSTATION\n164\n163\n162\n25\n24","565\n#\n+\n$\n$\n+\n#\n+\n+\n#\n+\n+\n+\n$\n+\n+\n#\n$\n+\n#\n+\n#\n+\n#\n#\n#\n#\n#\n#\n#\n+\n#\n(035W) 43070","","","","28 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181\n++\n+\n+\n+ +\n+\n+\n+\n#\nSTATION 30126\nIt\nDAY NUMBER\n+\n+\n(1975)\n#\n+\n+\n+\n+\nFIG. 13 Frequency Biases for Zaire.\n+\n+\n+\n+\n29","168\n29\n28\n30","571\n(STM)\n0.0001\n1975\n10%\n-0.002\n5°\n0.003\n8\n68\n67\n1896\n1870\n1.4\n-0.07\n0\n0\n1\n(STD)\n0.0001\n1975\n10%\n0.000\n0.000\n5°\n7\n68\n67\n1896\n1870\n1.4\n0,00\n0\n0\n1\nAS A RESULT OF VARIABLE ELEVATION ANGLE CUT-OFFS, SIGMA LIMITS ON CLOCK ERROR,\n0.0001\n1975\n10°\nNONE\n0.012\n-0.012\n6\n68\n63\n1896\n1428\n24.7\n0.47\nVARIATIONS FROM THE DMAAC STANDARD SOLUTION FOR STATION 10070 (USA)\n4\n0\n1\n0.0001\n1975\n5°\nNONE\n0.012\n-0.014\n5\n68\n64\n1896\n1775\n6.4\n0.76\n4\n0\n0\nAND TROPOSPHERIC REFRACTION UNCERTAINTIES\nSOLUTION\n1975\n10°\nNONE\n10%\n0.007\n-0.044\n4\n68\n64\n1896\n1453\n23.4\n-0.42\n3\n0\n1\n1975\n10%\n0.000\n0.000\n5°\nNONE\n3\n68\n67\n1896\n1870\n1.4\n0.00\n0\n0\n1\nTable 1\n1975\n10°\nNONE\nNONE\n0.012\n-0.012\n2\n68\n63\n1896\n1428\n24.7\n0.47\n4\n0\n1\n(NGS)\n1974\n-0.018\n-0.066\n10°\nNONE\nNONE\n0.9\n-0.36\n1\n67\n67\n1252\n1241\n0\n0\n0\nPASSES DELETED IN FINAL SOLUTION\nPASSES WITH CLOCK SIGMA > 0001\nTROPO. REFR. CORR. UNCERTAINTY\nPASSES WITH LESS THAN 7 POINTS\nGEODETIC HEIGHT DIFFERENCE (m)\nDATA POINTS IN FINAL SOLUTION\nSIGMA LIMIT ON CLOCK ERROR\nLONGITUDE DIFFERENCE (SEC)\nLATITUDE DIFFERENCE (SEC)\nPASSES IN FINAL SOLUTION\nTOTAL DATA POINTS INPUT\nPERIOD OF OCCUPATION\nPERCENT DATA DELETED\nTOTAL PASSES INPUT\nELEVATION CUTOFF","572\n(STM)\n0.0001\n1975\n10%\n5°\n0.000\n0.000\n8\n57\n54\n1470\n1398\n4,9\n-0.03\n3\n0\n0\n(STD)\n0.0001\n1975\n10%\n0.000\n5°\n0.000\n7\n57\n54\n1470\n1398\n4.9\n0,00\n3\n0\n0\nAS A RESULT OF VARIABLE ELEVATION ANGLE CUT-OFFS, SIGMA LIMITS ON CLOCK ERROR,\nVARIATIONS FROM THE DMAAC STANDARD SOLUTION FOR STATION 30188 (HAWAII)\n0.0001\n1975\n10°\nNONE\n-0.003\n0.013\n6\n57\n52\n1470\n1107\n24.7\n1.08\n3\n2\n0\n0.0001\n1975\n5°\nNONE\n0.016\n0.018\n5\n57\n1470\n1293\n12,0\n51\n1.59\n6\n0\n0\nSOLUTION\nAND TROPOSPHERIC REFRACTION UNCERTAINTIES\n1975\n10°\nNONE\n10%\n0.004\n-0.005\n4\n57\n53\n1470\n1128\n23.3\n0.31\n2\n2\n0\n1975\n10%\n5°\nNONE\n0.000\n0.000\n3\n57\n54\n1470\n1398\n4.9\n0.00\n3\n0\n0\nTable 2\n1975\n10°\nNONE\nNONE\n-0.003\n0.013\n2\n57\n52\n1470\n1107\n24,7\n1.08\n3\n2\n0\n(NGS)\n1974\n10°\nNONE\nNONE\n0.022\n0.013\n1\n57\n57\n1108\n1.5\n-0.42\n1091\n0\n0\n0\nPASSES DELETED IN FINAL SOLUTION\nPASSES WITH CLOCK SIGMA > $0001\nTROPO. REFR. CORR. UNCERTAINTY\nPASSES WITH LESS THAN 7 POINTS\nGEODETIC HEIGHT DIFFERENCE (m)\nDATA POINTS IN FINAL SOLUTION\nSIGMA LIMIT ON CLOCK ERROR\nLONGITUDE DIFFERENCE (SEC)\nLATITUDE DIFFERENCE (SEC)\nPASSES IN FINAL SOLUTION\nTOTAL DATA POINTS INPUT\nPERIOD OF OCCUPATION\nPERCENT DATA DELETED\nTOTAL PASSES INPUT\nELEVATION CUTOFF","573\n(STM)\n0.0001\n1975\n10%\n5°\n-0.003\n-0.001\n8\n52\n47\n1178\n1078\n8.5\n0.23\n2\n0\n3\n(STD)\n0.0001\n1975\n10%\n5°\n0.000\n0.000\n7\n52\n47\n1178\n1078\n8.5\n0.00\n2\n0\n3\nAS A RESULT OF VARIABLE ELEVATION ANGLE CUT-OFFS, SIGMA LIMITS ON CLOCK ERROR,\n0.0001\n1975\n0.010\n10°\nNONE\n-0,004\n6\nVARIATIONS FROM THE DMAAC STANDARD SOLUTION FOR STATION 30120 (BOLIVIA)\n52\n48\n1178\n21.8\n921\n-1,21\n0\n2\n2\n0.0001\n1975\n5°\nNONE\n0.012\n0.009\n5\n52\n49\n1178\n1122\n4.8\n-1.95\n0\n0\n3\n1975\n10°\nNONE\n10%\n0.009\n0.010\nAND TROPOSPHERIC REFRACTION UNCERTAINTIES\nSOLUTION\n4\n52\n49\n1178\n935\n20.6\n-0.17\n2\n0\n1\n1975\n10%\n5°\nNONE\n0.001\n0.007\n3\n52\n1178\n1147\n2.6\n-0.06\n51\n0\n0\n1\nTable 3\n1975\n10°\nNONE\nNONE\n0.009\n-0.001\n2\n52\n50\n1178\n948\n19.5\n-1.23\n0\n2\n0\n(STD)\n0.0001\n1973\n10%\n5°\n0.045\n0.038\n40\n32\n1\n944\n764\n0.58\n19.1\n3\n2\n3\nPASSES DELETED IN FINAL SOLUTION\nPASSES WITH CLOCK SIGMA > .0001\nTROPO. REFR. CORR. UNCERTAINTY\nPASSES WITH LESS THAN 7 POINTS\nGEODETIC HEIGHT DIFFERENCE (m)\nDATA POINTS IN FINAL SOLUTION\nSIGMA LIMIT ON CLOCK ERROR\nLONGITUDE DIFFERENCE (SEC)\nLATITUDE DIFFERENCE (SEC)\nPASSES IN FINAL SOLUTION\nTOTAL DATA POINTS INPUT\nPERIOD OF OCCUPATION\nPERCENT DATA DELETED\nTOTAL PASSES INPUT\nELEVATION CUTOFF","(STM)\n0.0001\n1975\n10%\n5°\n0,000\n-0.002\n7\n52\n47\n1276\n1139\n10.7\n-0.03\n5\n0\n0\n(STD)\n0.0001\n1975\n10%\n5°\n0,000\n0.000\n6\n52\n47\n1276\n1139\n10.7\n0.00\n5\n0\n0\nAS A RESULT OF VARIABLE ELEVATION ANGLE CUT-OFFS, SIGMA LIMITS ON CLOCK ERROR,\nVARIATIONS FROM THE DMAAC STANDARD SOLUTION FOR STATION 10073 (THAILAND)\n0.0001\n1975\n10°\nNONE\n0.002\n-0.024\n*Large RMS of residuals was responsible for failure to delete two poor quality passes.\n5\n52\n45\n1276\n913\n28.4\n-1.52\n6\n0\n1\n0.0001\n1975\n5°\nNONE\n-0.018\n-0.051\n4\n52\n49\n1276\n1186\n3*\n7.1\n-4.56\nSOLUTION\n0\n0\nAND TROPOSPHERIC REFRACTION UNCERTAINTIES\n1975\n10°\nNONE\n10%\n-0.015\n-0.044\n3\n52\n47\n1276\n968\n24.1\n1.29\n4\n0\n1\nTable 4\n1975\nNONE\n10%\n5°\n0.000\n0.000\n2\n52\n47\n1276\n1139\n10.7\n0.00\n5\n0\n0\n1975\n10°\nNONE\nNONE\n0.002\n-0.024\n1\n52\n45\n1276\n913\n28.4\n- -1.52\n6\n0\n1\nPASSES DELETED IN FINAL SOLUTION\nPASSES WITH CLOCK SIGMA > $0001\nTROPO. REFR. CORR. UNCERTAINTY\nPASSES WITH LESS THAN 7 POINTS\nGEODETIC HEIGHT DIFFERENCE (m)\nDATA POINTS IN FINAL SOLUTION\nSIGMA LIMIT ON CLOCK ERROR\nLONGITUDE DIFFERENCE (SEC)\nLATITUDE DIFFERENCE (SEC)\nPASSES IN FINAL SOLUTION\nTOTAL DATA POINTS INPUT\nPERIOD OF OCCUPATION\nPERCENT DATA DELETED\nTOTAL PASSES INPUT\nELEVATION CUTOFF","575\n(STM)\n0.0001\n1975\n10%\n5°\n-0.003\n0.018\n7\n48\n39\n1160\n914\n21,2\n-0.04\n9\n0\n0\n(STD)\n0.0001\n1975\n10%\n5°\n0.000\n0.000\n6\n48\n1160\n970\n41\n16.4\n0.00\n7\n0\n0\nAS A RESULT OF VARIABLE ELEVATION ANGLE CUT-OFFS, SIGMA LIMITS ON CLOCK ERROR,\nVARIATIONS FROM THE DMAAC STANDARD SOLUTION FOR STATION 30126 (ZAIRE)\n0.0001\n1975\nNONE\n10°\n0,028\n-0.001\n5\n48\n43\n1160\n866\n25.3\n0,04\n3\n2\n0\nSOLUTION\n0.0001\nAND TROPOSPHERIC REFRACTION UNCERTAINTIES\n1975\n5°\nNONE\n0.026\n0.011\n4\n48\n46\n1160\n1118\n3.6\n-0.14\n2\n0\n0\n1975\n10°\nNONE\n10%\n0.016\n-0,016\n3\n48\n44\n1160\n889\n23.4\n0.15\n2\n2\n0\nTable 5\n1975\n10%\n5°\nNONE\n0.000\n0.000\n2\n48\n1160\n970\n41\n16.4\n0.00\n7\n0\n0\n1975\n10°\nNONE\nNONE\n0.028\n-0.001\n48\n43\n1160\n866\n25.3\n1\n0.04\n3\n2\n0\nPASSES DELETED IN FINAL SOLUTION\nPASSES WITH CLOCK SIGMA > .0001\nTROPO. REFR. CORR. UNCERTAINTY\nPASSES WITH LESS THAN 7 POINTS\nGEODETIC HEIGHT DIFFERENCE (m)\nDATA POINTS IN FINAL SOLUTION\nSIGMA LIMIT ON CLOCK ERROR\nLONGITUDE DIFFERENCE (SEC)\nLATITUDE DIFFERENCE (SEC)\nPASSES IN FINAL SOLUTION\nTOTAL DATA POINTS INPUT\nPERIOD OF OCCUPATION\nPERCENT DATA DELETED\nTOTAL PASSES INPUT\nELEVATION CUTOFF","(STM)\n0.0001\n1975\n10%\n5°\n-0.012\n-0.004\n7\n49\n1225\n1029\n16.0\n41\n0.21\n7\n0\n1\nS\n(STD)\n0.0001\n1975\n10%\n5°\n0.000\n0.000\n6\n49\n44\n1225\n1110\n9.4\n0,00\n4\n0\n1\nAS A RESULT OF VARIABLE ELEVATION ANGLE CUT-OFFS, SIGMA LIMITS ON CLOCK ERROR,\nVARIATIONS FROM THE DMAAC STANDARD SOLUTION FOR STATION 30203 (KENYA)\n0.0001\n1975\n10°\nNONE\n-0.018\n-0.013\n5\n49\n42\n1225\n30.5\n851\n-0.13\n4\n2\n1\n0,0001\nSOLUTION\n1975\n5°\nNONE\n0.000\n-0,009\n4\n49\n44\n1225\n1110\n9,4\n-0.15\nAND TROPOSPHERIC REFRACTION UNCERTAINTIES\n4\n0\n1\nS\n1975\n10°\nNONE\n10%\n-0.019\n-0.013\n3\n49\n43\n1225\n878\n28.3\n0.27\n4\n2\n0\nTable 6\n1975\n5°\nNONE\n10%\n0.003\n-0.001\n2\n49\n45\n1225\n6.9\n1141\n0.04\n4\n0\n0\n1975\n10°\nNONE\nNONE\n-0.019\n-0.011\n1\n49\n43\n1225\n878\n28.3\n-0.08\n4\n2\n0\nPASSES DELETED IN FINAL SOLUTION\nPASSES WITH CLOCK SIGMA > .0001\nTROPO. REFR. CORR. UNCERTAINTY\nPASSES WITH LESS THAN 7 POINTS\nGEODETIC HEIGHT DIFFERENCE (m)\nDATA POINTS IN FINAL SOLUTION\nSIGMA LIMIT ON CLOCK ERROR\nLONGITUDE DIFFERENCE (SEC)\nLATITUDE DIFFERENCE (SEC)\nPASSES IN FINAL SOLUTION\nTOTAL DATA POINTS INPUT\nPERIOD OF OCCUPATION\nPERCENT DATA DELETED\nTOTAL PASSES INPUT\nELEVATION CUTOFF","577\nANALYSIS OF GEOCEIVER RECEIVER DELAYS\nFran B. Varnum\nDefense Mapping Agency Topographic Center\n6500 Brookes Lane\nWashington, D.C. 20315\nDepartment of Geodesy and Surveys\nAbstract\nThe \"DOPPLR\" point positioning program solves for time and frequency bias\nunknowns in addition to position coordinates. This report presents the\nresults obtained with very carefully controlled tracking data in which the\ntime and frequency bias values are known a priori. These values are compared\nwith solution values.\nAcknowledgement\nThe author wishes to thank personnel of the Satellite Geophysics Division,\nDMATC, and in particular Mr. William Winter for cooperative assistance in\ncollecting the precisely controlled data used in this experiment.","578\nIntroduction\nA widely used Doppler Point Positioning Program 1 was developed by the\nDepartment of Geodesy and Surveys of the Defense Mapping Agency.\nAs those of you who have used this program are aware, it solves for\na frequency and a time bias in addition to the normal coordinates.\nBench mark position\nevaluations of Doppler positioning accuracy utilizing\nthis program, have, so far as I know, compared the resulting positions\nwith known values, and generally ignored the computed values for\nthe frequency and time biases. This is certainly reasonable in so\nfar as under normal tracking conditions, insufficient control exists\nfor evaluating the computed values of these parameters. Four sets of\nvery carefully controlled tracking data were taken in Herndon, Virginia,\nsolely for the purpose of comparing the computed values for the frequency\nand time biases with a priori ones. Clearly, in the least-squares\nadjustment of real tracking data, errors very highly correlated with\neither a frequency or a time bias may be \"absorbed\" by these unknowns,\nand, thereby, go unnoticed. For example, in the referenced point positioning\nprogram, the effects of relativity are ignored, and since these effects\nmay be regarded as introducing a fixed frequency bias in any given satellite\npass, they are incorporated in or \"absorbed\" by the frequency bias\nparameter. Similarly, receiver delay together with any average along-track\nephemeris error--clearly two entirely different error sources--will appear\nin the time bias variable.\nPerhaps other unsuspected errors are being absorbed by these unknowns,\nin which case solution values somewhat different than the a priori values\nwill be observed. While the specific cause of error will not be\nidentified by this process, at least the magnitude of the residual\nerror--if present--will be identified. It should be noted, that in\nthe sub-meter range of positioning accuracy, the process of minimizing\nthe sum of the squares of the residuals with any given data set may not\nnecessarily lead to the best absolute position determination. Some\npositional shift with corresponding shift in frequency and/or time\nbias value may erroneously occur in the interest of minimizing residuals.\nWith this in mind, it is additionally interesting to observe the\nmagnitude of the error in the frequency and time bias solution values,\nsince these are probably more accurately controllable than position in\nan absolute sense.\n1 DOPPLR--A Point Positioning Program Using Integrated\nObservations. Doppler Satellite\nTECH REPORT NO. DMATC 76-1. R. Smith, C. Schwarz,\nand W. Googe.","579\nData Sets\nThere were two sets of data taken for this study at two different times.\nEach of these sets, in turn, is subdivided according to which of two\nsatellites was tracked, thus, giving rise to four data sets : 1Q, 1Z,\n2Q, and 2Z. The Q and Z designations identify the two satellites while\n1 and 2 respectively identify the time frames in which the data were\ntaken. All data were taken with the same receiver. Table 1 summarizes\nthe data set designations.\nDATA SET\nSATELLITE NO.\nTRACKING DATES\nNO OF PASSES\nQ\n30200\n13\n1\nApril 16-22, 1976\nZ\n30190\n18\nQ\n30200\n20\n2\nMay 5-14, 1976\nZ\n30190\n32\nTable 1\nTime Bias -- Explanation\nWhen a Navy Navigation Satellite is tracked with a Geoceiver, the\nsatellite itself is the source of timing signals to start and\nstop the Doppler counting mechanism within the Geoceiver. The satellite\nclock is maintained within about 50us of universal time coordinated (UTC)\nby the Navy Astronautics Group (NAG) . A specific time in the satellite\ntime frame will be designated as ts. Upon detection and reconstruction\nwithin the Geoceiver, a given time mark will have undergone a delay with\nrespect to UTC. This delay is the sum of the propagation delay (tp) and\nthe receiver delay (tr) Each delayed time mark is used to start/stop\na count and to simultaneously trigger the readout of the local\nGeoceiver clock (t ) . If the Geoceiver clock is synchronized to\ng\nUTC, the following relation exists:\n(1)\ntg = ts + +\nThe carrier signal from the satellite is not delayed in the receiver.\nAs a consequence, the actual Doppler cycles counted are not those\noriginally associated with the satellite UTC time marks.\nThe necessary time shift required to identify the proper UTC time\ninterval (at the satellite) for each count is the time bias, and in the","580\nabsence of any other source, the time bias equals the receiver delay.\nAnother possible source of this bias, however, is a timing error\n(equivilent to an along-track position error) in the DMA precise\nephemeris. 2\nA Priori Values of Time Bias\nThe receiver delay is used for the a priori value of the time bias.\nThe extent to which the least-squares solution value for the time bias\ndiffers from the receiver delay is a measure of the residual timing\nerror [and other correlated errors] in the point positioning system.\nReceiver delay was determined in two ways:\n1. Bench measurement.\n2. Dynamic measurement.\nBench Measurements\nA special test generator 3 which simulates the satellite signal (400 MHZ)\nwith timing modulation was both displayed (modulation) on an oscilloscope\nand input to the Geoceiver. The detected and reconstructed modulation\nwithin the Geoceiver was also displayed and the time delay observed.\nThis observation was made over the full operation range of signal level to be\nexpected in normal operation. Since the recovery of modulation in the\nreceiver is inevitably contaminated with receiver noise, the measurement\nwas made repeatedly and averaged. The measurement indicated that the\nreceiver delay is invariant with signal level, and equal to 1150us.\nDynamic Receiver Delay Measurement\nAll tracking data utilized in this study were taken with the Geoceiver\nclock synchronized to UTC within +3us and driven by a Hewlett Packard\ncesium frequency standard. The dynamic receiver delay measurement\nconsists of computing a value for the receiver delay for each nominal\n30-second observation used in the point positioning solution. The\nmeasurement is independent of the point positioning computations and is\nregarded as accurate within the tolerances maintained over the relative\nsynchronization of the satellite and ground clocks. In this measurement\nEquation 1 is used to solve for tr for each Geoceiver observation.\nThere are typically 20-30 determinations per pass, and a set of 20 passes\n2 The TRANET net employs its own precise clocks to provide satellite\nclock correction to UTC. The NAG maintenance of clock epoch is\nindependent of the precise ephemeris computations.\n3 Built by ITT for use with 5500 Doppler receiver.","581\nwill yield typically 400 measurements. These measurements will, of course,\nvary from one to the next due to receiver noise. They might also vary\nfrom pass to pass due to a shift in the satellite and/or ground clock\nepoch error. In a special test of this process, the mean and standard\ndeviation were computed for 903 such determinations from 40 passes on\none satellite taken over a two-week period. A chi-square test of this\nsample supported the hypothesis that the measurements were, in fact,\nnormally distributed about their mean (95% confidence level) . Figure 1\nis a frequency histogram of this data set with a 20us class interval.\n200\n160\n120\n80\n60\n810\n1090\nDYNAMIC REC'R DELAY MEASUREMENTS\n20us INTERVALS\nFIGURE 1\nResults of the dynamic measurement of receiver delay are shown in\nTable 2. Since the dynamic receiver delay measurements for a given\nsatellite are almost identical for different data sets taken at different\ntimes (1Z/2Z values differ by only 3HS and 1Q/2Q are also within 3us),\nthe approximately 50us difference between satellites is considered to be","582\nsignificant and, probably, due to clock epoch error in the satellite.\nFurthermore, since the receiver delay measurements utilizing satellite\nZ agree almost exactly with the bench measurement, the error is probably\nin satellite Q. The main point to be made from these results is simply\nthat the receiver delay for this particular piece of equipment is quite\nfirmly established at 1150us. 4\nDYNAMIC-\nRECEIVER DELAY MEASUREMENT (us)\nSTATIC\nDATA SET\nDYNAMIC\nSTATIC\nus\n1\nQ\n1198\n1150\n48\n2\nQ\n1201\n1150\n51\n1\nZ\n1142\n1150\n-8\n2\nZ\n1145\n1150\n-5\nTable 2\nOne might question \"why not accept the bench measurement and leave it at\nthat?\" To which the answer is--an electronic measurement of this type must\nbe regarded with suspicion until it can be confirmed independently.\nAdditional concern regarding the dependability of static measurements of\nreceiver delay arise out of the experience that the built-in static (Mode 3)\nreceiver delay measurements made on the Geoceiver are not reliable.\nResidual Time Bias\nAs previously explained, the difference between the receiver delay and the\npoint positioning least-squares solution for time bias is a measure of\nunmodelled time and time-correlated errors in the Doppler point positioning\nsystem. The values in Table 3, column 5 are these measures.\nRECEIVER DELAY\nTIME BIAS\nRESIDUAL\nEQUIV\nPOSITION\nLS SOLUT.\nDYNAMIC\nSTATIC\nTIME BIAS\nALONG-TRACKSHIFT (RMS)\nDATA SET\n(us)\n(us)\n(us)\n(us)\nERROR (m)\n(m)\n1Z\n1115\n1142\n1150\n-35\n0.26\n0.09\n2Z\n1128\n1145\n1150\n-22\n0.16\n0.06\n1Q\n1365\n1198\n1150\n+215\n-1.57\n0.50\n2Q\n1070\n1201\n1150\n-80\n0.58\n0.14\nTable 3\nSatellite epoch errors do not introduce time bias but will cause an\n4\nerror in the dynamic determination of receiver delay. The delay\nmeasurement taken with satellite Q will, therefore, not be used.","583\nThese residuals are remarkably low, and might easily be attributed to the\nnet effect of along-track ephemeris error. The values in Table 3, column 6\nare net along-track position errors that would account for the residual\ntime biases. These values were determined by introducing the effect of a\nnet along-track error into each data set as required to force the residual\ntime bias to zero. 5 The perturbation is computed by:\nAN = ON AA\naA\nwhere AN = perturbation applied to measured Doppler.\nN = predicted Doppler count.\nLA = along-track position shift.\nA = along-track position.\nThe last column in Table 3 is the shift in computed position which resulted\nwhen the time bias was constrained to the value of the receiver delay (1150us).\nIn the summer of 1976, a question arose within the Doppler community\nas to the possible existance of a time bias on the order of 500us within the\nCELEST ephemeris. Part of the purpose of this study was to investigate this\npossibility. These results rather conclusively demonstrate that such a\ntiming bias does not exist.\nFrequency Bias\nAs mentioned in the introduction, the \"DOPPLR\" point position program also\ncomputes the frequency offset between the satellite and Geoceiver reference\noscillator. This offset is nominally 32 khz or -80 parts in 1 X 106.\nThe\nfrequency bias computed in the point positioning program, however, includes\nthe relative difference between satellite and ground based oscillators and\npossibly some effects due to frequency correlated errors. Since a cesium\noscillator was used as the reference in this experiment, the absolute\nfrequency of the reference is known within 1 part in 1 X 1012 The\ncomputed frequency biases 6 were, therefore, devoid of any effect due to\nthe receiver reference oscillator.\n5 The functional relationship between computed time bias and (AA) is\nlinear and found to be about 137us/meter for a well distributed data set.\n6 A frequency bias is computed for each pass with a given data set.","584\nValues of satellite frequency offset as determined by the Navy Astronautics\nGroup were used as a priori values of absolute frequency transmitted by the\nsatellite. The relativistic effects predicted by both the Special and the\nGeneral Theories of Relativity were computed and used in the determination\nof the frequency bias residuals7. The residual frequency bias (Af) is\ncomputed from:\nI\nAf = fs++f -\nwhere: fs = transmitted frequency offset in satellite rest frame.\nof = relativistic Doppler shift.\nE = point positioning solution for frequency offset.\no\n8\nFigure 2 is a plot of the frequency bias residuals for data set (2Z) . The\nmean residual frequency bias for this data set is -0.2 parts in 1 X 1010.\n.4\nFREQUENCY BIAS RESIDUALS\nFOR 18 PASSES IN\n.2\nDATA SET 2Z\n-.2\n-.4\n-.6\n-.8\nFIGURE 2\n7 The net effect of both effects is to introduce a red shift of approximately\n2 parts in 1 X 10 10 which increases the apparent negative offset in the\nsatellite frequency.\n8 of is in cycles/sec., but is expressed here as a fraction of the\nnominal 400 MHz carrier signal.","585\nTable 4 is a summary of these results for all four data sets.\nMEAN FREQ. OFFSET RES .\nPARTS IN 1 X 1010\nDATA SET\n1Q\n+0.28\n1Z\n-0.20\n2Q\n-0.15\n2Z\n- -0.21\nTable 4\nThese results are remarkable. For comparison purposes, the residual\noffsets are about an order of magnitude less than the relativistic effect\nwhich rather conclusively demonstrates the non-existance of significant\nerrors related to or correlated with absolute frequency.\nThe question arises at this point as to the correlation between frequency\nand time bias. What happens to these frequency residuals if the time\nbias is constrained to the receiver delay value? Table 5 gives this\nresult. The column (At) gives the difference between the unconstrained\nand constrained time bias. Column (APos) gives the RMS position shift\nthat occurred (same as last column in Table 3) . Column (Af ) gives the\noriginal residual frequency bias (same as in Table 4) , while column (Af') 1\ngives the residual frequency bias in the solutions utilizing the constrained\ntime bias value of 1150us (all frequency offsets are in parts in 1 X 1010).\nNote that in each case, the frequency bias residual is reduced by utilizing\nthe a priori value of time bias. However, the correlation is very weak,\naveraging 5 parts in 1 X 1014 for the four data sets.\nAf ,\nAt (us)\nAPos (m)\nAfo\nDATA SET\n0.28\n0.16\n1Q\n+215\n0.5\n0.09\n-0.20\n-0.19\n1Z\n-35\n0.14\n-0.15\n-0.09\n2Q\n-80\n-0.20\n2Z\n-22\n0.06\n- -0.21\nTable 5","586\nThese results indicate that when the point position program solves for\nboth time and frequency biases for small data sets (<20 passes), a\nposition error (in the sub-meter range) may result. However, more\nimportantly these results prove that the solutions for the time and\nfrequency biases are very accurate and real indeed in the \"DOPPLR\"\npoint positioning program.","587\nWORKSHOP ON POINT POSITIONING\nAND TERRESTRIAL ADJUSTMENTS\nSix papers were presented during the formal part of the Workshop on\nWednesday, October 13. These included:\n\"Effect of Geoceiver Observations upon the Classical\nTriangulation Network\", by R. E. Moose and S. W.\nHenriksen,\n\"Updating Survey Networks - A Practical Application\nof Satellite Doppler Positioning\", by J.F. Dracup,\n\"Adjustment of Terrestrial Networks using Doppler\nSatellite Data\", by M. Tanenbaum,\n\"Control Network Extension through Satellite Trans-\nlocation\", by L. H. Spradley,\n\"An O.R.B. Doppler Program Analysis and its\nApplication to European Data\", by J. Usandivaras\nand P. Paquet, and\n\"Concepts in the Combination of Geodetic Networks\",\nby D. B. Thomson and E. J. Krakiwsky.\nIn addition, two papers were tabled and distributed among the partici-\npants. These were:\n\"Errors in Doppler Positions obtained from Results of\nTranscontinental Traverse Surveys\", by B. K. Meade, and\n\"Determination of NAD 1983 coordinates of Map Corners\",\nby T. Vincenty.\nAlthough the papers generated a lot of interest, the tightness of the\nschedule restricted interventions at this stage to minor queries, leaving\nmost of the questioning in depth -- of these as well as of other relevant\npapers presented during the plenary sessions -- and the ensuing debate to\nthe open Workshop sessions on Thursday, October 14.\nThe first problem discussed was that of the transformation parameters\nexisting between the Doppler reference system and individual classical\nlocal triangulation systems. It was stated that the zero longitude of the\nWGS 72 system was determined by minimizing the longitude differences between\nthe earlier adopted Doppler longitude values at 50 stations in the U.S.A.\nand their gravimetrically obtained new values. The effect of this change\nwas to rotate the old adopted reference system by 0.5\" with the average\ndifferences in longitude between the two systems, remaining after this\nrotation, amounting to about 0.5 meters.\nA separate evaluation which followed showed that the rotation elements\nin a 7-parameter similarity transformation between the Doppler derived\nvalues on the new WGS 72 system and the corresponding terrestrial values of a","588\nlarge number of stations on the U.S. High-Precision-Geodimeter-Traverse\nsystem were of the order of 0.06 (Y to Z), 0.03 (Z to X) and 0.16 (X to Y)\nseconds-of-are, with corresponding standard errors of 0.06, 0.03 and 0.03\nseconds respectively. After much discussion, it was generally agreed that,\nfor practical purposes, the procedure for a geodetically well defined, well\nobserved and properly adjusted system of terrestrial coordinates should be\nto limit the transformation from the Doppler system only to the 3 translation\nparameters, excluding any rotations. However, if any of the criteria above\nwere not satisfied, it was suggested that a full 7-parameter transformation\ncould be considered, on the understanding that this was a temporary solution\nprior to putting right the deficiencies of the terrestrial system.\nThe second problem discussed by the Workshop was that of using Doppler\nderived positions for strengthening existing national and continental\nterrestrial control networks and for establishing a basic control system\nwhere none already exists. Considering that Doppler observations are made\nin a different reference system from that of the local geodetic network,\nalternative methods for combining these two sets of observations were\nconsidered.\nOn the other hand, it was suggested that countries wishing to remain on\ntheir current geodetic reference system should reduce the Doppler derived\npositions onto that system. Since differences in positions are not too\nsensitive to small changes in the values of the translation parameters, the\nproblem could be solved by using only approximate values of these parameters,\nhowever obtained.\nOn the other hand, one could adopt the Doppler reference system as the\nbasic reference framework. In a classical two-dimensional mode of adjustment,\nthis would require the adoption of a nominally geocentric spheroid and the\nreduction of the terrestrial observations onto it. The problem would\ndisappear in a 3-D mode of computation and adjustment.\nThe relative merits of individual point positioning and the short-arc\nmethod, in the context of the provision of basic control were also discussed,\nas were the merits of treating the observed range-differences as correlated\nor uncorrelated, without however reaching a clear consensus.\nAttention was drawn to the risks of interpreting and using the variance-\ncovariance information, derived in conjunction with and as a by-product of\nDoppler positions. It was emphasized that this information is only based on\ninternal consistency, whereas the finally adopted variance-covariance matrix\nfor the Doppler positions should include externally derived contributions of\nsources of systematic error or bias.\nIt was also restated that the scale in the Doppler system is provided by\nthe adopted values of GM (the product of the Universal Gravitational Constant\nby the Mass of the Earth) and C (velocity of light in vacuo). Long arc\ncomputations would be affected by the former whereas short arc could be in-\nfluenced by the latter. However, because of a large amount of evidence\nsuggesting that the Doppler scale is too large by 1 ppm, Doppler derived\nresults should be corrected by a corresponding scaling down.","589\nOther topics discussed included the use of Doppler derived positions in\ndelineating boundary lines described in international and commercial treaties\nin terms of geographical coordinates on a specified datum, and the potential\nreal time mode of usage of Doppler in Civil Engineering situations.\nThe open sessions of the Workshop were attended by approximately 70 to\n75 participants, many of whom contributed to a highly spirited and often\ncontroversial debate.","590","591\nEFFECT OF GEOCEIVER OBSERVATIONS UPON THE\nCLASSICAL TRIANGULATION NETWORK*\nRobert E. Moose\nSoren W. Henriksen\nNational Geodetic Survey\nNational Ocean Survey, NOAA, Rockville, Maryland\nAbstract\nThis paper investigates the use of\nGeoceiver observations as a means of improving\ntriangulation network adjustment results. A test\nnetwork of real data is used in this study, which\nis comprised of 32 separate projects and contains\n838 first-order and 489 second-order stations in\nthe States of Mississippi, Louisiana, and Alabama.\nStatistics are provided on a sequence of adjust-\nments of this network in which the number of\nazimuth, base line, and Geoceiver observations\nwere systematically varied. From an analysis of\nthis sequence of adjustments, three important\nconclusions are made. First, the most effective\nseparation for Geoceiver observations is about 250 km\nand greater. Second, there is a limit to the\nimprovement in the a posteriori standard error that\nGeoceiver observations can effect in a triangulation\nnetwork. Third, Geoceiver observations are an\neffective means of controlling distortions in the\nlocal network. The theory of how Geoceiver observa-\ntions combine with the classical observations is\nexplained.\nIntroduction\nThe National Geodetic Survey (NGS) is assembling data for the\nproposed readjustment of the North American network of triangu-\nlation. To correct the known areas of distortion and weakness\nin the existing network, the following additional observations\nare being considered: very long base lines (VLBI) satellite,\nDoppler, transcontinental traverse (TCT) , geodimeter base lines,\nand astronomic azimuths. These observations will be included\nin the adjustment in order to strengthen the network.\n*Geoceiver is a trade name for the Doppler satellite tracking\ninstrument manufactured by Magnavox Corporation. Doppler\nsatellite tracking instruments made by other companies are\navailable. While these results are based upon Geoceiver\nobservations, there is no reason to suspect that any other\ncomparable Doppler satellite tracking instrument would not give\nthe same results.","592\nOne of the methods that will be used to improve the large\nscale configuration of the triangulation network is a planned\nnetwork of approximately 150 Geoceiver positions. The\nGeoceiver, a relatively new technological development in\ngeodesy, is used to measure the Doppler shift in the two\ncoherently related signals transmitted by the Navy Navigation\nSatellite System (NNSS) The adjustment of a large number of\nthese observations gives the position determination for the\nGeoceiver station used in the space rectangular coordinates of\nthe Naval Weapons Laboratory (NWL) 9D system. The RMS\ndifference residual for these position determinations is\ngenerally in the range from 0.15 m to 0.30 m in the X, Y, and\nZ directions. The sequence of steps to effect a transformation\nof this position in the geocentric NWL 9D system to the\nellipsoidal coordinate system of the North American Datum (NAD)\nis given by Meade (1974) There is, first, a coordinate origin\nshift from the geocentric origin to the NAD origin. The XYZ\nspace rectangular coordinates are then transformed into the\no, X, and h ellipsoidal coordinates of the NAD. The origin\nshift that is applied is the mean of the origin shifts that were\nrequired at 36 reliable Geoceiver stations to correct the\nDoppler coordinates to the transcontinental traverse coordinates.\nMeade found that there is a small systematic difference of\nabout 1.0 ppm between the NWL 9D coordinates and the TCT\ncoordinates. It is common practice to bring the Doppler\ncoordinates into closer agreement with the TCT coordinates by\napplying a correction to the 9D coordinate system. This\ncorrection is expressed by Anderle (1974) as a small scale\nchange and a rotation, performed in ellipsoidal coordinates, on\nthe NWL 9D coordinate system, giving a new coordinate system\ncalled NWL 10F. The correction transformation is:\n910F\n99D\n10F = 19D + 0.260 (A east is positive)\nh10F = h9D - 5.27 m (h height above a\ncommon ellipsoid)\nThe new origin shift parameters to transform into the TCT\ncoordinate system are given by Vincenty (1975) as:\nstd. error\nmean (meters)\nof mean (m)\nAX = + 19.60\n0.22\nAY = - 155.02\n0.18\nAZ = - 175.12\n0.18\nMeade shows that these Doppler coordinates now have a mean\ndifference from the TCT coordinates of only 1.03 m in latitude,\n1.01 m in longitude, and 1.25 m in height. The contemplated","593\nsystem of Geoceiver stations includes about 65 stations that are\nalso on the TCT. When all these stations are used, there will\nbe a better determination of the systematic difference between\nthe 9D and TCT coordinate systems. The agreement then between\ntransformed Doppler and TCT coordinates is expected to be better.\nThe a priori positional standard error for a Geoceiver\nobservation used in the adjustments in this paper is 0.9 m in\nlatitude and 1.2 m in longitude with no correlation assumed to\nexist between the two components. NGS has adopted this standard\nerror for use in Geoceiver observation evaluation studies only.\nIt is generally agreed that Geoceiver observations used as\npositional constraints will greatly improve the large scale\nconfigurations of the network.\nOn the smaller scale, weaknesses in the triangulation network\nhave traditionally been strengthened by observing more lines,\nmore distances, or more azimuths in the network. The\nstrengthening of a network by observing additional lines is\nseldom done because of the expense of moving personnel and\nequipment back to the area and rebuilding the observation\ntowers. Even though the distances between main scheme network\nstations may be easily and accurately measured with an\nelectro-optical distance measuring instrument (EDM) using an\nEDM instrument for observing additional distances is often not\na practical solution because the stations are not intervisible\nwithout observation towers. Strengthening a network by means\nof additional azimuth observations is expensive because the\nastronomic field party must not only observe the astronomic\nazimuth of a network line but also the astronomic position of\nthe azimuth station. These observations require a skilled\nobserver and quite often much time is lost due to overcast sky\nconditions. The Geoceiver has none of these drawbacks; it is\nportable and easy to operate. Observations are not expensive\nto obtain as the major item, the satellite, is provided by the\nU. S. Navy; intervisibility of network stations is not\nnecessary, and since the instrument operates in the radio-\nfrequency range, overcast skies are of no concern.\nAn obvious question is: Why can't additional Geoceiver\nobservations be used to provide scale and azimuth constraints to\nthe local system? Since Geoceivers are new, not much is known\nabout the interaction of their observations with classical\ntriangulation networks. It is toward alleviating this lack of\nunderstanding that this paper is directed. In general, we\nwould like to know how Geoceiver observations affect the\ntriangulation network, and particularly, how many Geoceiver\nobservations (and their location) are needed to improve a weak\ntriangulation network.","594\nIn this investigation, the test network is comprised of 32\nseparate projects, which contain 838 first-order and 489\nsecond-order stations in the States of Mississippi, Louisiana,\nand Alabama. This is the same network used by Dracup (1975)\nOne major difference, based on the suggestion of Dracup, has\nbeen the removal of the transcontinental traverse projects so\nthat the test network would be similar to most of the\ntriangulation in the United States. Within the combined\nnetwork, there are five existing Geoceiver stations.\nTransferred\nDoppler\nNumber\nStation\nLocation\nFrom\n10022\nKnob 1914\nNorth\nGreenville AFB 1957\n10003\nWinn 1929\nWest\npoint near Little RM A\n20016\nLittle 1934\nSouth\npoint near Kelley 1971\n51009\nKelley 1971\nEast\nWebster 1939 RM 1\n10023\nWebster 1929\nCenter\nFigure 1 shows the first-order, main scheme network and\nlocations of the five stations where Geoceiver observations\nwere made. Figure 2 shows the combined first-order, main\nscheme and second-order, main scheme networks. Figure 3 shows\nthe locations of the 18 lengths, either base lines or geodimeter\nlines, in the first-order, main scheme network. Twenty-seven\ngeodimeter lines in the first-order area project around\nstation Kelley 1971 have been removed to give a more balanced\nsystem of length observations. Figure 4 shows the location of\nthe 22 azimuth observations that orient the first-order network.\nTable 1 shows the principal characteristics of the 13 test\nnetworks, formed from the observational data, that were adjusted\nand used in the analyses described later.\nEffect of Geoceiver Observation Upon the Length and\nAzimuth Standard Errors\nIn this section, as well as sections 3 and 4, only the\naccidental errors which exist in the observations are\nconsidered. It is realized that systematic errors are\nprobably present, but no means of detecting them were apparent\nto the authors.\nAn important question when considering the employment\nof Geoceiver observations as constraints in an existing tri-\nangulation network is: What is the best arrangement of\nGeoceiver stations? What quantity are we concerned with here?\nSince the local surveyor can directly observe the length or\nazimuth of any line in the National network, it is desirable\nthat these observables in the National network be of such an\naccuracy that the local surveyor cannot detect discrepancies,\nTraditionally, therefore, the quality of a geodetic network has","595\nMISSISSIPPI GEOCEVER TEST AREA\nKNOB 1914\nWEBSTER\n1937\nKIN\nWINN 1929\n4\nKELLEY 1971\nLITTLE 1934\nNORTH\n__Geoceiver test area first-order network.\nFIG.\n1","596\nMISSIS GEOCEVER 'EST DEEN\nNORTH\nFIG. 2 -Geoceiver test area first- and second-order networks.","597\nMISSISSIPPI\nNORTH\n--Geoceiver test area first-order network base\nFIG.\n3\nlines.","598\n\".\"\nMISSISSIPPI GEOCEVER TEST AREA\nNORTH\n4 -- -Geoceiver test area first-order network azimuths.\nFIG.","Orientation\nCenter\nCenter\nCenter\nNSEW\nNSEW\nNSEW\nNSEW\nN-S\nN-S\nN-S\nN-S\nE-W\nE-W\nE-W\nE-W\nN-S\nGeoceiver\nSeparation\n426 km\nTable 1. -- Data used in the various adjustments.\n-\n-\n-\n-\n-\n-\n-\n266\n350\n266\n181\n253\n350\n253\n578\nNumber\n--\n5\n5\n5\n2\n2\n2\n2\n2\n2\n2\n2\n1\n1\n5\n2\nAzimuths\n0\n8\n18\n0\n0\n0\n18\n0\n0\n0\n18\n18\n18\n22\n22\n0\nTriangulation Networks\nDistances\n0\n8\n15\n0\n0\n0\n15\n0\n0\n0\n15\n42\n42\n63\n63\n0\nDirections\n7297\n7202\n7202\n7297\n7202\n7202\n7202\n7297\n7202\n7202\n7202\n7202\n7202\n12195\n12195\n7202\nStations\n838 1st\n498 2nd\n838 1st\n498 2nd\nOrder\nOrder\nOrder\nOrder\n854\n838\n838\n854\n838\n838\n838\n854\n838\n838\n838\n838\n838\n838\nVariance\nin Unit\nWeight\n1.369\n1.343\n1.342\n1.371\n1.345\n1.345\n1.345\n1.371\n1.344\n1.345\n1.345\n1.347\n1.347\n1.273\n1.272\n1.345\nAdjust-\nB1/2\nment\nc't\nD'+\nB+\nE*\nF*\nG*\nC'\nC\"\nD'\nD\"\nE*\nH\nB\nC\nD","600\nbeen judged by the size of the length and azimuth standard\nerror between nearby stations. The Geoceiver observations may\nthen be thought of as being for the purpose of effecting a\nreduction in the size of the length and azimuth standard errors.\nThe investigation is carried out by performing a series of\nadjustments in which the number of base lines, azimuths, and\nGeoceiver stations in the first-order network is varied. The\ndistance and azimuth standard errors in each of these solutions\nare computed at 44 selected lines in the network. The\ndescription of these lines is given in table 2. The lines,\nchosen SO that they span the open areas between the arcs, are\nused to observe the movement of one arc relative to another.\nIn general, each of the twenty-five areas (see figure 5) has a\nline oriented north-south and east-west. These lines are the\nsame as those used by Dracup (1975) .\nThe optimum arrangement and spacing of Geoceiver stations are\ninvestigated first. Adjustments C, D, C' , D' , C\", D\", and H\nare adjustments of the 838 station, first-order, main scheme\nnetwork. These adjustments do not contain any base lines or\nazimuths. The scale and azimuth constraint are provided by two\nGeoceiver observations.\nOrienta-\nSepara-\nAdjust-\ntion (km)\ntion\nStations\nment\n426\nnorth-south\nLittle 1934\nKnob 1914\nC\nnorth-south\n266\nLittle 1934\nWebster 1939\nC'\nThackers 1934*\nnorth-south\n350\nLittle 1934\nC\"\n181\nWinn 1929\neast-west\nWebster 1939\nD\n253\nKelley 1971\neast-west\nWebster 1939\nD'\n350\nArcola 1939*\neast-west\nRock 1939*\nD\"\n578\nMorris 1914*\nnorth-south\nChalmette 2 1931*\nH\nThe length and azimuth standard errors computed in these seven\nadjustments are given in table 3. As expected, the length and\nazimuth standard errors between pairs of stations vary in size\ndepending upon the location of the stations in the network\nrelative to the network constraints. Since only the orientation\nand spacing of the Geoceiver stations vary in this set of\nadjustments, the preferred arrangement would be the one in\nwhich the size of the length and azimuth standard errors is\nsmallest. To find which adjustment has the better arrangement,\nthe results in the D' adjustment are compared line for line to\nthe results in the other six adjustments. These ratios are\ngiven in table 4.\n*Pseudo-Geoceiver stations. A Geoceiver observation was\nsimulated at these stations to give the desired Geoceiver obser-\nvation separation.","601\nTable 2. --Description of test lines.\nStation\nArea,\nStation\n/km\nLine\nCAPLEVILLE SE BASE 1914\nBATESVILLE 1956\n1,1\n10%/ 76.1\nEVANSVILLE 1929\nWEEKS 1934\n1,2\n265 / 83.2\nBOBO 1956\nMEEKS 1939\n2,1\n10°/ 64.8\nWHILKINSON 1929\nKEATON 1934\n2,2\n280 / 93.5\nINDIANOLA 1939\nSTRAIGHT 1957\n3,1\n3°/ 44.8\nSILENT SHADE 1957\nSHIVERS 1929\n3,2\n90%/ 74.2\nPALUSKA 1939\nLEXINGTON 1958\n4,1\n9°/ 47.2\nKEIRN 1957\nMOORE 1934\n4,2\n274°/ 41.1\nCOUNTRY 1957\nSLIKER 1931\n5,1\n5 % 64.7\nHOMESTEAD 1929\nBENTONIA 1959\n5,2\n274 / 71.5\nRICHLAND 1958\nFANNIN 1931\n6,1\n354°/ 60.7\nPERSIMMON 1959\nPINE 1934\n6,2\n255 / 46.2\nHAWKINS 1931\nJEFF 1947\n7,1\n2°/ 63.2\nTYLER 1929\nCRYSTAL 1945\n7,2\n272 % 63.5\nBRANDON 1931\nSHARP 1945\n8,1\n4°/ 29.6\nFLORENCE 1945\nSHILOH 1945\n8,2\n259 / 31.7\nCENTRAL 1945\nBETHEL 1946\n9,1\n21°, 42.7\nCHOCTAW 1945\nCLEM 1934\n9,2\n269 / 41.1\nFOSTER 1929\nMCCOMB 1947\n10,1\n275 / 77.8\nTOLER 1946\nBROCK 1939\n11,1\n355 / 39.7\nPIKE 1947\nSMITH 1934\n11,2\n280°/ 34.2\nMALONE 1914\nTHAXTON 1967\n14,1\n10°/ 75.0\nRIDGE 1934\nLEBANON 1935\n14,2\n283°/ 54.7\nLOCHINVAR 1967\nWEBSTER 1939\n15,1\n12°/ 73.2\nRANDOLPH 1967\nEUPORA 1939\n15,2\n10°/ 69.3\nBUSH 1934\nBARR 1935\n15,3\n280 / 70.6\nREFORM 1939\nLOBUTCHA 1958\n16,1\n4°/ 36.4\nPALMERTREE 1934\nBEVEL 1935\n16,2\n277 / 64.4\nDRY 1958\nCARSON 1930\n17,1\n0°/ 53.6\nGRIMES 1934\nSMITH 1935\n17,2\n264 o/ 61.2\nFOREST EAST BASE 1930\nTISDALE 1939\n18,1\n1°/ 94.9\nWILLIAMS 1934\nGRANTHAM 1935\n18,2\n285 / 30.9\nLITTLE 1934\nMCLAURIN 1935\n19,1\n273°/ 46.1\nPLEASANT 1914\nBOOG 1939\n20,1\n7°/113.3\nKARR 1935\nBRAKEFIELD 1939\n20,2\n294°/ 8 82.8\nFEDERAL 1935\nGALLOWAY 1939\n20,3\n277° / 88.1\nBRADSHAW 1939\nMILL 1934\n21,1\n52°/162.6\nWARREN 1935\nEUTAW 1939\n21,2\n263°/ 77.0\nWOLF 1930\nHOUSE 1939\n22,1\n355 / 77.9\nCLAYBORN 1935\nDANIELS 1938\n22,2\n272 / 80.2\nLITTLE 1939\nWEDFORD 1942\n23,1\n347 / 48.3\nTINGLE 1935\nCOON 2 1938\n23,2\n264°/ 92.8\nROCK 1939\nFULLER 1930\n25,1\n0%/ 72.9\nMOUNDVILLE 1939\nJAMISON 1887\n25,2\n257 / 87.4\n*\nThe tabulation gives the azimuth and length of the line.\n10°/76.1: 10° = azimuth of line from south, 76.1 = distance between\npoints in kilometers.","602\nMISSISSIPPI GEOCEVER TEST AREA\n1,1\n14,1 1\n1,2\n14,2\n20,2\n20,1\n15,1\n20,3\n2,2\n3,1\n4,1\n16,1\n16,2\nAND\n21,1\n25,\n25,2\n17,1\n5,1\n21,2\n17,2\n5,2\n8,2\n18,\n22,1\n8,1\n7,2\nX\n18,2\n22,2\n9.\n11,\n23,1\n10,1\n19,1\n11,2\n23,2\nNORTH\nFIG. 5 ~Geoceiver test area line accuracies.","0.161/256\n0.291/222\n0.309/231\n0.204/298\n0.174/266\n0.292/216\n0.295/215\n0.359/212\nExplanation of tabulation 10.419/181: 0.419 = o for length in meters, 181 = proportional\n0.380/219\n0.314/206\n0.377/248\n0.194/231\n0.301/246\n0.167/283\n0.839\n0.865\n0.916\n0.955\n0.772\n0.877\n0.978\n1.007\nH\n0.969\n1.001\n1.009\n1.912\n0.996\n0.879\n0.196/209\n0.358/181\n0.383/187\n0.273/222\n0.223/207\n0.371/170\n0.368/172\n0.455/205\n0.237/188\n0.372/199\n0.214/221\n0.421/181\n0.445/187\n0.366/177\nTable 3. - -Distance and azimuth standard errors.\nD\"\n1.032\n1.042\n1.129\n1.142\n1.009\n1.082\n1.228\n1.238\n1.087\n1.165\n1.048\n1.181\n1.183\n1.201\n0.184/224\n0.327/198\n0.353/202\n0.243/250\n0.203/227\n0.335/189\n0.337/188\n0.404/188\n0.424/196\n0.340/190\n0.432/216\n0.218/205\n0.345/215\n0.194/244\nC\"\n1.130\n1.152\n1.192\n1.222\n1.086\n1.166\n1.253\n1.275\n1,274\n1.264\n1.265\n1.195\n1.251\n1.160\npart in thousands or 181 = 1:181000, 1.150 = o in azimuth.\n0.224/183\n0.436/164\n0.312/194\n0.253/182\n0.409/155\n0.408/156\n0.401/161\nAdjustment\n0.461/165\n0.494/168\n0.402/161\n0.523/179\n0.268/167\n0.431/172\n0.245/193\nD'\n1.418\n1.435\n1.504\n1.526\n1.393\n1.454\n1.572\n1.581\n1.516\n1.524\n1.534\n1.472\n1.541\n1.468\n0.198/207\n0.220/210\n0.356/177\n0.358/177\n0.351/184\n0.381/187\n0.266/228\n0.431/175\n0.457/182\n0.371/174\n0.468/200\n0.237/189\n0.378/196\n0.213/222\nC'\n1.436\n1.458\n1.486\n1.368\n1.432\n1.491\n1.512\n1.568\n1.571\n1.560\n1.495\n1.526\n1.451\n1.420\n1.150\n0.450/103\n0.889/105\n0.439/102\n0.704/105\n0.452/104\n0.396/104\n0.647/100\n0.701/102\n0.584/104\n0.825/101\n0.652/97\n0.648/98\n0.722/99\n0.655/99\n1.774\n1.845\n1.851\n1.789\n1.830\n1.943\n1.948\nD\n1.871\n1.866\n1.887\n1.776\n1.827\n1.747\n1.777\n0.419/181*\n0.223/208\n0.355/178\n0.358/177\n0.201/204\n0.351/184\n0.380/188\n0.272/223\n0.449/185\n0.368/176\n0.465/201\n0.238/189\n0.378/196\n0.217/218\n0.963\n1.052\n1.176\n1.197\n1.033\n1.103\n1.140\nC\n1.085\n1.168\n1.066\n1.010\n1.150\n1.164\n1.174\nArea,\n6,2\n7,1\n7,2\n4,2\n5,1\n5,2\n6,1\n1,2\n2,2\n3,1\n3,2\n4,1\nLine\n1,1\n2,1\n*","604\n0.114/260\n0.115/276\n0.140/305\n0.135/304\n0.367/212\n0.148/268\n0.127/270\n0.316/237\n0.240/228\n0.271/270\n0.263/264\n0.258/273\n0.161/227\n0.228/282\n0.186/288\nH\n0.887\n0.818\n0.716\n0.727\n0.968\n0.785\n0.786\n0.913\n1.015\n0.851\n0.861\n0.887\n1.110\n0.801\n0.837\n0.149/198\n0.155/205\n0.206/208\n0.198/208\n0.473/164\n0.210/188\n0.180/190\n0.373/201\n0.277/198\n0.313/226\n0.324/226\n0.314/221\n0.183/199\n0.278/232\n0.231/232\nD\"\n1.137\n1.072\n1.043\n1.050\n1.258\n1.127\n1.126\n1.119\n1.188\n1.040\n1.052\n1.055\n1.264\n0.977\n1.046\n0.133/222\n0.138/230\n0.178/240\n0.171/240\n0.429/182\n0.185/214\n0.158/216\n0.359/209\n0.266/206\n0.300/244\n0.290/239\n0.295/239\n0.172/211\n0.262/246\n0.211/254\nC\"\n1.181\n1.129\n1.072\n1.079\n1.268\n1.139\n1.139\n1.224\n1.292\n1.149\n1.153\n1.173\n1.343\n1.107\n1.132\nTable 3. --Continued.\nAdjustment\n0.167/177\n0.175/181\n0.233/183\n0.224/183\n0.518/150\n0.234/169\n0.201/170\n0.412/182\n0.304/180\n0.359/204\n0.347/199\n0.355/198\n0.198/184\n0.316/204\n0.257/208\nD'\n1.487\n1.437\n1.414\n1.419\n1.587\n1.478\n1.477\n1.448\n1.496\n1.377\n1.389\n1.409\n1.552\n1.345\n1.391\n0.143/206\n0.149/213\n0.193/221\n0.186/221\n0.452/172\n0.198/200\n0.170/202\n0.384/195\n0.284/192\n0.332/220\n0.321/216\n0.319/221\n0.181/201\n0.283/228\n0.225/238\nC'\n1.432\n1.390\n1.335\n1.341\n1.495\n1.386\n1.386\n1.524\n1.580\n1.475\n1.478\n1.458\n1.558\n1.397\n1.397\n0.294/101\n0.312/102\n0.419/102\n0.403/102\n0.748/100\n0.548/100\n0.723/101\n0.687/101\n0.681/104\n0.624/103\n0.526/102\n0.814/96\n0.399/99\n0.344/99\n0.369/99\nD\n1.885\n1.846\n1.839\n1.842\n1.974\n1.893\n1.893\n1.856\n1.907\n1.827\n1.830\n1.807\n1.957\n1.782\n1.833\n0.145/204\n0.150/211\n0.194/220\n0.186/220\n0.452/172\n0.198/201\n0.169/202\n0.374/201\n0.281/195\n0.338/216\n0.326/213\n0.326/217\n0.195/187\n0.296/218\n0.247/217\nC\n1.079\n1.016\n0.960\n0.968\n1.189\n1.042\n1.042\n1.057\n1.129\n0.976\n0.994\n1.032\n1.223\n0.953\n0.993\nArea,\nLine\n8,1\n8,2\n9,1\n9,2\n10,1\n11,1\n11,2\n14,1\n14,2\n15,1\n15,2\n15,3\n16,1\n16,2\n17,1","0.205/299\n0.293/323\n0.168/184\n0.213/216\n0.437/260\n0.387/214\n0.356/248\n0.403/404\n0.290/265\n0.291/267\n0.304/264\n0.264/183\n0.404/230\n0.142/514\n0.166/528\nH\n0.830\n0.703\n1.151\n1.060\n0.951\n0.939\n0.949\n0.711\n0.904\n0.843\n0.855\n1.128\n0.869\n0.979\n0.971\n0.258/238\n0.423/224\n0.191/162\n0.269/171\n0.493/230\n0.420/197\n0.391/225\n0.542/300\n0.333/231\n0.373/209\n0.380/211\n0.312/155\n0.508/183\n0.143/508\n0.168/521\nD\"\n1.019\n1.005\n1.335\n1.321\n1.094\n1.091\n1.067\n0.906\n1.028\n1.089\n1.100\n1.376\n1.171\n1.038\n1.033\n0.321/240\n0.239/256\n0.369/257\n0.183/169\n0.247/187\n0.474/239\n0.412/201\n0.385/229\n0.492/331\n0.337/231\n0.350/229\n0.291/166\n0.463/200\n0.144/507\n0.168/520\nC\"\n1.043\n1.184\n1.156\n1.166\n1.395\n1.197\n1.232\n1.225\n1.130\n1.060\n1.397\n1.327\n1.227\n1.223\n1.221\n-Continued.\nAdjustment\n0.293/208\n0.634/256\n0.368/209\n0.415/188\n0.422/190\n0.334/144\n0.556/167\n0.146/501\n0.171/512\n0.482/197\n0.206/150\n0.293/157\n0.539/210\n0.453/182\n0.428/206\nD'\n1.273\n1.334\n1.415\n1.433\n1.662\n1.498\n1.259\n1.254\n1,368\n1.371\n1.631\n1.624\n1.390\n1.396\n1.361\nTable 3\n0.258/237\n0.401/237\n0.190/163\n0.258/179\n0.507/223\n0.434/191\n0.407/216\n0.545/298\n0.340/226\n0.358/218\n0.371/216\n0.301/160\n0.486/191\n0.145/502\n0.170/515\nC\n1.395\n1.334\n1.443\n1.399\n1.407\n1.595\n1.425\n1.476\n1.471\n1.326\n1.613\n1.532\n1.513\n1.514\n1.504\n0.593/103\n0.924/103\n1.132/100\n1.548/104\n0.773/100\n0.779/100\n0.804/100\n0.522/93\n0.955/97\n0.760/96\n0.910/96\n0.330/94\ndeleted\n0.851/97\n0.889/99\n2.065\n1.939\n1.904\n1.900\nD\n1.827\n1.826\n2.027\n1.881\n1.875\n1.880\n1.764\n1.869\n1.894\n1.900\n0.524/216\n0.438/189\n0.434/203\n0.639/254\n0.371/208\n0.369/211\n0.386/208\n0.300/161\n0.488/190\n0.395/184\n0.472/185\n0.275/223\n0.410/232\n0.194/159\ndeleted\n1.299\n1.093\n1.053\n1.047\n0.861\n1.020\n1.031\n1.045\nC\n0.985\n0.930\n1.303\n1.007\n1.061\n1.075\nArea,\n21,2\n23,2\n22,1\n22,2\n23,1\n25,1\n25,2\nLine\n17,2\n18,1\n18,2\n19,1\n20,1\n20,2\n20,3\n21,1","606\nTable 4. - Standard errors, ratios of o l and oa\nC'/D'\nArea,\nD\nP/D'\nC/D,\nD\"/p\nC\"/p,\nH\n4/D\nLine\n1,1\n0.935\n1.675\n0.909\n0.913\n0.876\n0.779\n1.034\n1.234\n0.758\n0.779\n0.840\n0.639\n1,2\n0.925\n1.670\n0.908\n0.901\n0.858\n0.769\n1.031\n1.224\n0.764\n0.776\n0.829\n0.657\n2,1\n0.923\n1.629\n0.916\n0.910\n0.846\n0.781\n1.017\n1.230\n0.766\n0.783\n0.825\n0.658\n2,2\n0.895\n1.700\n0.890\n0.870\n0.826\n0.721\n1.016\n1.206\n0.738\n0.738\n0.812\n0.620\n3,1\n0.884\n1.638\n0.888\n0.884\n0.813\n0.724\n0.990\n1.186\n0.757\n0.756\n0.812\n0.646\n3,2\n0.877\n1.633\n0.877\n0.863\n0.801\n0.698\n0.988\n1.190\n0.726\n0.714\n0.790\n0.599\n4,1\n0.870\n1.845\n0.886\n0.873\n0.792\n0.682\n1.001\n1.253\n0.712\n0.728\n0.797\n0.592\n4,2\n0.884\n1.768\n0.897\n0.875\n0.821\n0.719\n1.001\n1.236\n0.720\n0.726\n0.803\n0.603\n5,1\n0.875\n1.613\n0.875\n0.893\n0.815\n0.726\n0.969\n1.227\n0.733\n0.751\n0.793\n0.609\n5,2\n0.874\n1.608\n0.871\n0.878\n0.810\n0.709\n0.974\n1.213\n0.747\n0.748\n0.801\n0.626\n6,1\n0.853\n1.872\n0.873\n0.875\n0.779\n0.654\n0.982\n1.284\n0.691\n0.724\n0.780\n0.554\n6,2\n0.869\n1.779\n0.881\n0.881\n0.802\n0.688\n0.985\n1.259\n0.724\n0.744\n0.802\n0.603\n7,1\n0.870\n1.594\n0.867\n0.907\n0.819\n0.714\n0.948\n1,236\n0.748\n0.781\n0.797\n0.622\n7,2\n0.877\n1.588\n0.877\n0.902\n0.826\n0.723\n0.956\n1.232\n0.757\n0.783\n0.806\n0.637\n8,1\n0.856\n1.760\n0.868\n0.892\n0.796\n0.683\n0.963\n1.268\n0.726\n0.765\n0.794\n0.597\n8,2\n0.851\n1.783\n0.857\n0.886\n0.789\n0.657\n0.967\n1.285\n0.707\n0.746\n0.786\n0.569","607\nTable 4. -Continued.\nArea,\nC'/D'\nD\nD/D\nC\nD\"/D,\nc/p,\nD\"\nC\"/D,\nH\nH/D\nLine\nD'\nD\n9,1\n0.828\n1.798\n0.832\n0.884\n0.764\n0.601\n0.944\n1.301\n0.679\n0.738\n0.758\n0.506\n9,2\n0.830\n1.799\n0.830\n0.884\n0.763\n0.603\n0.945\n1.298\n0.682\n0.740\n0.760\n0.512\n10,1\n0.872\n1.571\n0.872\n0.913\n0.828\n0.708\n0.942\n1.244\n0.749\n0.793\n0.799\n0.610\n11,1\n0.846\n1.705\n0.846\n0.897\n0.791\n0.632\n0.938\n1,281\n0.705\n0.762\n0.771\n0.531\n11,2\n0.846\n1.711\n0.841\n0.895\n0.786\n0.632\n0.938\n1.282\n0.705\n0.762\n0.771\n0.532\n14,1\n0.932\n1.815\n0.908\n0.905\n0.871\n0.767\n1.052\n1.282\n0.730\n0.773\n0.845\n0.631\n14,2\n0.934\n1.803\n0.924\n0.911\n0.875\n0.789\n1.056\n1,275\n0.755\n0.794\n0.864\n0.678\n15,1\n0.925\n2.014\n0.942\n0.902\n0.836\n0.755\n1.071\n1.327\n0.709\n0.755\n0.834\n0.618\n15,2\n0.925\n1.980\n0.940\n0.905\n0.836\n0.758\n1.064\n1.317\n0.715\n0.757\n0.830\n0.620\n15,3\n0.898\n1.918\n0.918\n0.882\n0.831\n0.727\n1.035\n1.282\n0.733\n0.749\n0.832\n0.630\n16,1\n0.914\n1.864\n0.984\n0.924\n0.869\n0.813\n1.004\n1.261\n0.788\n0.814\n0.865\n0.715\n16,2\n0.896\n1.975\n0.937\n0.880\n0.829\n0.722\n1.039\n1.325\n0.709\n0.726\n0.823\n0.596\n17,1\n0.875\n2.047\n0.961\n0.899\n0.821\n0.724\n1.004\n1.318\n0.714\n0.752\n0.814\n0.602\n17,2\n0.880\n2.024\n0.938\n0.880\n0.816\n0.700\n1.020\n1.335\n0.720\n0.745\n0.826\n0.607\n18,1\n0.832\n1.917\n0.850\n0.878\n0.766\n0.608\n0.967\n1.332\n0.678\n0.733\n0.773\n0.513\n18,2\n0.922\n1.602\n0.941\n0.927\n0.888\n0.816\n0.989\n1.243\n0.799\n0.818\n0.856\n0.706","608\nTable 4. -Continued\nC'/D\nD\"/D;\nArea,\nD\nC\nD\"\nC\"/D,\nP/D'\nC/D,\nH\n1/D\nLine\nD'\nD'\nD'\n19,1\n0.880\n0.918\n0.843\n0.727\n---\n0.943\n0.813\n0.817\n0.653\n20,1\n0.941\n2.100\n0.972\n0.915\n0.879\n0.811\n1.088\n1.353\n0.725\n0.787\n0.883\n0.684\n20,2\n0.958\n1.879\n0.967\n0.927\n0.909\n0.854\n1.084\n1.343\n0.760\n0.781\n0.876\n0.673\n20,3\n0.951\n2.077\n1.014\n0.914\n0.899\n0.832\n1.105\n1.381\n0.790\n0.784\n0.897\n0.697\n21,1\n0.860\n2.442\n1.008\n0.855\n0.776\n0.636\n1.048\n1.386\n0.676\n0.712\n0.819\n0.559\n21,2\n0.924\n2.100\n1.008\n0.905\n0.872\n0.788\n1.082\n1.401\n0.765\n0.771\n0.888\n0.678\n22,1\n0.863\n1.877\n0.890\n0.899\n0.812\n0.701\n0.989\n1.338\n0.729\n0.770\n0.817\n0.596\n22,2\n0.879\n1.905\n0.914\n0.900\n0.829\n0.720\n0.982\n1.326\n0.730\n0.768\n0.814\n0.597\n23,1\n0.901\n1.563\n0.898\n0.934\n0.871\n0.790\n0.960\n1.242\n0.781\n0.828\n0.839\n0.679\n23,2\n0.874\n1.718\n0.877\n0.914\n0.833\n0.727\n0.951\n1.294\n0.729\n0.782\n0.799\n0.580\n25,1\n0.993*\n5.206*\n2.705*\n0.979\n0.986\n0.973\n1.172*\n1.512*\n0.836*\n0.824\n0.979\n0.778\n25,2\n0.994*\n5.322*\n2.759*\n0.982\n0.982\n0.971\n1.173*\n1.515*\n0.835*\n0.824\n0.977\n0.774\nol\n0.8880\n1.8136\n0.9061\n0.9003\n0.8348\n0.7344\n0.0342\n0.1873\n0.0481\n0.0253\n0.0494\n0.0807\nsl\no\n1.0015\n1.2812\n0.7324\n0.7658\n0.8248\n0.6224\na\ns a\n0.0472\n0.0534\n0.0310\n0.0304\n0.0474\n0.0614\n*These values were not used in subsequent computations\nbecause for some unknown reason they differed too much from\nthe mean.","609\nThe means of the ratios with respect to D' are listed below:\nAzimuth\nDistance\nAdjustment\nStandard Error\nStandard Error\n1.00\n1.00\nD\n,\n1,81\n1.28\nD\n0.90\n0.73\nC\nC'\n0.88\n1.00\nD\"\n0.90\n0.77\nC\"\n0.83\n0.82\n0.73\n0.62\nH\nThe above table may be interpreted as follows. On the\naverage, the distance standard error of a line in adjustment D\nwill be 1.81 times greater than the distance standard error of\nthe same line in adjustment D'\nTo test whether there is any orientation bias, pseudo-\nGeoceiver stations are used in the C\" and D\" adjustments to\nachieve a set of adjustments with the same station separation\nbut with different orientation. The orientation of the C\"\nstations is north-south and the D\" stations is east-west. The\ndistance standard errors in the C\" adjustment are 8 percent\nsmaller than in the D\" adjustment. This is probably due to the\nsmaller a priori latitude standard error of the north-south\nGeoceiver stations. The azimuth standard errors in the D\" adjust-\nment are 6 percent smaller than in the C\" adjustment. This again\nis probably due to the smaller a priori latitude standard error.\nThere is then a small preference in orientation of Geoceiver\nstations depending upon whether one wants to improve the distance\nstandard errors or azimuth standard errors the most.\nThe variation of the distance standard error in these seven\nadjustments is shown in figure 6.\nThere is rapid reduction in distance standard error as the\nseparation between Geoceiver stations increases to about 250 km.\nAt this point, there is a dramatic change in the effectiveness\nof further separation to reduce the standard error.\nThe graph of the variation of the azimuth standard error is\nshown in figure 7.\nThe azimuth standard errors in this set of data continued to\ndecrease as the distance between the two Geoceiver stations\nincreased. However, the rate of decrease became less and less.\nThus we conclude that Geoceiver stations need to be separated\nby at least 250 km, to most effectively improve the scale\naccuracy of a network. The azimuth accuracies are dependent\nonly upon distance; therefore, the most effective way of","610\nERP\n2.0\nSTO\nD\nO\nD\nD'\nC\n1.0\nNEW\nC'\no\nH\n100\n400\n500\n200\n300\nSEPARATION\nOF\nGEOCEIVER\nSTATIONS\n(KM.)\nVariation of the distance standard error.\nFIG. 6\n2.0\no\nD\nC'\n1.0\nNEEM\nO\nC\"\nD'\nC\nO\nD'\nH\n100\n200\n300\n400\n500\nSEPARATION\nOF\nGEOCEIVER\nSTATIONS\n(KM.)\nFIG. 7 -- Variation of the azimuth standard error.","611\nimproving azimuth accuracies with Geoceiver stations is to\nseparate the stations as much as possible.\nAnother important question is: What is the density of\nGeoceiver observations that can benefit an existing network by\nreducing the standard errors of distance and azimuth?\nOne Geoceiver station is a trivial case; there is no effect\nupon the accuracies. At least two Geoceiver position observa-\ntions are needed to effect a length and/or an azimuth constraint.\nThe case of two or more Geoceiver stations is difficult to\nanalyze because, as shown previously, the distance and azimuth\nstandard errors are directly dependent upon the separation\nbetween Geoceiver stations. Any attempt at analysis be varying\nthe number of Geoceiver stations in the test area would be\ncomplicated by the uneven spacing of the available Geoceiver\nstations. For this reason, it was decided to perform the\nanalysis by varying the number of base lines and azimuths in\nthe basic first-order, main scheme network.\nThe B, B1/2, B + , D 1 , D'+, and c't adjustments are used in the\nanalysis.\nThe B series of adjustments contain all five of the Geoceiver\nobservations while the D series contain only two. Reference\nmay\nbe made to table 1 for the complete makeup of the data sets.\nThe point at which Geoceiver observations ceased to have\nan\nappreciable effect upon the solution was sought by first\nadjusting the network using no observed distances and azimuths\nthen using one-half of the distances and azimuths, and finally\nusing all of the distances and azimuths. The distance and\nazimuth standard errors from these adjustments are given in\ntables 3 and 5.\nAs in the previous section, the analysis is accomplished by\ncomparing the length and azimuth standard errors over the 44\nsample lines. The ratios from the various pair combinations of\nadjustments are given in table 6. The means of the ratios with\nrespect to adjustment B+ are:\nAzimuth\nDistance\nAdjustment\nStandard Error\nStandard Error\nB+\n1.00\n1.00\nB1/2\n1.07\n1.13\nB\n1.39\n1.37","612\nTable 5. --Distance and azimuth standard errors.\nAdjustment\nArea,\nB+\nB1/2\nD't\nLine\nC'+\nB\n1,1\n0.370/205*\n0.299/254\n0.308/247\n0.309/246\n0.307/248\n0.946\n0.745\n0.767\n0.782\n0.779\n1,2\n0.389/214\n0.264/315\n0.314/265\n0.270/207\n0.269/309\n0.952\n0.732\n0.767\n0.773\n0.772\n2,1\n0.326/199\n0.268/242\n0.271/239\n0.272/238\n0.271/239\n0.979\n0.757\n0.841\n0.782\n0.781\n2,2\n0.385/243\n0.254/368\n0.278/337\n0.258/362\n0.258/362\n0.840\n0.612\n0.675\n0.654\n0.652\n3,1\n0.202/221\n0.139/323\n0.150/299\n0.140/320\n0.140/320\n0.940\n0.724\n0.787\n0.752\n0.752\n3,2\n0.309/240\n0.201/369\n0.223/333\n0.205/361\n0.206/361\n0.801\n0.535\n0.614\n0.574\n0.574\n4,1\n0.178/265\n0.129/365\n0.132/358\n0.136/346\n0.131/359\n0.772\n0.580\n0.653\n0.613\n0.614\n4,2\n0.169/243\n0.121/341\n0.136/302\n0.122/338\n0.122/338\n0.793\n0.614\n0.678\n0.649\n0.649\n5,1\n0.302/214\n0.234/277\n0.230/281\n0.251/258\n0.233/278\n0.890\n0.638\n0.661\n0.722\n0.660\n0.211/339\n5,2 0.321/223\n0.209/342\n0.243/295\n0.211/339\n0.674\n0.925\n0.652\n0.740\n0.674\n6,1\n0.222/273\n0.162/374\n0.164/370\n0.160/379\n0.170/358\n0.543\n0.729\n0.511\n0.596\n0.543\n0.128/360\n6,2\n0.187/247\n0.127/363\n0.150/308\n0.128/361\n0.659\n0.838\n0.634\n0.718\n0.660\n0.218/290\n7,1\n0.314/201\n0.216/293\n0.241/262\n0.217/291\n0.694\n0.997\n0.678\n0.811\n0.691\n0.219/290\n7,2\n0.314/202\n0.217/292\n0.237/268\n0.218/291\n0.749\n0.018\n0.734\n0.860\n0.747\n*\nExplanation of tabulation 10.370/205: 0.370 = o for length\n0.946\nin meters, 205 = proportional part in thousands or\n205 = 1:205000. 0.946 = o in azimuth.","613\nTable 5. --Continued.\nAdjustment\nArea,\n1/2\nB+\nLine\nB\nc + +\nD'+\nB\n8,1\n0.124/238\n0.093/318\n0.099/299\n0.094/316\n0.094/314\n0.886\n0.672\n0.758\n0.689\n0.691\n8,2\n0.127/250\n0.085/371\n0.096/331\n0.086/368\n0.087/366\n0.806\n0.565\n0.669\n0.587\n0.587\n9,1\n0.161/265\n0.091/470\n0.101/421\n0.092/462\n0.094/457\n0.744\n0.417\n0.563\n0.439\n0.443\n9,2\n0.155/265\n0.088/466\n0.098/418\n0.090/459\n0.091/454\n0.754\n0.428\n0.574\n0.449\n0.453\n10,1\n0.403/193\n0.248/314\n0.273/285\n0.249/313\n0.249/312\n1.022\n0.658\n0.811\n0.666\n0.669\n11,1\n0.170/233\n0.100/396\n0.110/362\n0.101/391\n0.102/388\n0.850\n0.495\n0.645\n0.508\n0.512\n11,2\n0.146/235\n0.086/396\n0.094/364\n0.087/391\n0.088/388\n0.850\n0.505\n0.650\n0.518\n0.522\n14,1\n0.323/232\n0.242/310\n0.254/296\n0.253/296\n0.251/299\n0.855\n0.658\n0.683\n0.706\n0.703\n14,2\n0.243/225\n0.193/283\n0.201/272\n0.202/271\n0.200/274\n0.943\n0.784\n0.808\n0.839\n0.832\n15,1\n0.287/255\n0.231/316\n0.239/306\n0.242/303\n0.240/304\n0.761\n0.605\n0.637\n0.660\n0.650\n15,2\n0.278/249\n0.226/307\n0.233/298\n0.235/295\n0.234/297\n0.781\n0.627\n0.661\n0.677\n0.668\n15,3\n0.270/261\n0.197/358\n0.206/343\n0.202/349\n0.201/351\n0.806\n0.644\n0.689\n0.681\n0.678\n16,1\n0.171/212\n0.145/251\n0.150/242\n0.147/248\n0.147/247\n1.053\n0.929\n0.977\n0.952\n0.952\n16,2\n0.244/264\n0.160/402\n0.165/391\n0.162/397\n0.162/397\n0.704\n0.534\n0.578\n0.578\n0.570\n17,1\n0.207/259\n0.162/331\n0.170/314\n0.164/326\n0.165/324\n0.775\n0.595\n0.679\n0.631\n0.628","614\nTable 5. --Continued.\nAdjustment\nArea,\nB1/2\nLine\nB+\nB\ncit\nD'+\n17,2\n0.225/272\n0.143/429\n0.156/393\n0.144/424\n0.144/424\n0.751\n0.576\n0.630\n0.616\n0.608\n18,1\n0.335/283\n0.216/440\n0.236/401\n0.221/429\n0.223/425\n0.700\n0.430\n0.541\n0.464\n0.463\n18,2\n0.177/175\n0.144/215\n0.156/198\n0.144/215\n0.144/215\n1.142\n0.999\n1.048\n1.017\n1.015\n19,1\ndeleted\n0.183/252\n0.194/238\n0.185/249\n0.185/249\n0.881\n0.950\n0.895\n0.900\n20,1\n0.440/258\n0.358/316\n0.367/309\n0.386/293\n0.382/297\n0.810\n0.669\n0.700\n0.742\n0.729\n20,2\n0.379/218\n0.332/249\n0.338/245\n0.351/236\n0.345/240\n0.844\n0.672\n0.707\n0.724\n0.713\n20,3\n0.361/244\n0.305/288\n0.312/282\n0.322/274\n0.315/280\n0.839\n0.697\n0.732\n0.754\n0.734\n21,1\n0.481/338\n0.290/561\n0.311/522\n0.302/539\n0.302/538\n0.584\n0.392\n0.458\n0.459\n0.446\n21,2\n0.307/251\n0.258/299\n0.265/290\n0.266/290\n0.264/292\n0.771\n0.657\n0.696\n0.725\n0.698\n22,1\n0.315/247\n0.239/326\n0.256/304\n0.244/318\n0.245/317\n0.818\n0.616\n0.686\n0.653\n0.648\n22,2\n0.327/245\n0.255/314\n0.268/299\n0.263/306\n0.262/307\n0.833\n0.625\n0.692\n0.660\n0.655\n23,1\n0.276/175\n0.236/204\n0.246/196\n0.239/202\n0.240/202\n1.147\n0.974\n1.036\n0.990\n0.992\n23,2\n0.431/264\n0.337/275\n0.360/258\n0.346/268\n0.345/269\n0.904\n0.656\n0.744\n0.680\n0.681\n25,1\n0.309/236\n0.130/559\n0.131/557\n0.133/550\n0.132/554\n0.744\n0.641\n0.672\n0.762\n0.703\n25,2\n0.368/237\n0.153/571\n0.154/568\n0.156/562\n0.155/565\n0.736\n0.634\n0.665\n0.756\n0.697","615\nTable 6. - -Standard errors, ratios of ol and 'a.\n1/2\nB1/B\nD/B\nArea,\nB\n3/B+\n/D'+\nLine\n1.027\n1.006\n1,1\n1.24\n1.030\n1.24\n1.004\n1.27\n1.029\n1.60\n1.046\n1.189\n1.27\n1.019\n1.004\n1,2\n1.47\n1.001\n1.30\n1.048\n1.60\n1.055\n1.004\n1.011\n1.23\n1.011\n2,1\n1.22\n1.57\n1.032\n1.001\n1.29\n1.111\n1.000\n1.36\n1.016\n2,2\n1.51\n1.094\n1.003\n1.75\n1.065\n1.37\n1.103\n1.33\n1.007\n1.000\n3,1\n1.45\n1.079\n1.039\n1.000\n1.30\n1.087\n1.41\n1.025\n0.995\n3,2\n1.54\n1.109\n1.39\n1.000\n1.50\n1.148\n1.83\n1.073\n0.992\n1.38\n1.054\n1.38\n1.023\n4,1\n1.84\n1.057\n1.002\n1.33\n1.126\n1.33\n1.008\n1.000\n4,2\n1.40\n1.124\n1.81\n1.057\n1.000\n1.29\n1.104\n1.33\n1.017\n0.996\n5,1\n1.31\n1.091\n1.036\n0.998\n1.40\n1.132\n1.69\n1.010\n1.000\n5,2\n1.54\n1.163\n1.36\n1.034\n1.000\n1.42\n1.135\n1.65\n1.025\n0.988\n6,1\n1.38\n1.060\n1.41\n1.000\n1.43\n1.166\n1.91\n1.063\n1.000\n1.47\n1.181\n1.35\n1.008\n6,2\n1.001\n1.74\n1.039\n1.32\n1.132\n0.995\n1.116\n1.30\n1.009\n7,1\n1.45\n1.58\n1.024\n0.996\n1.47\n1.196\n1.30\n1.009\n0.995\n1.45\n1.092\n7,2\n1.020\n0.997\n1.172\n1.55\n1.39\n1.35\n1.011\n1.000\n8,1\n1.33\n1.064\n1.028\n0.997\n1.32\n1.128\n1.68\n0.988\n1.129\n1.38\n1.023\n8,2\n1.49\n1.039\n1.000\n1.78\n1.43\n1.184","616\nTable 6. --Continued.\nB1/2\nD/\nArea,\nB\nc/+\nB/B+\nD%\n/B+\nD'+\nLine\nB\n9,1\n1.77\n1.110\n1.45\n1.033\n0.979\n1.78\n1.350\n1.90\n1.062\n0.991\n9,2\n1.76\n1.114\n1.44\n1.034\n0.989\n1.76\n1.340\n1.88\n1.058\n0.991\n10,1\n1.62\n1.101\n1.28\n1.004\n1.000\n1.55\n1.232\n1.55\n1.017\n0.995\n11,1\n1.70\n1.100\n1.38\n1.020\n0.990\n1.72\n1.303\n1.90\n1.034\n0.992\n11,2\n1.70\n1.093\n1.38\n1.023\n0.989\n1.68\n1.287\n1.74\n1.034\n0.992\n14,1\n1.34\n1.050\n1.28\n1.037\n1.008\n1.30\n1.038\n1.69\n1.068\n1.004\n14,2\n1.26\n1.041\n1.25\n1.036\n1.010\n1.20\n1.031\n1.59\n1.061\n1.008\n15,1\n1.24\n1.035\n1.25\n1.039\n1.008\n1.26\n1.053\n1.81\n1.074\n1.015\n15,2\n1.23\n1.031\n1.25\n1.035\n1.004\n1.25\n1.054\n1.78\n1.065\n1.013\n15,3\n1.37\n1.046\n1.31\n1.020\n1.005\n1.25\n1.070\n1.75\n1.053\n1.004\n16,1\n1.18\n1.034\n1.16\n1.014\n1.000\n1.13\n1.052\n1.47\n1.025\n1.000\n16,2\n1.52\n1.031\n1.29\n1.012\n1.000\n1.32\n1.082\n1.91\n1.067\n1.014\n17,1\n1.28\n1.049\n1.24\n1.018\n0.994\n1.30\n1.141\n1.79\n1.056\n1.005\n17,2\n1.57\n1.091\n1.30\n1.007\n1.000\n1.30\n1.094\n1.82\n1.056\n1.013\n18,1\n1.55\n1.093\n1.44\n1.032\n0.991\n1.63\n1.258\n1.95\n1.077\n1.002\n18,2\n1.23\n1.083\n1.16\n1.000\n1.000\n1.14\n1.049\n1.43\n1.016\n1.002","617\nTable 6. - -Continued.\ngl/2\nArea,\nB\nB/B+\nD'\nP/B\nD/\ncit\nLine\nB+\n+\n19,1\n1.060\n--\n1.011\n--\n1.000\n1.078\n1.022\n0.994\n20,1\n1.23\n1.025\n1.23\n1.067\n1.010\n1.21\n1.046\n1.71\n1.090\n1.018\n20,2\n1.14\n1.018\n1.19\n1.039\n1.017\n1.26\n1.052\n1.65\n1.061\n1.015\n20,3\n1.18\n1.023\n1.19\n1.033\n1.022\n1.20\n1.050\n1.62\n1.053\n1.027\n21,1\n1.66\n1.072\n1.32\n1.041\n1.000\n1.49\n1.168\n2.18\n1.138\n1.029\n21,2\n1.19\n1.027\n1.20\n1.023\n1.008\n1.17\n1.059\n1.73\n1.062\n1.039\n22,1\n1.32\n1.071\n1.32\n1.025\nC.996\n1.33\n1.114\n1.73\n1.052\n1.008\n22,2\n1.28\n1.051\n1.29\n1.027\n1.004\n1.33\n1.107\n1.72\n1.048\n1.008\n23,1\n1.17\n1.042\n1.21\n1.017\n0.996\n1.18\n1.064\n1.45\n1.018\n0.998\n23,2\n1.28\n1.068\n1.29\n1.024\n1.003\n1.38\n1.134\n1.66\n1.038\n0.998\n25,1\n2.38*\n1.008*\n0.47*\n1.015\n1.008\n1.16*\n1.049*\n1.69*\n1.097\n1.084\n25,2\n2.40*\n1.006*\n0.46*\n1.013\n1.006\n1.16*\n1.049*\n1.70*\n1.099\n1.085\nol\n1.400\n1.0749\n1.303\n1.0215\n1.0000\nsl\n0.175\n0.0431\n0.076\n0.0128\n0.0080\noa\n1.365\n1.1264\n1.717\n1.0524\n1.0079\nsa\n0.164\n0.0839\n0.157\n0.0247\n0.0196\n*\nThese values were not used in subsequent computations be-\ncause for some unknown reason they differed too much from\nthe mean.","These data D'+ are solution plotted relative on figures to 8 the and B 9. series of adjustments\n618\nlocation\nThe\nof\nthe\nD'\nand\nis also shown.\nThese become figures smaller show that as the the number distance of observed distances\nazimuth\nstandard\nand\nerrors\nazimuth increases.\nand\nx\na\n2.0\nD'\nGEOCEIVERS\n2\n5\nB\nD'+\n1.0\n1/2\nB\nB+\n5 GEOCEIVERS\nNUMBER 5 OF DISTANCE 10 OBSERVATIONS\n15\n20\n25\nFigure 8. -variation of the distance standard error.","619\nD'\n2.0\nH\n2 GEOCEIVERS\nB\nD'+\n1.0\n2\nB\nB+\n5 GEOCEIVERS\n25\n5\n15\n20\n10\nNUMBER OF AZIMUTH OBSERVATIONS\nVariation of the azimuth standard error.\nFIG. 9\nThe following additional comments are important.\n.\n1. . from When there are no other constraints in the we\nGeoceiver see the ratio D'/B that the adjustment containing solution, five\ndistance positions shows an improvement of 30 percent\nstandard errors and 71 percent in azimuth standard in\npositions. errors over the adjustment constrained by two Geoceiver\n2. When the adjustments contain base line and azimuth\nobservations, as in the ratio D'+/B+ the five-Geoceiver\nadjustment standard shows only a 2 percent improvement in distance\nerrors errors and a 5 percent improvement in azimuth standard\nobservations. over the adjustment that contains only two Geoceiver","620\n3. In section 2 where no distances and azimuth observations\nwere involved in the adjustments (see ratio C'/D' - table 4)\n,\nthere was a 13-percent improvement in the distance standard\nerrors for the C' solution (in which two Geoceiver stations are\noriented north-south) When base line and azimuth observations\nare included in these adjustments (see the ratio C'+/D'+), there\nis no noticeable difference in the distance standard errors\nbetween the two solutions.\nAll of these items taken together indicate that as the\nnumber of base line and azimuth observations increases in a\nnetwork, there is a reduction in the usefulness of Geoceiver\nobservations as a means of reducing the distance and azimuth\nstandard errors.\nThese results agree with those of Ashkenazi and Cross (1975) when\na simulated network was used. He also observed this reduction\nin the rate of improvement in the standard errors as the number\nof constraints in a system was increased. Paraphrasing from\nthe conclusions of Ashkenazi, \"For every well connected network\nthere is a limit to the number of base lines and azimuths that\nserve any useful purpose in constraining the system. Base lines\nand azimuths added to the system beyond this sufficient number\nserve only to slowly reduce the standard errors.\"\nThe study area is approximately 350 km from east to west and\n550 km from north to south. The first-order, main scheme\nnetwork contains approximately 386 quadrilateral or more complex\nfigures. For this particular first-order, main scheme network,\nthe effectiveness of the five Geoceiver observations to reduce\nthe distance and azimuth standard errors seems to disappear\nwhen the network contains about 20 distance and 25 azimuth\nobservations. In other words, this arrangement of five\nGeoceiver stations would cause a reduction in the distance and\nazimuth standard errors of this triangulation network, only if\nthere is less than one base line observation per 20 quads and\none azimuth observation per 15 quads. A general guideline for\nusing Geoceiver observations may now be stated: \"If the first-\norder, main scheme network in a given area contains less than\none base line observation per 20 quads and one azimuth\nobservation per 15 quads, then Geoceiver observations may be\nused to improve the internal accuracy.\"\nIn adjustment B+, the distance standard errors range from\n0.085 to 0.358 meter with a mean of 0.197 meter, and the azimuth\nstandard errors range from 0.392 to 0.999 with a mean of 0.645.\nThe standard errors can be reduced only slightly beyond this\npoint by additional length, azimuth or position observations in\nthe adjustment.\nAs pointed out by Ashkenazi and Cross (1975) the controlling\nfactors are the large number of observed directions,","621\ntheir standard errors, and how \"well connected\" the network is.\nIn this adjustment the a posteriori mean standard error for the\n7,202 observed directions is 0.385. The length and azimuth\nstandard errors in this network are thus most dependent upon\nthe set of direction observations and their standard errors.\nAny other set of observations, Geoceiver, for instance, would\nhave to be large and well-connected to appreciably reduce the\nnetwork length and azimuth standard errors.\nEffect of Geoceiver Observations Upon\nthe Positional Accuracies\nIn an adjustment where the new network is appended to the\nexisting network, the new stations have a positional uncertainty\nthat is due in part to the uncertainty in the position of the\nstation or stations in the existing network used as constrained\npositions in the new adjustment and, in part, because of the\nobservational errors in the new network. Geoceiver observations\nare a means of obtaining geodetic positions independent of the\ntriangulation system. In this experiment the analysis method used\nwas to vary the amount of observational data and the number of\nGeoceiver stations in each of four adjustments and to note the\nchange in the 95 percent positional error ellipses at 44\nselected first-order stations (see figure 10)\nA series of four adjustments of the first-order network and\nthe first-order, second-order combined networks are performed\nin which the constraints are different for each adjustment. The\nname of each station at which a positional error ellipse is\ncomputed and the dimension, in meters of the semi-major and\nsemi-minor axes, are given in table 7.\nAdjustment E* is an adjustment of the 838 stations in the\nfirst-order, main scheme network. The network contains 42\ngeodimeter lines, or base lines, and 18 azimuth observations.\nStation Webster 1939 was heavily constrained. The a priori\nvariance allowed in latitude and longitude was 1\" 0 X 10-20\nAdjustment E* is the same as adjustment E* except\nthat\nthe\nGeoceiver determined position for station Webster 1939 was\nconstrained in latitude to a standard deviation of 0.9 meter and\nin longitude to a standard deviation of 1. 2 meters.\nAdjustment F* is an adjustment of the 838 stations in the\nfirst-order, main scheme network and 498 stations in the second-\norder, main scheme networks. The combined networks contained\n63 geodimeter lines, or base lines, and 22 azimuth observations.\nThe Geoceiver-determined position for station Webster 1939 was\nagain the constrained position.","622\nMISSISSIPPI GEOCEVER TEST AREA\n18\n1\n9\n25\n12\n42\n6\n20\n30\n8\n26\n29\n3\n7\n19\n39\n41\n36\n4\n21\n5\n16\n33\n35\n14\n31\n24\n15\n23\n44\n10\n11\n28\n34\n32\n27\n22\n13\n17\n40\n2\n43\n37\n38\nFIG. 10 -- -Geoceiver test area position accuracies.","623\nTable 7. Error ellipse, with semi-major and\nsemi-minor axes in meters.\nAdjustment\nStation\nÉ*\nNo.\nE*\nF*\nG*\nKNOB 1914\n1\n1.170\n3.080\n2.886\n1.429\n0.958\n2,727\n2.555\n1.248\nLITTLE 1934\n2\n1.255\n3.111\n2.950\n1.457\n0.943\n2.727\n2.583\n1.267\nWINN 1929\n3\n0.997\n2.956\n2.835\n1.331\n0.757\n2.734\n2.587\n1.302\nKELLEY 1971\n4\n1.733\n3.081\n2.845\n1.499\n0.779\n2.960\n2.791\n1.297\nEUTAW 1939\n5\n0.942\n2.977\n2.828\n1.304\n0.696\n2.675\n2.544\n1.174\nBOBO 1956\n6\n0.826\n2.942\n2.813\n1.328\n0.646\n2.663\n2.530\n1.219\nBRADSHAW 1939\n7\n0.597\n2.912\n2.797\n1.270\n0.545\n2.611\n2.515\n1.144\nBUSH 1934\n8\n0.491\n2.889\n2.800\n1.286\n0.415\n2.591\n2.502\n1.168\nCAPLEVILLE SE BASE 1914\n9\n1.167\n3.059\n2.892\n1.483\n0.957\n2.748\n2.544\n1.261\nCENTRAL 1945\n10\n0.975\n3.007\n2.878\n1.361\n0.707\n2.657\n2.542\n1.202\nCLAYBORN 1935\n11\n0.964\n3.015\n2.886\n1.366\n0.711\n2.644\n2.527\n1.183\nEVANSVILLE 1929\n12\n1.077\n3.011\n2.854\n1.431\n0.797\n2.715\n2.563\n1.275\nFOSTER 1929\n13\n1.478\n3.172\n2.987\n1.569\n1.135\n2,839\n2.664\n1.388\nGRIMES 1934\n14\n0.616\n2.921\n2.823\n1.288\n0.472\n2,593\n2.504\n1.151\nHAWKINS 1931\n15\n1.051\n3.007\n2.865\n1.364\n0.785\n2.707\n2.569\n1.250\nHOMESTEAD 1929\n16\n1.071\n2.988\n2.857\n1.363\n0.788\n2.737\n2.586\n1.287","624\nTable 7 -Continued.\nAdjustment\nStation\nNo.\nE*\nE*\nF*\nG*\nLITTLE 1939\n17\n1,285\n3.132\n2.963\n1.475\n0.939\n2.714\n2.567\n1.254\nMALONE 1914\n18\n1.061\n3.046\n2.892\n1.460\n0.941\n2.715\n2.527\n1.229\nPALMERTREE 1934\n19\n0.372\n2.880\n2.796\n1.266\n0.322\n2.569\n2.492\n1.149\nRANDOLPH 1967\n20\n0.557\n2.907\n2.810\n1.305\n0.536\n2.606\n2.497\n1.153\nRICHLAND 1958\n21\n0.590\n2.908\n2.810\n1.275\n0.451\n2.598\n2.509\n1.166\nTOLER 1946\n22\n1.196\n3.082\n2.931\n1.440\n0.876\n2,711\n2.579\n1.258\nTYLER 1929\n23\n1.199\n3.046\n2.893\n1.418\n0.870\n2.751\n2.601\n1.296\nWOLF 1930\n24\n0.839\n2,976\n2.855\n1.328\n0.577\n2.614\n2.510\n1.151\nMEEKS 1939\n25\n0.646\n2.911\n2.802\n1.279\n0.559\n2,627\n2.524\n1.206\nBARR 1935\n26\n0.354\n2.877\n2.793\n1.273\n0.331\n2.570\n2.491\n1.138\nBETHEL 1946\n27\n1.132\n3.058\n2.914\n1.414\n0.828\n2.695\n2.568\n1.241\nDANIELS 1938\n28\n1.216\n3.100\n2.934\n1.441\n0.860\n2.693\n2.550\n1,226\nWEEKS 1934\n29\n0.866\n2.974\n2,849\n1.390\n0.782\n2.676\n2.513\n1.198\nGALLOWAY 1939\n30\n1.018\n3.003\n2.827\n1.331\n0.746\n2.687\n2.557\n1.210\nSHILOH 1945\n31\n0.828\n2.966\n2.849\n1,321\n0.599\n2.627\n2.522\n1.174\nTISDALE 1939\n32\n1.131\n3.069\n2,923\n1.417\n0.841\n2.687\n2.556\n1.228","625\nTable 7 Continued.\nAdjustment\nStation\nNo.\nE*\nE*\nF*\nG*\nSMITH 1935\n33\n0.615\n2.918\n2.821\n1.285\n0.474\n2.596\n2.501\n1.139\nJEFF 1947\n34\n1.211\n3.065\n2.914\n1.439\n0.873\n2.735\n2.595\n1.281\nBENTONIA 1959\n35\n0.793\n2.941\n2.829\n1.301\n0.576\n2.639\n2.531\n1.196\nSTRAIGHT 1957\n36\n0.812\n2.929\n2.820\n1.295\n0.589\n2,660\n2.542\n1.223\nWEDFORD 1942\n37\n1.570\n3.259\n3.040\n1.586\n1.235\n2,830\n2.626\n1.355\nLUMBERTON 1943\n37A\n2.988\n1.510\n2.609\n1.314\nLEE 1935\n38\n1.463\n3.203\n3.008\n1.539\n1.149\n2,801\n2.625\n1.342\nBEVEL 1935\n39\n0.383\n2.881\n2.797\n1.266\n0.306\n2,567\n2.491\n1.133\nSMITH 1934\n40\n1.253\n3.107\n2.950\n1.461\n0.934\n2 726\n2.586\n1.272\nLOBUTCHA 1958\n41\n0.450\n2.892\n2.806\n1.275\n0.347\n2.571\n2.492\n1.134\nLEBANON 1935\n42\n0.824\n2.970\n2.841\n1.360\n0.725\n2.650\n2.511\n1.180\nBROCK 1939\n43\n1.346\n3.143\n2.977\n1.507\n1,016\n2.759\n2.610\n1.309\nCRYSTAL 1945\n44\n1.006\n3.007\n2.871\n1.360\n0.737\n2.676\n2.552\n1,291\nMajor axis mean\n0.964\n3.009\n2.873\n1.381\nMajor axis S. d. *\n0.333\n0.094\n0.065\n0.090\nMinor axis mean\n0.730\n2.684\n2.554\n1.226\nMinor axis s.d. *\n0.228\n0.081\n0.055\n0.065\n*s.d. - standard deviation.","626\nAdjustment G* contains, in addition to the data contained in\nadjustment F*, four more Geoceiver stations, Winn 1929,\nLittle 1934, Knob 1914, and Kelley 1971, entered as constrained\npositions.\nThe first adjustment, E*, where station Webster 1939 is\nheavily constrained, was used to determine the error propagation\ncharacteristics of the network. The positional error ellipses\ncomputed in this adjustment are relative to the Geoceiver\nposition of station Webster 1939. The computed 95 percent\npositional error ellipses are shown in figure 11. The positional\nerror varies with distance from 0.3 meter at Barr 1935, near\nthe fixed station, to 1.5 meters at Wedford 1942, near the edge\nof the area.\nThe first test performed was adjustment E*. This adjustment\nproduced error ellipses quite consistent in size and orientation.\nThe mean error ellipse had a semi-major axis of 3.009 meters\nwith a standard deviation of 0.094 meter, and a semi-minor axis\nof 2.684 meters with a standard deviation of 0.081 meter. The\nerror ellipses for this adjustment are shown in figure 12. The\norientation of the major axis of the error ellipses was 90°\n(east-west) with very little variation. There is a small\nsystematic variation in the size of the error ellipses with\ndistance from the constrained station. The variation between\nstation Barr 1935, located near the constrained station, and\nstation Wedford 1942, near the edge of the network, was 0.3\nmeter.\nIn the next test, adjustment F*, only a 1-percent reduction\noccurred in the size of the error ellipses when the second-\norder network was included. These error ellipses are shown in\nfigure 13. The error ellipses were again consistent in size\nand orientation. The mean of the semi-major axis was 2.873\nmeters, with a standard deviation of 0.065 meter, and the mean\nof the semi-minor axis was 2.55 meters, with a standard\ndeviation of 0.066 meter. The orientation of the major axis\nof the error ellipses had only a slightly larger variation from\n90° than the first-order network alone. From this test, based\non this particular set of data, it appears that the inclusion\nof the second-order projects does not significantly improve the\npositional accuracies at the 44 selected stations over that\nwhich was obtained from the adjustment of only the first-order\nprojects.\nThe third test, adjustment G*, was an adjustment of the first-\nand second-order networks with the five Geoceiver stations,\nWebster 1939, Knob 1914, Little 1934, Winn 1929, and Kelley 1971,\nas constrained positions. The addition of the five Geoceiver","627\nMISSISSIPPI GEOCEVER TEST AREA\nNORTH\n588\no 5 10 15\nSCALE (M)\nFIG. 11 -- -Geoceiver test area E* adjustment error ellipses.","628\nNORTH\nSCALE\n(M)\nFIG.\n12","629\n\".\"\nMISSISSIPPI 'EST area\n<<00\nNORTH\n500ml\no 5 10 15\nSCALE (M)\nFIG. 13 --Geoceiver test area F* adjustment error ellipses.","630\nstations produced an appreciable reduction in the size of the\nerror ellipses. The relative size and orientation of the\nerror ellipses throughout the whole network were again much the\nsame (figure 14). The mean of the semi-major axis dimension was\n1.381 meters with a standard deviation of 0.090 meter. The mean\nof the semi-minor axis dimension was 1.226 meters with a\nstandard deviation of 0.065 meter. This improvement in the\naccuracy of the positions over those obtained in the adjustment\nwhere one Geoceiver position was used seems to be in direct\nproportion to the increase in the square root of the number (n)\nof Geoceiver stations. The actual improvement was 2.08, which\nis close to the square root of 5 (2.24). The variation between\nstations Barr 1935 and Wedford 1942 was again 0.3 meter.\nEffect of Geoceiver Observations Upon\nthe Final Position\nThis experiment was performed to determine if the Geoceiver\nobservations have a significant effect upon the final positions.\nThe four adjustments, E*, E*, F*, and G*, in which the amount of\nobservational data or the number of Geoceiver stations is\ndifferent were considered. The differences in these four data\nsets are given in table 1. The analysis was based upon the\nfinal positions at the 44 first-order stations shown in\nfigure 10. The adjusted positions at these stations are given\nin table 8.\nThe first comparison was of the final positions produced by\nthe adjustment of the first-order network when the position of\na centrally located station, Webster 1939, was rigidly\nconstrained to 3.1 X 10-9 meters in latitude and 2.4 X 10- in\nlongitude (adjustment E*), and when the same station was\nconstrained to 0.9 meter in latitude, 1.2 meters in longitude\n(adjustment E*). Table 8 shows that these changes are not\nappreciable; however, no change was expected. It is felt that\nthe mean changes of -0.93 mm in latitude and -2.25 mm in\nlongitude should not have occurred. This problem is being\ninvestigated.\nThe second comparison (F*-E*, table 9) isolated the\ncontribution of the second-order observations. The final\npositions from the adjustment of the first-order network\n(adjustment E*) was compared to the final positions from the\nadjustment of the first- and second-order networks (adjustment\nF*) In both of these adjustments, station Webster 1939 was\nconstrained to 0.9 meter in latitude and 1.2 meters in\nlongitude.","631\n*ISSISS:PP:\nNORTH\nO 5 10 15\nSCALE\n(M)\n14 --Geoceiver test area G* adjustment error ellipses.\nFIG.","632\nTable 8. -- -Adjusted positions, final seconds of and l.\nPreliminary\nAdjustment\nE*\nNo.\nPosition\nE*\nF*\nG*\nName\n1\n15.54700\n15.44372\n15.44375\n15.45625\n15.46069\nKNOB 1914\n29.70900\n29.79028\n29.79037\n29.80112\n29.79247\n15.4591*\n29.7816*\n42.68631\n42.69108\nLITTLE 1934\n2\n42.81400\n42.68634\n42.68513\n32.79600\n32.87719\n32.87728\n32.87981\n32.87487\n42.6907*\n32.8949*\n51.55882\n51.54979\n51.55642\nWINN 1929\n3\n51.66800\n51.55880\n30.47800\n30.54665\n30.54675\n30.55215\n30.54470\n51.5586*\n30.5265*\n01.93772\n01.93775\n01.92660\n01.93044\nKELLEY 1971\n4\n02.09247\n00.21970\n00.28646\n00.28655\n00.27834\n00.27154\n01.9356*\n00.2739*\nEUTAW 1939\n5\n46.71900\n46.58564\n46.58567\n46.57762\n46.58214\n54.22200\n54.26251\n54.26260\n54.25592\n54.24935\nBOBO 1956\n6\n51.34000\n51.28017\n51.28020\n51.28053\n51.28646\n55.75400\n55.82297\n55.82306\n55.83467\n55.82671\n42.38600\n42.26163\n42.26166\n42.26052\n42.26518\nBRADSHAW 1939\n7\n01.94400\n02.01473\n02.01482\n02.01014\n02.00303\nBUSH 1934\n8\n03.14800\n03.05619\n03.05622\n03.05815\n03.06370\n38.52000\n38.62372\n38.62381\n38.62908\n38.62142\nCAPLEVILLE SE BASE 1914\n9\n12.54900\n12.48872\n12.48875\n12.48454\n12.49018\n30.09700\n30.17597\n30.17606\n30.19373\n30.18499\n22.44020\n22.43765\n22.44369\nCENTRAL 1945\n10\n22.56500\n22.44018\n17.72200\n17.79536\n17.79545\n17.79492\n17.78927\n12.69083\n12.68758\n12.69296\nCLAYBORN 1935\n11\n12.82800\n12.69081\n28.83700\n28.91245\n28.91254\n28.91293\n28.90730\n34.85605\n34.86205\nEVANSVILLE 1929\n12\n34.91300\n34.86452\n34.86454\n24.84000\n24.90492\n24.90502\n24.92563\n24.91728\n47.72401\n47.73106\n13\n47.86600\n47.72906\n47.72909\nFOSTER 1929\n00.23800\n00.27816\n00.27825\n00.27671\n00.27164\n27.04935\n27.04938\n27.04808\n27.05369\nGRIMES 1934\n14\n27.17500\n29.71500\n29.79204\n29.79213\n29.78918\n29.78275\n57.45082\n57.45085\n57.44641\n57.45305\nHAWKINS 1931\n15\n57.57700\n21.49800\n21.57031\n21.57040\n21.56906\n21.56293\n*Geoceiver-determined positions.","633\nTable 8 --Continued.\nPreliminary\nAdjustment\nName\nNo.\nPosition\nÉ*\nE*\nF*\nG*\nHOMESTEAD 1929\n16\n53.15100\n53.01600\n53.01603\n53.00769\n53.01452\n21.09800\n21.16775\n21.16784\n21.16765\n21.16104\nLITTLE 1939\n17\n31.29400\n31.14408\n31.14411\n31.13380\n31.13893\n25.62400\n25.67611\n25.67620\n25.66666\n25.66153\nMALONE 1914\n18\n47.58504\n47.51091\n47.51094\n47.51153\n47.51666\n50.01443\n50.09420\n50.09430\n50.10818\n50.09937\nPALMERTREE 1934\n19\n39.64000\n39.54174\n39.54177\n39.53900\n39.54460\n45.73000\n45.82250\n45.82260\n45.82436\n45.81726\nRANDOLPH 1967\n20\n01.52080\n01.42908\n01.42911\n01.43629\n01.44152\n28.95731\n29.05229\n29.05238\n29.05964\n29.05170\nRICHLAND 1958\n21\n12.96410\n12.84950\n12.84953\n12.84629\n12.85224\n59.45200\n59.53510\n59.53520\n59.53764\n59.53085\nTOLER 1946\n22\n45.18900\n45.06304\n45.06307\n45.06191\n45.06815\n49.33300\n49.41429\n49.41438\n49.41551\n49.41038\nTYLER 1929\n23\n54.87700\n54.75489\n54.75492\n54.75234\n54.75920\n58.88000\n58.93921\n58.93930\n58.93722\n58.93136\nWOLF 1930\n24\n19.69200\n19.55924\n19.55927\n19.55169\n19.55678\n28.59700\n28.66637\n28.66646\n28.66767\n28.66164\nMEEKS 1939\n25\n19.96500\n19.86313\n19.86316\n19.85721\n19.86327\n06.21600\n06.26692\n06.26701\n06.26925\n06.26182\nBARR 1935\n26\n09.96200\n09.86381\n09.86384\n09.86467\n09.86975\n40.49200\n40.57422\n40.57432\n40.57402\n40.56656\nBETHEL 1946\n27\n47.03900\n46.91529\n46.91531\n46.91365\n46.91985\n58.32100\n58.39825\n58.39834\n58.39874\n58.39346\nDANIELS 1938\n28\n42.69100\n42.54932\n42.54934\n42.53822\n42.54295\n38.00000\n38.01832\n38.01841\n38.00569\n38.00010\nWEEKS 1934\n29\n23.56200\n23.48918\n23.48921\n23.49039\n23.49580\n09.47700\n09.57357\n09.57366\n09.58548\n09.57701\nGALLOWAY 1939\n30\n27.35000\n27.21822\n27.21825\n27.21768\n27.22191\n01.30500\n01.37769\n01.37779\n01.37320\n01.36568","634\nTable 8 --Continued,\nPreliminary\nAdjustment\nName\nNo.\nPosition\nE*\nE*\nF*\nG*\nSHILOH 1945\n31\n26.96900\n26.83712\n26.83714\n26.83529\n26.84120\n14.59200\n14.66855\n14.66864\n14.66655\n14.66055\nTISDALE 1939\n32\n32.50900\n32.37682\n32.37685\n32.37267\n32.37833\n15.87300\n15.94502\n15.94511\n15.94554\n15.94032\nSMITH 1935\n33\n49.22000\n49.09322\n49.09325\n49.08729\n49.09246\n32.45700\n32,53772\n32.53781\n32.53460\n32.52814\nJEFF 1947\n34\n47.38200\n47.25478\n47.25481\n47.25547\n47.26218\n49.35600\n49.41039\n49.41048\n49.41234\n49.40686\nBENTONIA 1959\n35\n45.86930\n45.73965\n45.73967\n45.74186\n45.74811\n43.97770\n44.05457\n44.05467\n44.05446\n44.04798\nSTRAIGHT 1957\n36\n10.27530\n10.15277\n10.15280\n10.14661\n10.15302\n11.36170\n11.42431\n11.42440\n11.42446\n11.41753\nWEDFORD 1942\n37\n04.99800\n04.87460\n04.87463\n04.86477\n04.86986\n25.53900\n25.55116\n25.55125\n25.54041\n25.53573\nLUMBERTON 1943\n37A\n52.01800\n51.88174\n51.88752\n--\n--\n17.35100\n17.41792\n17.41323\nLEE 1935\n38\n43.71500\n43.58025\n43.58027\n43.57546\n43.58115\n37.65500\n37.71459\n37.71468\n37.71555\n37.71096\nBEVEL 1935\n39\n02.15000\n02.03768\n02.03771\n02.03503\n02.04018\n39.97900\n40.07201\n40.07210\n40.06896\n40.06199\nSMITH 1934\n40\n04.09000\n03.96199\n03.96202\n03.96063\n03.96671\n37.13600\n37.22074\n37.22083\n37.22259\n37.21764\nLOBUTCHA 1958\n41\n37.64280\n37.52578\n37.52581\n37.52137\n37.52672\n14.32790\n14.41633\n14.41643\n14.41586\n14.40900\nLEBANON 1935\n42\n17.25650\n17.16617\n17.16620\n17.17247\n17.17734\n43.51347\n43.60217\n43.60226\n43.60891\n43.60055\nBROCK 1939\n43\n21.84500\n21.70385\n21.70387\n21.70215\n21.70841\n49.13100\n49.21721\n49.21730\n49.21936\n49.21458\nCRYSTAL 1945\n44\n35.76000\n35.62935\n35.62938\n35.62624\n35.63258\n41.18000\n41.25508\n41.25517\n41.25105\n41.24524","635\nTable 9. --Position differences in meters of and A.\nF* - E*\nG* - E*\nF* - G*\nNo.\nE* - G*\n1\n0.38750\n0.52514\n-0.13764\n-0.52607\n0.26875\n0.05250\n0.21625\n-0.05475\n2\n-0.03751\n0.14694\n-0.18445\n-0.14787\n0.06325\n-0.06025\n0.12350\n0.05800\n3\n-0.27993\n-0.07440\n-0.20553\n0.07378\n0.13500\n-0.05125\n0.18625\n0.04875\n4\n-0.34565\n-0.22661\n-0.11904\n0.22568\n-0.20525\n-0.37525\n0.17000\n0.37300\n5\n-0.24955\n-0.10943\n-0.14012\n0.10850\n-0.16700\n-0.33125\n0.16425\n0.32900\n6\n0.01023\n0.19406\n-0.18383\n-0.19499\n0.29025\n0.09125\n0.19900\n-0.09350\n7\n-0.03534\n0.10912\n-0.14446\n-0.11005\n-0.17700\n-0.29475\n0.17775\n0.29250\n8\n0.05983\n0.23188\n-0.17205\n-0.23281\n0.13175\n-0.05975\n0.19150\n0.05750\n0.04433\n-0.17484\n-0.04526\n9\n-0.13051\n0.44175\n0.22325\n0.21850\n-0.22550\n0.07905\n10\n0.10819\n-0.18724\n-0.10881\n-0.01325\n-0.15450\n0.14125\n0.15225\n-0.16678\n-0.06665\n11\n-0.10075\n0.06603\n0.00975\n-0.13100\n0.14075\n0.12875\n12\n-0.26319\n-0.07719\n-0.18600\n0.07657\n0.20875\n-0.30900\n0.51525\n0.30650\n0.06107\n-0.21855\n-0.06200\n13\n-0.15748\n0.12675\n0.16300\n-0.03850\n-0.16525\n-0.17391\n-0.13454\n14\n-0.04030\n0.13361\n0.23225\n-0.07375\n-0.23450\n0.16075\n-0.20584\n-0.06913\n15\n-0.13764\n0.06820\n0.18450\n-0.03450\n-0.18675\n0.15225\n0.04588\n16\n-0.25854\n-0.04681\n-0.21173\n-0.00475\n-0.17000\n0.16525\n0.16775","636\nTable 9. - -Continued.\nÉ* - G*\nF* - E*\nG* - E*\nF* - G*\nNo.\n-0.15903\n0.15965\n-0.31961\n-0.16058\n17\n0.12825\n0.36450\n-0.36675\n-0.23850\n-0.17825\n0.17732\n-0.15903\n0.01829\n18\n-0.12925\n0.12675\n0.22025\n0.34700\n-0.17360\n-0.08866\n-0.08587\n0.08773\n19\n0.17750\n0.13100\n0.04400\n-0.13350\n-0.16213\n-0.38564\n0.22258\n0.38471\n20\n0.19850\n0.01475\n0.18150\n-0.01700\n-0.18445\n-0.08494\n-0.10044\n0.08401\n21\n0.10625\n-0.10875\n0.16975\n0.06100\n-0.15841\n-0.03596\n0.15748\n-0.19344\n22\n0.09775\n-0.10000\n0.12825\n0.02825\n-0.13361\n-0.07998\n0.13268\n-0.21266\n23\n-0.19850\n0.14650\n0.19625\n-0.05200\n-0.23498\n-0.07719\n-0.15779\n0.07626\n24\n0.15075\n0.11825\n0.03025\n-0.12050\n-0.18445\n0.00341\n-0.18786\n-0.00434\n25\n-0.12975\n0.18575\n0.12750\n0.05600\n0.18321\n-0.15748\n-0.18414\n0.02573\n26\n0.19150\n-0.19400\n0.18650\n-0.00750\n-0.14136\n-0.19220\n0.14074\n-0.05146\n27\n0.11975\n0.13200\n-0.12200\n0.01000\n-0.14663\n0.19747\n-0.34472\n-0.19809\n28\n0.13975\n0.45550\n-0.45775\n-0.31800\n-0.16771\n-0.20522\n0.03658\n0.20429\n29\n0.21175\n-0.08600\n0.08375\n0.29550\n-0.13113\n-0.11439\n0.11346\n-0.01767\n30\n0.30025\n-0.30275\n0.18800\n-0.11475\n-0.12648\n0.12586\n-0.18321\n-0.05735\n31\n0.20000\n-0.20225\n0.15000\n-0.05225\n-0.04681\n0.04588\n-0.17546\n-0.12958\n32\n0.11750\n-0.11975\n0.13050\n0.01075","637\nTable 9. --Continued.\nNo.\nF* - E*\nG* - E*\nF* - G*\nE* - G*\n33\n-0.18476\n-0.02449\n-0.16025\n0.02356\n-0.08025\n-0.24175\n0.16150\n0.23950\n34\n0.02046\n0.22847\n-0.20801\n-0.22940\n0.04650\n-0.09050\n0.13700\n0.08825\n35\n0.06789\n0.26164\n-0.19375\n-0.26226\n-0.00525\n-0.16725\n0.16200\n0.16475\n36\n-0.19189\n0.00682\n-0.19871\n-0.00775\n0.00150\n-0.17175\n0.17325\n0.16950\n37\n-0.30566\n-0.14787\n-0.15779\n0.14694\n-0.27100\n-0.38800\n0.11700\n0.38575\n37A\n-0.17918\n0.11725\n38\n-0.14911\n0.02728\n-0.17639\n-0.02790\n0.02175\n-0.09300\n0.11475\n0.09075\n39\n-0.08308\n0.07657\n-0.15965\n-0.07750\n-0.07850\n-0.25275\n0.17425\n0.25050\n40\n-0.04309\n0.14539\n-0.18848\n-0.14632\n0.04400\n-0.07975\n0.12375\n0.07750\n41\n-0.13764\n0.02821\n-0.16585\n-0.02914\n-0.01425\n-0.18575\n0.17150\n0.18325\n42\n0.19437\n0.34534\n-0.15097\n-0.34627\n0.16625\n-0.04275\n0.20900\n0.04040\n43\n-0.05332\n0.14074\n-0.19406\n-0.14136\n0.05150\n-0.06800\n0.11950\n0.06575\n44\n-0.09734\n0.09920\n-0.19654\n-0.10013\n-0.10300\n-0.24825\n0.14525\n0.24600\nDO\n-0.09000\n0.08514\n-0.17523\n-0.08600\n0.14902\n0.14919\n0.02296\n0.14921\nS\nAl\n0.02869\n-0.13485\n0.16251\n0.13254\n0.17202\n0.15420\n0.03115\n0.15422\nS","638\nThere was a resulting mean change of 0.090 meter, with a\nstandard deviation of 0.149 meter in latitude and 0.172 meter\nin longitude. The addition of the second-order observations\nresulted in a mean shift of 0.9 meter in the positions for the\n44 selected first-order analysis stations. This suggests that\nthere were one or more second-order projects that have an\nappreciable influence upon the final positions to those first-\norder stations that are in the vicinity of the second-order\nprojects.\nThe shifts in final positions produced by adding more\nGeoceiver observations to the basic set of triangulation data\nwere investigated next.\nThe third comparison (G*-E*, table 9) was of the final\npositions from the adjustment of the first-order network with\nstation Webster 1939 constrained (adjustment E*) with the final\npositions from the adjustment of the first- and second-order\nnetworks with five constrained stations (Webster 1939, Knob\n1914,\nLittle 1934, Winn 1929, and Kelley 1971) using adjustment G*.\nThis comparison resulted in mean changes of 0.085 meter, with a\nstandard deviation of 0.149 meter in latitude, and 0.135 meter,\nwith a standard deviation of 0.154 meter in longitude.\nThe fourth comparison (F*-G*, table 9) isolated the influence\nof the addition of Geoceiver observations upon the final\npositions of the 44 selected first-order analysis stations. The\nfinal positions from the adjustment of the first- and second-\norder networks, with station Webster 1939 as the constrained\nstation (adjustment F*) , was compared with the final positions\nfrom the adjustment of the first- and second-order networks with\nthe five constrained stations listed in the third test,\nadjustment G*. The mean change in the comparison of the final\npositions was -0.175 meter with a standard deviation of 0.023\nmeter in latitude and 0.162 meter with a standard deviation of\n0.031 meter in longitude. The small standard deviation of 0.02\nand 0.03 meter indicates that a rather uniform shift of -0.175\nmeter in latitude and 0.162 meter in longitude has occurred\nthroughout the test area.\nThe mean final positions in the four adjustments, *, E*,\nF*,\nand G*, are plotted relative to the initial preliminary\nposition in figure 15.\nThe previous method of analysis, i.e., the comparison of the\nfinal positions from adjustments involving Geoceiver stations,\nis very much dependent upon the agreement of the Geoceiver-\ndetermined positions and the positions at the same stations\nobtained through the triangulation network. A similar analysis\nin another area would not necessarily give the previous results.","639\nI\nG **\nE\nF*\n0.1METER\nFIG. 15 Movement vectors. .\nExplanation of figure:\n(meters)\n-0.09000\nF* - E*\nso\n0.02869\nA1\n0.08514\nG* - E*\nso\n-0.13485\nAr\n-0.17523\nF* - G*\nso\n0.16251\nA\nÉ* - G*\n-0.08600\nso\n0.13254\nAX\nAdjustment É* - First-order network, one fixed station.\nAdjustment E* - First-order network, one constrained station.\nAdjustment F* - First- and second-order network, one con-\nstrained station.\nAdjustment G* - First- - and second-order network, five con-\nstrained stations.\nI is the preliminary position in all of the adjustments.","640\nIt is now possible to state additional conclusions. The *,\nE*, and F* solution seems to form a set in which a similar mean\nshift of the network has occurred. The *, E*, and F* adjust-\nments all have the same positional constraint, the Geoceiver\nposition of station Webster 1939. The Geoceiver-determined\nposition for station Webster 1939 is significantly different\nfrom the initial position of station Webster 1939 obtained by\ntriangulation; this results in the 0.1 meter shift seen in\nfigure 15. This error is well within the 1 meter a priori\nstandard error for a Geoceiver position. The addition of four\nmore Geoceiver positional constraints serves to reduce the mean\nshift of the network, as shown by solution G* in the same\nfigure. Here again, we have the reduction in the Geoceiver\nposition standard errors by the factor n, where n = 5, the\nnumber of Geoceiver stations. Geoceiver observations would\nappear to be the means of controlling the distorting influence\nof a project of inferior quality such as the one detected in the\nsecond comparison. As n increases, the Geoceiver station\npositions become more and more constrained and consequently\nbecome more and more effective at preventing network distortions.\nConclusions\nIn interpreting the results of this report, the reader must\nremember that while the theory is applicable to any network, the\ninferences from the data are strictly speaking applicable only\nto the particular network with which the authors worked. This\nis probably not a severe limitation because the full network was\nfirst skeletonized to what might be considered a representative\nfirst-order network. This network was further abstracted by the\nremoval of most of the measured distances, the removal of still\nmore measured distances, and finally the removal of all\nmeasured distances. A solution was obtained for each of these\ngeneralized networks. For most of these networks, solutions\nwere also obtained in which there were different numbers of\nGeoceiver positions. It should, therefore, be possible to make\na comparison, without too much error, between one or more of\nour generalized networks and other networks generalized in the\nsame way. Then, the results can be extrapolated to the fuller\nnetwork, except in situations where the network is pathological.\nPerhaps the most important conclusion (see section 2) is that\nas soon as a network contains a small number of distance and\nazimuth observations (20 and 25 respectively in our example)\nthe network becomes \"rigid.\" The effect of adding Geoceiver\nobservations is almost entirely to decrease slowly the standard\nerror of the network scale and orientation. The shape and size\nof the network remain practically unchanged, until a large\nnumber of Geoceiver observations are added. The standard\ndeviation in location or orientation is inversely proportional\nto the square root of the number of stations at which Geoceiver\npositions were observed.","641\nSecondly, in a network not containing measured distances, the\nscale, location, and orientation of the network are determined\nby the Geoceiver observations. Behavior of the standard\ndeviations of location and orientation is the same as for a\nnetwork containing measured distances, but behavior of the\nstandard deviations of shape and scale is less clear.\nAccording to theory (appendices 1 and 2 ) , the error in scale\nis inversely proportional to the distance between Geoceiver\npositions (when only two Geoceiver observations are involved) ;\nwhile the error in shape is determined almost entirely by the\nmeasured directions.\nThe data for networks containing only two Geoceiver observa-\ntions and no measured distances agree only approximately with\nwhat would be expected from theory. While theory (appendix 2)\npredicts that the standard deviation in a coordinate should be\ninversely proportional to the distance between Geoceiver\npositions, the agreement of this conclusion between the data\npresented in Dracup's paper (1975) and this paper (section 2\nand table 4) is shown to be only approximate. The average\nvalue of the standard deviation (in length of a side) changes\nby about 50 percent when the distance between Geoceivers is\nincreased from 181 km to 426 km, while the change from 181 km\nto 256 km, is still about 50 percent.\nThere are two ways of accounting for this anomaly. One is\nto accept the variation of average standard deviation with\ndistance as an empirical fact. An alternative (appendix 2 )\nto note that while the theory assumes that the standard\ndeviations are computed with one Geoceiver at the origin of\ncoordinates, this assumption does not hold true for the cases\nused. It appears that the adjustment is about a different\ncenter in each case. Then a comparison of standard deviations\nat the same points in the different networks would not give\ninformation on the variation of standard deviations with\ndistance.\nWhile base line and azimuth observations are preferred, the\nadjustments which were run using this test network indicate\nthat Geoceiver observations may be used in lieu of the more\ntraditional base lines and azimuths to provide scale and\norientation in the local network.","642\nAPPENDIX 1. MATHEMATICAL ANALYSIS OF A GEODETIC NETWORK\nCONTAINING MEASURED DIRECTIONS, DISTANCES, AND COORDINATES\nSince three different kinds of quantities--directions dis-\ntances, and coordinates were to be combined into one set of\nequations, it seemed best to use a set of unknowns more closely\nrelated to the observables than the conventional coordinates of\nstations. The set adopted was the dimensionless ratio, Xi,Yi, of\neach coordinate, X, to coordinate X2 coordinates X1 , 1 were\nleft out. Three new unknowns were introduced to make up for the\nthree dropped. These were f, the scale of the unknowns with\nrespect to length, and Ax,Ay, the coordinates of point P1 with\nrespect to a selected origin.\nThen we have as the set of observation equations\nY\nA\nX\nBINGLE\ndY\n[1]\nAXI\nA\ndx\nX2\ndY\nAl\nAl2\n=\nO\ndf\nl\ndY\no\ndg\n0\nwhere [1] denotes a vector of 1's, g is the vector Ax,Ay, and the\nsubscripts 0, 1, and X refer to directions, distances, and co-\nordinates respectively.\nThe covariance E2 of the unknowns is then related to the co-\nvariance 22 with components 2? 22, and & of the observations\nXX' Ye' and Ye by\n=\nwhere {iz denotes the inverse of .\nBreaking the matrix A into its components and multiplying out,","643\n[\nATELZA,\n+\n+\n=\n[1]TEX2AX1\nNET2\nB11\nB 12\nB 13\n13\nB21\nB 22\nB23\n=\n23\nB31 B32 B33\nwhere [Y ] ] has been substituted for Al2' to which it is approxi-\nmately equal. N is the number of Geoceivers in the network.\nWe now take a look at those elements of E2 that lie along the\nmain diagonal, and separate them into three kinds of variance:\n2 dx' pertaining to the shape of the network; I2af' pertaining\nto the scale of the network; and 2ag' pertaining to the location\nof the network. Note that in this analysis no attention has been\npaid to the network's orientation. The orientation was ignored\nbecause its standard deviation behaves so much like the standard\ndeviation of location that the conclusions about standard devia-\ntions of location can be applied immediately to standard devia-\ntion of orientation without having to complicate the analysis.\n(Orientation, like location, is determined by two quantities,\nfor example, the ratio of northing and easting of a particular\npoint with respect to a fixed point. Since the equations have\nbeen linearized, the fact that orientation is a ratio is irrele-\nvant; the errors appear linearly.)\nUsing Schur's well-known lemma, we obtain","644\n-1\nB11\n=\n-1\nB22-\n=\ndf\n22\n2\nF3b31F3\n-1\n3\nwhere b jj denotes the adjoint of B jj and F denotes the off-dia-\ngonal submatrix coupling B jj and biji A number of facts are im-\nmediately obvious on comparing these three equations with the\nequation for E2. 2\nIn the equation 2 we see that both B33 and the accompanying\nterm contain the factor N, the number of Geoceivers\nin the network. The standard deviation of g, the location of\nthe origin of the network, is therefore inversely proportional\nto /N It is also independent, obviously, of the locations of\nthe Geoceivers or the distances between them and of the scale\nand shape of the network.\nIn the second equation the variances of the data from the\nGeoceivers and of the measured distances are coupled. Where the\nvariance of the measured distances is considerably smaller than\nthe variance 22 of the coordinates of the Geoceivers, [Y2], the\nsum of the squares of measured distances will have a predomin-\nating influence. In the network investigated the standard devi-\nations of the measured distances appear to be smaller than the\nstandard deviations of the equivalent distances from the\nGeoceivers. In addition, the measured distances are more numer-\nous by a factor of at least five to ten. Hence we would expect\nthe data from the Geoceivers to have little effect on scale of\nthe network and, in fact, this is what the results show. There\nis one exception to this, and that is when there are very few or\nno measured distances. In this case the second equation shows\nthat the factor on the right contains the quantity [x2], the sum\nof the squares of the distances of the Geoceivers from the origin.\nWhen only two Geoceivers are present, and one is at the point of\norigin, the standard deviation of scale is inversely proportional","645\nto the distance between the two Geoceivers. This prediction is\nonly approximately supported by the computations; the reason\nfor this discrepancy is discussed further in appendix 2.\nFinally, looking at the first equation, we see that the term\n11 does not contain directly either the number N or the dis-\ntances between Geoceivers or the sum of lengths of measured\ndistances. These quantities do enter indirectly into B11\nthrough the parts A and A of the observation matrix A. But\nX2\nfor a network in which the standard deviation of the coordinates\nof the Geoceivers and the measured distances are not much\nsmaller than the equivalent standard deviation of the direc-\ntions (multiplying the standard deviation of a direction by the\nlength of the line) the Geoceiver coordinates and the measured\ndistances obviously will not have much effect on the shape of\nthe network. This conclusion is fully supported by the results.\nDirections were compared before and after adding Geoceivers to\nnetworks that contained no measured distances, and a few measured\ndistances were compared. It was found that where about 20\nmeasured distances were already present, the shape (directions)\ndid not change at the 0.01 level. When no measured distances\nwere used, most of the changes were still below the 0.01 level,\nwhile those above that level tended to cluster in parts of the\nnetwork which were suspected to be weak.\nAll in all, the theory fully supports the experimental results.\nHowever, there has been sufficient interest in the way standard\nerrors of a network are affected by varying the spacing between\nGeoceivers that a more detailed examination of this point seems\nworthwhile; appendix 2 provides this information.","646\nAPPENDIX 2. EFFECT OF INCREASING DISTANCE BETWEEN\nGEOCEIVERS ON STANDARD DEVIATION OF COORDINATES\nWhat happens to a network containing only directions if two\npoints in the network are occupied by Geoceivers, so that the\ncoordinates of these two points are \"measured\"? The answer is\nimmediately derivable from the analysis in appendix 1 by dropping\nall terms involving length l and setting N equal to 2. The re-\nsult is that (putting one point at the origin for convenience)\nthe scale is proportional to the distance between the two points,\nwhile the ratios between coordinates are not affected; that is,\nthe shape of the network remains unchanged.\nAnother more graphic way of showing the effect of increasing\ndistance between two Geoceivers is to conceive of a geodesic\nbeing drawn connecting the two stations P and P This geodesic\nis the shortest distance; its standard error, being determined by\nthe standard errors of the end points, is constant regardless of\nthe length of the geodesic. But P and P' can also be thought of\nas being connected by a large number of other paths that start\nat P and proceed along the sides of the triangles of the network\nto end at P' . Now the standard error in any one of these alter-\nnative paths is determined by the standard errors in the lengths\nof the sides that make up this path. With a little ingenuity,\nwe can formulate the relationship between the standard error of\nthe geodesic, the length of the geodesic, and the standard\nlengths of the sides making up a particular alternative path.\nSince the error in the distance from P to P' must be the same\nwhether calculated along the geodesic or from an alternative\npath, and since increasing the distance increases the number of\nsides in alternative paths, the standard errors in the sides\nmust decrease to keep the total effect constant. This conclu-\nsion is intuitively obvious from the geometric picture presented.\nTo formulate the procedure algebraically is somewhat tricky\nalthough straightforward, and will not be given here.","647\nA final variation of proof goes as follows: Let Z be the\nvector from P1 and P2' the two points at which Geoceivers are\nplaced. Consider any sequence of sides (of triangles) forming a\ncontinuous path from P1 to PI and consider these sides as\nvectors Zi, i = 1 to I. If the coordinates of the ends of\nvector are X and i+1' ¥i+1' we have for the length r of\nvector Z\nr2=zTz\nand\nEd\nXi)\ndr = dz =\nYi)\nThe standard deviation o2 of r is then\n0\ncose\no2\n[cose\nsine]\n=\nsine\nwhere EZ and ZZY pertain to Xi)\nrespectively. Putting this in terms of the standard deviations\nof the individual segments, we have\n°X1,2\nCOS A\n°X2,3\ncost\n2\no2\nXXI,I-1\n[cos\n0\ncost sine\n=\nsine]\nsine\n0'11,2\n,-\nsine","648\nwhere o i,i+1 is the standard deviation of the segment from\npoint Pi to point P. i+1\nWe now write\nox2,\netc.\n=\n,\nThen\n2\nsin2020's\no2\ncos20\n+\n=\nl+1,l\nwhere the sum is now over a set of intervals on the X and Y axes\nthat are all positive.\nThen, since o2 must be constant, regardless of the size of k\nand l, i.e., of distance between P1 and P2' it follows that as k\nand l increase and must decrease. This\nin\nturn implies that corresponding variances of the end points of\nthe segments must decrease, since\n= + 'X'I' 2 etc.\nIt will be noted that this conclusion does not agree exactly\nwith Dracup's (1975) results.\nDracup's results\nDistance\nRelative error\nNo. of\nbetween\nCase\n(average)\nGeoceivers\nGeoceivers\n1:90,000\n181\n2\nD\n1:156,000\n436\n2\nC\n1:178,000\n436\n5\nB\n(maximum)\nNo computations were carried out specifically to identify the\ncause of the lack of agreement. However, an analysis of\ntables 3 and 5 giving ratios of standard deviations for the\nvarious cases shows that the ratios not only do not obey the","649\n(distance) - _1 law but vary from point to point in the network.\nA glance at the plots of error ellipses shows that the program\napparently adopted, for each different configuration of\nGeoceivers, a different center from which to compute standard\ndeviations. With this being the case, it follows that comparing\nstandard deviations of the same sides, for varying arrangements\nof Geoceivers, is comparing data which are affected by more\nthan just different distances between Geoceivers.","650\nAPPENDIX 3. STATISTICAL CONSIDERATIONS\nAll the adjustments in this report were carried out using as- -\nsumed values for the standard errors of the observations. These\nvalues are based on extensive experience of NGS in the analysis\nof errors in other smaller nets. We do not know, of course, that\nthese values actually apply in the present case. It would be\nhelpful to be able to find from the network being investigated\nbetter values for the standard errors of the observations. If\nall the observations are of one kind, this is no problem. But\nwhere, as in the present case, there are several kinds and\nclasses of observations, finding improved values is not easy. It\nmay even be impossible, as, for instance, if there are only one\nor two observations of a particular kind. In general, however,\neach kind of observation can be expected to be present in con-\nsiderable numbers, and estimates of the standard error of each\nkind made. The following formula is suggested for the purpose:\nvivil\nwhere Vj is the vector of residuals of observation of type i, ni\ni\nthe number of observations of type i, A the matrix of observa-\ntions, and A; that submatrix of A relevant to observations of\ntype i. k is a constant, whose value can be found to be\nwhere i = 1 to I.\nDerivation of the formula is easy enough that the authors have\nnot troubled to search the literature for earlier derivations. .\nA somewhat similar, but different, formula was apparently de-\nrived by Thiel (1963), and is quoted by Bossler (1972). .","651\nAPPENDIX 4. COMPARISON OF ADJUSTED NETWORKS WITH AND WITHOUT\nDATA FROM GEOCEIVERS: ADJUSTMENTS B, C, AND D\nThe networks used by Dracup (1975) in his analysis did not con-\ntain any measured lengths. They derived their scale solely from\nthe data of the Geoceivers. Hence the coordinates of points in\nthese networks cannot be compared with the coordinates of points\nin a Geoceiver-free network. But some guesses can be made as to\nthe behavior of the Geoceiver-containing networks with respect\nto a Geoceiver-free network containing a true scale.\nThe coordinates of points in networks B, C, and D are the same,\nafter adjustment, to within 3 cm. Assuming an average length of\n20 km for the sides of the triangles in the networks, this 3 cm\ncorresponds to about 0.2 maximum difference in directions. The\nnetworks, therefore, could be considered essentially the same in\nall three cases. But the case for considering the networks\npractically unchanged by introducing the data from the Geoceivers\nis even stronger if one examines the trend of these differences.\nThe difference of about 3 cm is nearly constant in longitude\nbetween networks C and D; it decreases in latitude to 0 from\nabout 3 cm. Comparing solutions C and D with the solution for\nnetwork B, we find that B agrees to within a centimeter or so in\nlatitude with C and to within a centimeter or so in longitude\nwith D, while there is a 3-cm nearly constant difference between\nB and C and D in longitude and latitude, respectively.\nIt seems clear from these numbers that the basic network\nremains similar under all introductions of Geoceiver data; that\nis, it changes size but not shape. Furthermore, on examining\nthe lists of residuals in directions we find that for all three\nnetworks (B, C, D) the residuals are within 0.02 of each other.\nComparing these residuals with those obtained by adjusting the\nnetwork containing measured distances, we find agreement to\nwithin 0.04 for the most part, with a few discrepancies as high\nas 0.2 and a very few higher than this.","652\nAPPENDIX 5. COMPARISON OF ADJUSTMENTS ON NETWORKS WITH AND\nWITHOUT DATA FROM GEOCEIVERS\nThe coordinates of the adjusted coordinates of each station\nwere compared for the cases:\na. No Geoceiver stations in the network.\nb. Central and southern Geoceiver stations in the network.\nC. Central and eastern Geoceiver stations in the network.\nd. All five Geoceiver stations in the network.\nIt was found that the adjusted positions were the same for all\nfour stations, to within 1 to 2 cm. Consequently, we can con-\nclude that the data from the Geoceivers did not affect the\ngeometry of the network in any way, but merely affected the\nstandard error of location of the network as a whole. In other\nwords, the network is rigid with respect to action on it from\nGeoceiver data.","653\nAPPENDIX 6. VARIATION OF VARIANCE OF SHAPE WITH\nLOCATION OF GEOCEIVERS\nThe shape portion of the matrix given in appendix 1 is in gen-\neral quite difficult to invert. However, there are several\nsimple cases which are interesting for this investigation. In\nparticular, for instance, when the network contains only direc--\ntions and one or two Geoceivers without any measured distances.\nIn these cases, the resulting matrices are easily inverted. The\nproblem can be simplied still further by assuming that one of\nthe Geoceivers is at the origin of coordinates or, what is almost\nthe same thing, by placing the origin at one of the Geoceivers.\nThe data from that Geoceiver do not contribute to the shape sub-\nmatrix at all. The contributions from the data of the other\nGeoceiver appear only as additions of k2ajj to consecutive ele-\n-\nments on the main diagonal. (k is the scale factor and 2.\nthe\nvariance of each given coordinate.) To get a clear picture of\nwhat is happening, we look first at the effect of specifying\nonly the second X-coordinate, then at the effect of specifying\nboth X- and Y-coordinates of the second Geoceiver. The variance\nof pseudo-coordinate i is\nB\nwhere the bar (-) indicates that data from Geoceivers are in-\ncluded, while absence of a bar refers to the Geoceiverless net- -\nwork. We expand numerator and denominator - 2 elements\nand\nCO-\nfactors of the jth row (the second Geoceiver being at point Pj)\n.\nWe get\njj'jj\n=\nwhere the superscripts indicate that the designated rows and\ncolumns have been deleted. Using a self-evident notation this\nbecomes","654\n(1)\nExtension to the case where data on both X- and Y-coordinates are\ngiven is somewhat more complicated, but the end result is\n(2)\nThis formula can be generalized fairly easily to the case\nwhere neither Geoceiver is at the origin. It will look very\nmuch like equation 2 but will go up to the fourth power of\n(k2033) and the sum of four (two pairs) of variances of the\noriginal matrix. For our purposes equation 1 is sufficient,\nsince equation 2 is analogous to it. For actual networks we can\nassume that the second term in the numerator is small compared\nto the first. Then, is is inversely proportional to\n(1 k2-202 which is a linear function of The value\nof\nof depends on the position of Pj in the network and cannot be\nexpected to vary monotonically as the distance between P1 and P\nj\nincreases. Hence, the portion\nATOX2 A1 0\nof the normal matrix will contribute a rather irregular variation\nof overall variance of a particular coordinate as the distance\nbetween Pi and Pj.\nNote that the contributions of other parts of the normal matrices\nhave been ignored. If we include them, we find that the actual\ndistance occurs in the denominator. This is over and\nabove whatever is contributed by the shape portion of the matrix.","655\nReferences\nAnderle, R. J. (Naval Weapons Laboratory, Dahlgren, Virginia),\nMarch 6, 1974 (personal communication to B. K. Meade,\nNational Geodetic Survey, NOS, NOAA, Rockville, Maryland).\nAshkenazi, V., and Cross, P. A. 1975: Strength of long lines\nin terrestrial geodetic control networks. Presented to\nXVI General Assembly of International Association of Geodesy,\nInternational Union of Geodesy and Geophysics, Grenoble,\nFrance, August, 25 pp.\nBossler, J. D. (The Ohio State University, Columbus) 1972:\nBayseian Inference in Geodesy. Ph. D. Dissertation, 79 pp.\nDracup, J. F. , 1975: Use of Doppler positions to control\nclassical geodetic networks. Presented to XVI General\nAssembly of International Association of Geodesy, International\nUnion of Geodesy and Geophysics, Grenoble, France, August,\n12 pp. National Ocean Survey Reprints 1975, National Oceanic\nand Atmospheric Administration, U. S. Department of Commerce,\nWashington, D. C. (in press). .\nMeade, B. K. , 1974: Doppler data versus results from high\nprecision traverse. Proceedings of International Symposium on\nProblems Related to the Redefinition of North American\nGeodetic Networks, The University of New Brunswick,\nFredericton, N.B., Canada, May 20-25. The Canadian Surveyor,\nvol. 28, No. 5, 462-466.\nThiel, H. , 1963: On the use of incomplete prior information in\nregression analysis. Journal of the American Statistical\nAssociation, 58, 401-414.\nVincenty, T. , 1975: Experiments with adjustments of geodetic\nnetworks and related subjects, unpublished at date of\npreparation of this paper.","656","657\nUPDATING SURVEY NETWORKS - A PRACTICAL APPLICATION\nOF SATELLITE DOPPLER POSITIONING\nJoseph F. Dracup\nChief, Horizontal Network Branch\nNational Geodetic Survey, NOS, NOAA\nRockville, Maryland 20852\nAbstract\nThe National Geodetic Survey (NGS) has carried out several tests\ninvolving Doppler-determined positions to control or to strengthen classical\ngeodetic networks. These studies have shown that improvements in scale and\norientation can be expected and, in fact, entire networks can be controlled\nby strategically placed Doppler positions. There are other uses to which\nthese positions may be employed. Among these applications are those directed\nto improving the relative positioning of badly constrained or poorly designed\nsystems, or to update positions located on land masses which may have shifted\nas a block, due to some tectonic event. The latter is a practical solution\nto an otherwise costly operation where the control is primarily used in\nhydrographic, topographic, or cadastre surveys. The study involved here is\nprimarily concerned with the updating of geodetic control on the Alaska\nPeninsula, which is known to be distorted due to past adjustment practices.\nMajor hydrographic surveys, in addition to the land definition projects by\nthe Bureau of Land Management (BLM), are underway in this area. It is\nessential that the control be determined to the highest accuracy that can be\nobtained from available observational data, with a further stipulation that\nthe positions remain unchanged until a new adjustment of the entire Alaskan\nnetwork is made. An examination of the adjusted results furnish good\nassurance that both conditions have been met. In addition, this test shows\nconclusively that networks of the type studied can be updated by judicious\nuse of Doppler positions. Also included is a review of the possibilities of\nlocal crustal motion and a shift of the entire Peninsula and another evalua-\ntion of the use of Doppler positions as basic control.\nIntroduction\nIn recent years publications by Meade (1974), Dracup (1975), and Moose\nand Henriksen (1976) have discussed the use of satellite Doppler positions\nto strengthen existing networks. At least one author noted such positions\ncould provide fundamental control in developing horizontal frameworks. The\napplication of this latter view will be illustrated dramatically as details\nof the New Adjustment of the North American Datum continue to unfold. In\nbrief, it is highly probable that numerous Doppler positions will be the\nmechanism employed to fit this vast network to a world reference frame.\nAlthough positions which have been determined by other means will be intro-\nduced into the solution, the predominance of Doppler data will probably tend\nto overshadow these contributions. This thought is offered on the presumption\nthat there will be no unresolvable problems in the Doppler positioning concept\nand that the promise of more accurate positions from other procedures will\nnot materialize prior to 1983, the completion date for the New Adjustment.","658\nAt present there can be few arguments that satellite Doppler positioning\nhas provided the geodesist and cartographer, among others, with a powerful\ntool for resolving previously difficult situations in an efficient and econo-\nmic manner. This paper is directed to one of these situations -- the updating\nof a network which may or may not have been affected by tectonic events but\nis certainly distorted, through past adjustment practices, to a point where\nit is suspected the adjusted results cannot meet present-day needs. A further\nstudy of the use of Doppler positions to control and/or strengthen networks\nis also included.\nIn many areas of the United States the problem of maintaining exact\ncontinuous consistency between networks is not of particular importance,\nalthough considered desirable, when the control is required primarily for\nregional hydrographic, topographic, and general surveys. Numerous coastal\nschemes, especially those in Alaska and other isolated sections fall in this\ncategory. If the need should arise, updating of additional segments could be\nmade with little difficulty anticipated, provided that the positions of the\ncommon stations were determined by or are located within the effective range\nof points positioned by Doppler or more accurate methods. Obviously, one\nmust be selective when taking this route to assure that unacceptable constraints\nand distortions are not left to be absorbed in later computations.\nLocality\nSurveys on the Alaska Peninsula were chosen for the tests. The National\nOcean Survey (NOS), conducting extensive hydrographic surveys in the area,\nneeded assurance that past tectonic events had not compounded known distor-\ntions in the network to a point where costly resurveys might be required.\nIn addition, this updated data would be useful to BLM in their surveys to\ndefine land boundaries as specified by the Alaska Native Claims Settlement\nAct. Added to these practical considerations, was a study to determine the\namount of horizontal crustal motion, if indeed any had occurred, since the\ninception of the earliest surveys.\nInasmuch as the Peninsula had been subjected to numerous seismic occur-\nrences and some volcanic activities, and because of its relationship to\nnearby plate boundaries, a definite possibility exists of a shift in the\nentire, or almost entire, land mass during the intervening period. Accordingly,\nthe locality appeared to offer excellent opportunities to carry out this\nstudy. Little is known about faults on the Peninsula and the assumption was\nmade that there had been no localized crustal motion. Should this assumption\nprove to be true, then there would be no need to reobserve the network even\nthough the entire land form had shifted. When this situation exists,\nexperience has shown that angulation remains essentially unchanged. A read-\njustment in this instance simply shifts the points to their present-day\nlocation. If the land mass had remained in place, the readjustment is certain\nto remove most existing distortions and constraints. There is little likeli-\nhood that recomputations will be necessary until the new adjustment of the\nentire Alaskan network takes place.\nA brief description of the locality appears in order at this point. The\nAlaska Peninsula extends about 800 km southwesterly from the major land mass","659\nof the State. It is situated on the boundary between the North American and\nPacific plates, and is included on the so-called \"Ring of Fire,\" a zone of\nactive volcanoes and earthquakes encircling the entire Pacific Ocean.\nAlthough\nsparsely populated and almost devoid of trees, the topography presents a\nnumber of interesting contrasts. To the north, there is a region known as the\n\"Valley of the Ten Thousand Smokes.\" which drew its name from the steam and\ngases escaping from numerous vents and fissures. Volcanoes and mountains\nof the Aleutian Range rise above the surrounding waters to a height of about\n2700 m. The shoreline is broken by many estuaries, inlets, and bays. All\nin all, it is a harsh land. However, this is overshadowed by economic contri-\nbutions, primarily fishing, to the overall benefit of the State; hence, the\nrequirement for large-scale hydrographic charts.\nThe Alaska Peninsula Network\nGeodetic surveys were first established on the Peninsula in 1901 and were\ncomputed on an independent astronomic datum. The North American 1927 Datum\n(NAD 27) was brought to Alaska via triangulation straddling the Alcan\nHighway during World War II. Prior to that time, small surveys established\noff the original 1901 net were accomplished in the period 1911 to 1941 to\ncontrol hydrographic surveys. For the most part these were along the south\nshore with spur nets to position control in the inlets and bays. As a\ngeneral rule the majority of stations were located to third-order accuracy,\nalthough in the extreme southwest a few stations were determined by second-\norder methods. During the years from 1944 to 1952, first-order triangulation\nwas observed along the entire north shore and a section on the northern\nportion of the south side between Wide Bay and Chignik Bay. At the same\ntime four of the six connections between the arcs were also observed to\nfirst-order standards. The other connections were accomplished by third-order\nmethods in an earlier period. A sketch of the network is shown by Fig. 1.\nTen taped base lines were measured between 1911 and 1952. All were\nconsidered to be first-order in the adjustments. However, the lines measured\nin 1911, 1923, and 1924 were actually of second-order quality. The difference\nin quality between base lines measured by NGS to first- and second-order\nstandards is so small that, except in the most detailed studies, it may be\nsafely ignored.\nFive first-order Laplace stations were observed during the period of\n1944 to 1952. While the spacing of the base lines are more or less uniformly\ndistributed, only one Laplace station was observed in the south shore network\n(see Fig. 2).\nPositions were determined for seven stations by Doppler procedures. Two\nof the determinations were made by the Defense Mapping Agency Topographic\nCenter (DMATC) in 1972. The other positions were observed by NGS personnel\nin 1975. See Fig. 3 for location of stations at which Doppler positions\nwere available. Additional details concerning these determinations will be\nfound in the following section.","Figure","+5850\n+5820\n+590\n+5730\n+5720\n+9050\n+5620\n+5550\n+5520\n+3450\nL5420\n155\n1330\n15530\n+\n15330\nAstronomic azimuths\nA B\n15630\n+\nBase lines\n15630\nA B\nB\nLocation of astronomic azimuths and base lines.\n15730\n+\n15730\nB\nA\nB\n15830\n+\nB\n15t30\nAB\n15930\n+\n15730\n16030\nAB\n+\n16030\nDOPPLER TEST PROJECT - ALASKA PENINSULA\n16130\n+\n16T30\nFigure 2.\nB B\n16230\n16230\n+\nA\nB\n16330\n16330\n52 say\n57204\n16:4f\n5904\n56204\n3850\n5820f\n55504\n15204\n54501\n54.04","662\nEvaluation of Doppler Positions\nSatellite Doppler positions were available at the stations given in table 1\nor transferred from nearby points through an adjustment of the tie observa-\ntions. Doppler data for the 51000 series stations were observed and reduced\nby the NGS and the 30000 series by DMATC. The DMATC observations were made\nusing a precise ephemeris generated from a different gravity model and reduced\nby a program different than the NGS observations. The stations are listed\nin order of longitude westward.\nTable 1. List of stations for which Doppler positions\nwere available.\nDoppler Sta.\nStation\nApprox.\n& and r\nObserved By\nNo.\nNumber\n57.7\n155.3\n1\nKEKURNOI 1919\nNGS\n51133\n2\nB 6 USE 1946\n58.7\n156.7\nDMATC\n*Note 1\n3\nKUMLIK 1925\n56.6\n157.4\nNGS\n51132\n4\nHEIDEN SE BASE 1949\n57.0\n158.6\nNGS\n51129\n5\nSTAR 1914\n55.9\n159.2\nNGS\n+Note 2\n6\nSOCK 1950\n56.0\n160.5\nNGS\n51130\n7\nBISHOP 1952\n55.2\n162.7\nDMATC\nSNote 3\n*Note 1: Reduced from GEO STA 30057 USE 1972 via distances and\ndirections to A 2 USE 1946, B 2 USE 1972, and B 6 USE 1946 and observations\nto several positioned objects.\n+Note 2: Reduced from STAR 1914 RM 2 1975 (51131) via distances and\ndirections involving STAR 1914 and PETREL 1945 and directions involving\nPERRY 1914.\nSNote 3: Reduced from SAT TRI STA 125 1965 (30056) via distances and\ndirections involving BISHOP 1952 and SIMEON USE 1952.\nThe Doppler positions were converted from the NWL 9D system to the NWL 10F\nsystem. This conversion accounts for a small scale discrepancy (-0.8263 ppm)\nand rotation to the proper longitude origin. Coordinates on the NWL 9D\nsystem ( , 1, h) are transformed to the NWL 10F system ( ', , X' , h') as follows:\n=\nX' = l + 0.260 (a east is positive)\nh' = h - approx. 5 m.\nwhere h and h' are heights above a selected common ellipsoid. See Meade (1974)\nand Vincenty (1976) for further details relative to these conversion formulas.\nMeade (1976) used the following procedure to shift the NWL 10F system\nDoppler coordinates to the NAD 27.","+5850\n45820\n+5750\n+590\n+5720\n+9050\n5620\n+5550\n+5520\n+3490\n45420\n155 $\n1330\nI\n15530\n15330\n+\nDoppler positions\nto stations given in tables 1, 2, 4, , and 8 and figure 4)\n15630\n15630\n+\n2\nFigure 3. Location of Doppler positions (Numbers correspond\n15730\n3\n15730\n+\nA\n15830\n15t30\n+\n4\n5\n15930\n15930\n+\n16030\n6\n16030\n+\nDOPFLER TEST PROJECT - ALASKA PENINSULA\n16130\n16T3C\n+\n16230\n16230\n+\n16330\n16330\n57204\n56504\n5750\n56204\n55 504\n55204\n58204\n54304\n14:04\n5904\n58524","664\n(1) Since the elevations and geoid heights in Alaska may have uncertainties\nof several meters, geodetic (ellipsoidal) heights were computed by converting\nthe Doppler coordinates to the Clarke Spheroid of 1866. This was\naccomplished by applying the mean shift (AX = +19.60 m, AY = -155.02 m,\nAZ = -175.12 m) as determined by Vincenty (1975) from data at 36 sites on the\nhigh precision traverse to the NWL 10F coordinates. The resulting geodetic\nheights and the corresponding NAD 27 geographic positions were used to\ncompute X,Y,Z coordinates.\n(2) Differences between the X, Y, Z coordinates on the two systems were\ncomputed. The sequence of computations follows:\n(a)\nX\nAX\nX,\nwhere , AY, and AZ are the mean\nAY\nY,\nvalues as determined by Vincenty\n=\nAZ\n(1975).\nZ.\nNWL 10F\nClarke 1866\nSystem\nSpheroid\n1/2\n((X2+Y2)\n(b)\nh\n/\nCos ) - N (Clarke 1866 Spheroid) is NAD 27\n=\n(c)\n$2\nX,Y, and Z are NWL\nX2\nAX2\nX-X\n7\n10F system coordinates\nY-Y2\nAY2\nY2\n7\nthus\nfrom (a).\n=>\n=\nAZ2\nZ-Z.\nh\nZ 2\n2\nand\nl\n27 are the published latitudes and longitudes for the\n7\nstations on- the NAD 27 and \"h\" for the points as computed in (b).\n.\nDoppler data which had been reduced by the NGS were available at 29 stations.\nDifferences at seven stations were in good agreement and the mean values were\nused to convert the Doppler coordinates on the NWL 10F system to the NAD 27.\nThe mean values in meters follow:\n40 = 0.2\nAX = + 12.2\nAY = -140.5\n0.5\n=\no = 0.1\nAZ = -174.9\nUsing the differences at the 29 stations, the mean values in meters are\nAX = + 14, AY = -144, AZ = -175 with a range of 20 m, 23 m, and 13 m respectively.\nDifferences in o, 1, and h at the seven Doppler stations used in the\nadjustment of the Alaska Peninsula network are given in table 2. Latitude\nand longitude differences are the published positions on the NAD 27 minus the\nNWL 10F system coordinates converted to the same datum. Corresponding vectors\nare also tabulated. Differences in the geodetic heights (Ah) were computed\nby subtracting the Doppler derived quantities from the published elevations\ncorrected for geoid heights. The geoid heights were scaled from the Geoid\nContour Map prepared by the Army Map Service (now DMATC) in 1967 and from\nless reliable sources. Geoid heights scaled from the Geoid Contour Map are\nprobably accurate to about 2-4 meters. No estimate can be given as to the","665\naccuracy of the geoid heights from other sources. It is reasonable to\nassume, however, that a major portion of the differences can be attributed\nto the procedures employed in obtaining the published elevations. These\nvariances were not totally unexpected, as may be drawn from a brief\ndiscussion of the source of the elevations which follows.\nAccurate elevation control is quite sparse on the Peninsula. A few\nconnections to tide gauges have been made, and in earlier periods elevations\nat selected points were secured from observations on the horizon.\nAdmittedly the latter procedure is not generally considered to produce\naccurate elevations. However, great care was exercised in making the\nmeasurements which were often taken at varying time intervals during a\nperiod of several days. To this meager amount of control, elevations\ndetermined from vertical angles (trigonometric leveling) were fitted on a\nproject-by-project basis. Elevations obtained in previous projects were\nusually held fixed. At one time least-squares adjustments of the observa-\ntions had been common practice, but more recently, closures were distributed\nby the most simple method, usually some sort of prorating according to\ndistance. The present policy of the NGS requires that least squares\nadjustments be made of all observational data.\nTable 2. Differences in o, 1, and h at \"Doppler\" stations.\nVector\nAzi,/Dist.\nAh (m)\nNo.\nStation\nAO\nAl\n95.6/16.5 m\n+3.4 *\n1\nKEKURNOI 1919\n-0!052\n-01994\n-0.776\n114.3/13.7\n+3.6 *\n2\nB 6 USE 1946\n-0.183\n-1.050\n99.0/18.1\n+7.7\n3\nKUMLIK 1925\n-0.091\nHEIDEN SE BASE 1949\n+0.130\n-0.950\n75.9/16.6\n+7.1\n4\n-0.481\n85.9/ 8\n+8\n**\n5\nSTAR 1914\n+0.019\n+0.095\n-0.429\n68.4/ 8.1\n+2.4\n6\nSOCK 1950\n+0.057\n+0.022\n347.6/ 1.8\n-0.2 *\n7\nBISHOP 1952\nAh is at the site of the Doppler observations.\n* Reliable geoid heights available.\nPublished elevation to meters only.\nThe relative locations of the \"Doppler\" stations and accompanying vectors\n(from table 2) are shown in figure 4. On first examination of the vectors, it\nis fairly evident that the network has been expanded with the most likely\nprimary cause being distortion in scale, although orientation also enters the\nproblem. While the effects of seismic events cannot be ruled out completely,\nthe pattern of the vector locations relative to the land mass tend to dispel\ngiving serious thoughts to this consideration. However, if the vectors were\nopposite to the example here, i.e., increasing in size from the east, one\nmight suspect that there were possible seismic contributions. Scale and\norientation distortions would still be regarded as the major causes. Meade\n(1976) reached the same conclusion from an evaluation of adjacent surveys to\nthe east.","666\nN\nScale 25 mm =100 km\nVector Scale 25 mm = 10 m\nFigure 4.\nSchematic of Doppler position locations and vectors\nThe principal reason for this test was to update the network and the\nadjustments were directed toward reaching this goal. A secondary purpose\nwas a continuance of the study of the use of Doppler positions as basic\ncontrol. Any additional information which would produce evidence regarding\ntectonics of the region must be viewed as a side benefit. Further comments\non future studies which could cast a better light on crustal deformations\nare discussed in the Conclusions.\nDetails of Adjustments\nThe network contains 15 projects or portions of projects, involving 295\nstations, which were observed between 1901 to 1952. Minimum constrained\nadjustments had been carried out for each of the surveys as part of an\nevaluation of the southwestern Alaskan network. In five of the adjustments\nthe variance of unit weight fell well beyond the admissible range of the\nchi square test and the a priori weights were scaled. The scaling was done\nonly after a careful analysis of residuals and observed directions to insure\nthat the causes of the large variances of unit weight were not due to a few\nobservations. In all instances the evaluation adjustments contained\npoor\nonly the horizontal directions.\nThe following adjustments were made:\nAdjustment A. The entire network including all direction observations,\nlength measurements and astronomic azimuths. Doppler position for station","667\nHEIDEN SE BASE 1949 which had been reduced to the NAD 27 was used as\ncontrol. This station is on the north shore, located about 250 km from\nthe eastern end of the network (see figure 3 - station 4)\nDoppler positions, also reduced to the NAD 27 for the other six stations\nat which observations had been obtained (or transferred to) were utilized\nbut without constraints. Published positions for all other stations were\nused as assumed values. By taking this route, the shifts in position and\naccompanying vectors made the evaluations of the shifts a simple matter.\nAdjustment B. This adjustment was the same as adjustment A except the\nseven Doppler positions were introduced as weighted observations. Results\nof this adjustment, with perhaps some very slight modifications to account\nfor previous computations on the east, will be published.\nAdjustment C. Same as adjustment B except all length measurements and\nastronomic azimuths were omitted. This is simply another test of using\nsatellite Doppler positions as basic control.\nSixty relative accuracy estimates between identical points in each\nadjustment were computed. These are in the form of standard errors for\nthe lengths and azimuths between selected stations. Various statistics and\nother data are found in tables 3 through 9.\nWeights. The a priori standard errors assigned to the observations\nare:\nDirections\no2 = (0.16) 2 + 2(0.001/DSin 1\")2\nFirst-order\nSecond-order o2 = (0.77)2 2 + 2(0.001/DSin 1\")2\nThird-order o2 = (1.'2)2 2(0.001/DSin 1\")2\nwhere D is the length of the line in meters. The scalars mentioned earlier\nranged from 1.825 to 4.976.\nAstronomic azimuths\nFirst-order o2 = (0.45) 2 + (0.80) 2 + (Tan $/0.80) 2 + (0.40.Sin ) 2\nBase lines\no2 = (K.10-3) 2 + D.0.5 ppm) 2 + (0.00005.Ah/3) 2\nFirst-order\nwhere K = (D/50) 1/2 with the result rounded off to the nearest whole unit.\nD is the length in meters and Ah is the difference of elevation also in\nmeters. The last term is ignored when Ah is determined by spirit leveling.\nDoppler positions\n00 = 0.9 m.\nor = 1.2 m.","668\nTable 3. Some statistics resulting from the adjustments.\n(The number of observations for each accuracy\nclass are enclosed by parenthesis.)\nDirections\nClass\nAdjustments\nA\nB\nC\n-\nAverage residual\n1\n0.452\n(1105)\n0!457\n0!444\n2\n0.645\n(126)\n0.643\n0.642\n3\n1.513\n(648)\n1.514\n1.508\nMaximum residual\n1\n2.286\n2.440\n2.305\n2\n2.679\n2.665\n2.649\n3\n12.867*\n12.896*\n13.102*\nAzimuths - Ave.\n1\n1.248\n(5)\n0.951\n1.368**\nMax.\n1\n2.519\n2.121\n2.679**\nLengths - Ave.\n1\n3 mm\n(10)\n3 mm\n102 mm** (1:40,900)\nMax.\n1\n9 mm\n10 mm\n293 mm* (1:19,300)\nDegrees of freedom\n879\n891\n876\nVariance of unit weight\n1.599\n1.602\n1.566\n* The largest residuals are isolated in the 1901 and 1911 surveys at\nthe extreme southwestern portion of the net. A11 residuals over 3\" were\neither in those surveys, at supplemental stations necessary to introduce\none of the Doppler positions, and at stations later reobserved to a higher\nstandard, but for which all observations were included.\n** Computed from differences of observed and adjusted quantities.\nA tabulation of conventional statistics obtained from the results of the\nadjustments is given in table 3. An examination of the direction residuals\nwould tend to indicate that few differences exist between these values in\neach of the adjustments; in fact, this essentially was the finding. However,\na careful review shows differences of as much as 0!6 between residuals\ndetermined in adjustments A and B, and differences amounting to 1.4 when\nthe results of adjustments A and C were compared. These results are somewhat\nlarger than those disclosed by Moose and Henriksen (1976) This may\npossibly be due to the narrow network, a minimum number of base lines and\nastronomic azimuths, spacing of Doppler positions, and the inclusion of\na variety of orders of work and a wide range of weights.\nThe first adjustment (A) showed that any localized crustal motion is\neither rather small or non-existent. Considering the long period of time\nover which the observations were obtained and the different field practices","669\nand instrumentation used, the results obtained in meshing 15 projects in a\nsimultaneous computation are more than satisfactory.\nNo additional evidence was uncovered to dispute the original conclusion\nthat scale and possibly orientation distortions resulting from the piece meal\nadjustment practices of the past were the principal, if not the entire, cause\nfor the differences between published and observed Doppler positions (table 2)\nIn any case, there is no doubt that the results of adjustment B will satisfy\nthe need for an updated and more accurate network in this section of Alaska.\nExamination of the Adjusted Data\nThe primary purpose for performing the adjustments--an updating of the\nAlaska Peninsula network has been achieved. A large amount of additional\ndata has been secured which has little bearing on the computations, but this\ninformation will add to our increasing knowledge of the employment of Doppler\npositions as basic control. Accordingly, some of these results have been\ntabulated. In the following discussions several comments are offered, not\nin the context of original thought, but simply to add to a rapidly accumulating\nDoppler positioning information bank.\nTable 4 is a tabulation of the distances between \"Doppler\" stations (see\nfigure 4 for sequence of lines) and the relative accuracy estimates. The\nrelative accuracy estimates are in the form of standard errors and are\ndisplayed as proportional parts for the lengths (L) and seconds for the\nazimuths (A). In the listings for this table, as well as tables 5 and 6,\nthe proportional part is given to the nearest thousand. For example, between\n\"Doppler\" stations 1 and 2, for adjustment A - L/A = 79/3.3, the standard\nerror for the length L approximates 1:79,000 and the standard error for the\nazimuth A is 3.3.\nTable 4. Relative accuracy estimates between Doppler positions.\nAdjustments\nA\nB\nC\n\"Doppler\" Sta.\nDist.\nL/A\nL/A\nL/A\nFrom\nTo\n128/1.7\n134 km\n79/3.3\n135/1.6\n1\n2\n184/1.0\n172/1.0\n91/2.0\n176\n1\n3\n245/0.7\n211/0.7\n156/1.6\n2\n4\n224\n157/1.4\n150/1.5\n108/2.1\n3\n4\n82\n144/0.9\n142/0.9\n88/1.7\n3\n5\n137\n231/0.6\n212/0.7\n151/1.5\n4\n6\n160\n114/1.7\n112/1.7\n78/2.6\n81\n5\n6\n236/0.8\n211/0.9\n144/1.6\n237\n5\n7\n233/0.9\n171/1.0\n175/1.6\n166\n6\n7\nThree comments are offered on the data in table 4. One, in comparing\nadjustments A and B, the introduction of the Doppler positions strengthens\nthe overall scale and orientation of the network by a ratio of about 1.6:1\nand 2:1, respectively. Two, it appears that to match the scale and\norientation improvements provided by the Doppler positions, several addi-\ntional base lines and astronomic azimuths would be required. A further","670\ninvestigation reveals that the spacing of lengths and astronomic azimuths\nis not much different than that suggested by Moose and Henriksen (1976)\nwhere a network becomes \"rigid\" (20 and 15 quads respectively). The major\ndifference is that here the network is made up of three orders of work of\nvarying quality within the orders, while Moose and Henriksen drew their\nconclusions from evaluation of first-order triangulation of the best quality.\nThree, adjustment C seemingly enforces the view that the Doppler data are\nan overall strengthening factor in this network. With regard to the relative\naccuracies of the Doppler positions, there are only small differences\nbetween the results obtained in adjustments B and C. Returning to the\nsecond comment, a continuing review tends to support Moose and Henriksen in\ntheir conclusion that networks become \"rigid\" by the introduction of very\nfew base lines and azimuths.\nThe locations of the base lines and astronomic azimuths are shown on\nfigure 2. With respect to the data given in table 5, few comments can be\noffered which are not readily evident. There is a significant reduction in\nthe relative length accuracies over the lines which were measured, when these\nmeasurements are omitted (adjustment C). However, in most instances, these\nlengths are considerably shorter than the average nearby triangulation lines\nand; as a general rule, the expansion figures are somewhat weak geometrically.\nIn terrain such as that found on the Alaska Peninsula, it is very difficult\nto locate the best type of site for base expansion sub nets. On the other\nhand, the azimuth accuracy estimates are essentially the same for all\ncomputations, although those determined in the solutions involving the\nDoppler positions are slightly better on the average.\nConclusions drawn from the data available in table 4 are not substantiated\nby other data given in tables 5, 6, and 7. In an overall reflection of\nthe previous commentary, the inclusion of Doppler positions almost certainly\nimproves the accuracy. However, this is not necessarily the case when\nindividual lines and local sections of a net are examined. The base line\ndata provided in table 5 are not representative of the network as a whole.\nAccuracy estimates and other statistical data tabulated in tables 6 and 7\nprovide a more realistic view of the situation and show that only slight\nimprovements, primarily in orientation, result when Doppler positions were\nintroduced. These data support the \"rigid\" network contention of Moose and\nHenriksen. The maximum o for the length and azimuth of the first-order\nobservations is over the line FEATHERLY 1946 to COLD 1920 in the eastern\nportion of the net, and the least proportional part involves the line\nSWEDE 1913 - KOROVINA 1913 located near the western end. Both lines are in\nthe south arc.\nTables 8 and 9 are largely self-explanatory. Data are tabulated according\nto longitude westward. Differences tabulated in table 9 show a reasonably\nsmooth distribution of the position distortions in accordance with the\nlocation of the stations and the sequence of previous adjustments. For the\nmost part, new work was fitted to old; and this is aptly demonstrated by\nexamining the differences at PERRY 1914 and STEWART 1949. The 1949 network\nwhich included STEWART was adjusted to the older net to the south.","671\nTable 5. Relative accuracy estimates involving base lines\nand astronomic azimuths.\nAdjustments\nApprox.\nA\nB\nC\nL/A\nL/A\nStation\nLength\n& and l\nL/A\nBase Line\n57.4\n156.4\n4.9 km\n357/3.0\n357/2!!7\n50/2.18\nWIDE BAY 1923\nB 6 USE 1946\n3.3\n58.7\n156.6\n310/2.3\n310/1.9\n28/2.2\n303/1.5\n2.8\n57.0\n156.9\n302/2.1\n64/1.5\nNAKOLILOK 1944\n414/2.1\n416/1.5\n80/1.5\nEGEGIK 1946\n7.0\n58.1\n157.6\n158.5\n251/2.4\n251/1.9\n38/1.9\nCHIGNIK BAY 1924\n2.3\n56.4\nHEIDEN 1949\n5.2\n57.0\n158.6\n382/1.7\n385/1.0\n101/1.1\n160.6\n366/1.7\n372/1.1\n113/1.1\nMOLLER 1950\n4.4\n55.9\n351/2.2\n65/2.4\nVOL 1941\n4.3\n55.2\n161.9\n351/2.6\nPAVLOF BAY 1911\n2.0\n55.2\n162.0\n253/5.0\n253/4.8\n23/4.9\nOPERL 1952\n5.7\n55.4\n162.8\n377/2.0\n378/1.5\n76/1.7\n*\nAstronomic Azimuth\n43/1.7\n41/2.2\nLEE 1944\n1.7\n57.4\n156.3\n43/2.0\n156.6\n64/2.0\n70/1.6\n62/2.0\nBASE 1946\n10.2\n58.7\n24/1.6\n24/1.1\n24/1.2\nMESHIK 1949\n**\n4.3\n56.9\n158.7\n128/1.1\nAS 1147 USLM 1950\n5.2\n56.0\n160.6\n133/1.6\n149/1.0\n126/1.8\n132/1.4\n88/1.7\nBISHOP 1952\n7.7\n55.2\n162.7\n*\nDistance in kilometers to station over which the azimuth was transferred.\n*Poor connection to network probably accounts for length accuracy estimate.\nTable 6. Relative accuracy estimates between arcs of triangulation.\nAdjustments\nStations\nA\nB\nC\nFrom\nTo\n*\n**\nL/A\nL/A\nL/A\n68/316°\n57.2 157.1\n84/2.'8\n108/2.2\n107/2.5\nDENNIS 1949\nFOUL 1944\nANKARA 1950\nIVANOF 1914\n45/305\n56.0 159.9\n78/4.8\n85/3.5\n84/3.5\n54/337\nFRANK 1950\nALIK 1913\n55.7 160.9\n120/2.6\n129/2.3\n115/2.3\nCATHEDRAL 1952\nMID 1924\n26/276\n55.6 161.9\n116/2.2\n134/1.8\n118/1.9\n35/307\n55.3 162.2\n88/2.4\n98/2.1\n92/2.2\nEAGLE 1952\nVOLWEST 1941\n114/2.3\n120/1.9\n87/2.0\nMOR 1923\nBLUFF 1923\n25/248\n55.0 162.8\nDistance in kilometers between stations/azimuth of line.\n*\n**Mean latitude and longitude of stations.","672\nTable 7. Relative accuracy estimates and other pertinent\ndata for 29 representative lines spread through-\nout the network.\nAdjustments\nA\nB\nC\n0.14 m\nLengths - Ave. o (1)\n0.17 m\n0.16 m\n0.37\n0.28\n0.28\nMax. O\n103,000\n120,000\n107,000\nAve. prop. part 1:\nLeast prop. part 1:\n63,000\n66,000\n65,000\nAve. length (km)\n16.6\n16.6\n16.6\nSample\n16\n16\n16\nAve. o (2)\n0.27 m\n0.24 m\n0.26 m\n0.40 *\n0.35\n0.40\nMax. o\n75,000\nAve. prop. part 1:\n78,000\n85,000\nLeast prop. part 1:\n45,000 *\n56,000 *\n56,000 *\n18.7\nAve. length (km)\n18.7\n18.7\nSample\n4\n4\n4\nAve. o (3)\n0.23 m\n0.21 m\n0.23 m\n0.54 **\n0.52 **\n0.53 **\nMax. o\n70,000\n63,000\nAve. prop. part 1:\n67,000\nLeast prop. part 1:\n46,000\n**\n47,000\n**\n46,000\nAve. length (km)\n13.7\n13.7\n13.7\nSample\n9\n9\n9\n1.35\nAzimuths - Ave. o\n(1)\n1.90\n1.29\n2.49\n1.78\n1.82\nMax. o\nAve. o (2)\n2.95\n2.60\n2.66\nMax. O\n3.68 *\n3.38 *\n3.36 *\nAve. o (3)\n2.68\n2.29\n2.40\nMax. o\n3.58 **\n3.28 **\n3.44 **\nNumber in parenthesis following \"Ave. 0\" indicates accuracy class.\nOver same line, points not directly connected.\nOver same line.\nTable 8. Difference in latitude and longitude of Doppler\npositions minus adjusted positions.\nAdjustments\nNo.\nStation\nA\nB\nC\n1\nKEKURNOI 1919\n+ 0.0324\n+ 0!0100\n- 0.0021\n- 0.1707\n+ 0.0036\n+ 0.0186\nB 6 (USE) 1946\n2\n+ 0.1194\n+ 0.0330\n- 0.0079\n- 0.2954\n- 0.0604\n- 0.0407\n3 KUMLIK 1925\n+ 0.0436\n+ 0.0238\n+ 0.0413\n- 0.0822\n+ 0.0178\n+ 0.0072\n4\nHEIDEN SE BASE 1949\nFixed\n- 0.0248\n- 0.0044\nFixed\n+ 0.0593\n+ 0.0482\n- 0.0402\n5\nSTAR 1914\n- 0.0380\n- 0.0213\n- 0.0540\n- 0.0175\n- 0.0238\n- 0.0154\n- 0.0270\n6\nSOCK 1950\n- 0.0012\n- 0.0107\n+ 0.0182\n- 0.0152\n+ 0.0464\n7\nBISHOP 1952\n+ 0.0226\n- 0.0044\n- 0.0632\n- 0.0205\n+ 0.0058","673\nTable 9. Differences in latitude and longitude with corresponding\nvectors for selected stations at about 30-50 km spacing\nthroughout the network.\nAdjustments\nApprox.\nA\nB\nC\nAO Al\nA Al\nA Al\nStation\nl\nVector*\nVector*\nVector*\n57.7\n- 0.'046 - 1..236\n- 0.075 - 1.070\n- 0.'094 - 1.004\nCOLD 1920\n20.53/93.9\n17.88/97.4\n16.90/99.9\n155.8\nTITCLIFF 1923\n57.3\n- 0.084 - 1.239\n- 0.111 - 1.102\n- 0.132 - 1.027\n20.90/97.2\n18.76/100.6\n156.3\n17.66/103.3\nBASE 1946\n58.7\n- 0.064 - 1.068\n- 0.150 - 0.834\n- 0.189 - 0.809\n17.33/96.6\n14.22/109.0\n156.6\n14.29/114.2\n56.6\n- 0.068 - 1.125\n- 0.085 - 1.019\n- 0.062 - 1.005\nWIK 1925\n19.32/96.2\n17.59/98.6\n157.1\n17.26/96.3\n- 0.031 - 1.044\n- 0.096 - 0.891\n- 0.107 - 0.873\nEGE 1946\n58.1\n17.12/93.2\n14.90/101.5\n157.3\n14.68/103.1\n57.5\n+ 0.048 - 0.990\n+ 0.006 - 0.882\n+ 0.021 - 0.882\nWOODY 1949\n16.53/84.8\n14.67/89.3\n157.7\n14.68/87.5\n56.4\n+ 0.011 - 0.973\n- 0.004 - 0.904\n+ 0.020 - 0.928\nANG 1920\n16.68/88.8\n15.49/90.5\n158.3\n15.92/87.7\n57.0\n+ 0.133 - 0.955\n+ 0.108 - 0.896\n+ 0.128 - 0.907\nHEIDEN NWB 1949\n16.65/75.7\n15.49/77.5\n158.7\n15.82/75.5\n55.9\n- 0.022 - 0.558\n- 0.021 - 0.519\n- 0.004 - 0.526\nPERRY 1914\n9.71/94.1\n9.03/94.0\n9.14/90.7\n159.1\n56.5\n+ 0.106 - 0.838\n+ 0.089 - 0.790\n+ 0.110 - 0.808\nSTEWART 1949\n14.71/77.1\n13.79/78.5\n14.24/76.2\n159,2\n55.6\n+ 0.009 - 0.370\n0\n- 0.342\n+ 0.035 - 0.374\nKARPA 1914\n160.1\n6.50/87.5\n6.00/89.9\n6.65/80.7\n55.9\n+ 0.084 - 0.434\n+ 0.072 - 0.405\n+ 0.098 - 0.440\nMOLLER NB 1950\n7.38/72.3\n8.23/68.3\n160.5\n7.97/70.9\n55.4\n+ 0.117 - 0.368\n+ 0.099 - 0.337\n+ 0.108 - 0.392\nTOLSTOI 1913\n7.43/60.8\n6.68/62.8\n161.5\n7.66/64.2\n55.8\n+ 0.197 - 0.354\n+ 0.182 - 0.320\n+ 0.206 - 0.363\nRUTH 1950\n8.68/45.3\n7.93/44.7\n8.97/44.8\n161.6\n+ 0.066 - 0.131\n+ 0.042 - 0.093\n55.0\n+ 0.005 - 0.101\nCOLD 1911\n3.10/48.8\n2.10/51.8\n1.80/85.5\n162.4\n+ 0.126 - 0.089\n+ 0.103 - 0.047\n+ 0.084 - 0.044\n55.2\nCOVE 1923\n4.21/21.9\n3.30/14.7\n2.72/16.6\n- 0.007 0.020\n55.1\n- 0.033 + 0.065\nSHORT 1952\n- 0.074 + 0.157\n0.41/237.8\n163.3\n1.55/229.1\n3.60/230.7\n- 0.011 + 0.048\n54.7\n+ 0.019 + 0.003\n- 0.099 + 0.104\nBROAD 1901\n0.58/354.6\n0.92/248.2\n3.58/211.1\n163.3\nDifferences in latitude and longitude are published values minus adjusted positions.\n* The vector is shown with the distance in meters and the azimuth in degrees,\ni.e., at COLD 1920 the distance is 20.53 meters and the azimuth is 93.9.","674\nConclusions\nThis test has shown very convincingly that Doppler positions can be\nused to update networks which have been distorted by past adjustment\npractices. When the update requirement involves seismic disturbances, there\nshould be no unresolvable problems except on those occasions where\ndiscontinuities (local crustal motion) exist. Although Alaska experiences\nmore earthquakes than any other State, the stations are widely spaced. Future\ninvestigations of the dense triangulation in California, now in the planning\nstage, are certain to provide many answers to this most serious problem in\nmaintaining viable networks.\nIn areas such as the Alaska Peninsula, where one must assume there is\nmovement because of the nearness of plate boundaries, reobservations of the\nDoppler sites at intervals of one or two decades would disclose eventually,\nwhether or not this is the case. Looking ahead, other developments such as\nVLBI (very long base line interferometry) and laser-ranging techniques will\nbe able to provide even more accurate information over much shorter time\nintervals. However, for this equipment to be carried into isolated areas such\nas the Alaska Peninsula, it must be more portable than that now available.\nReferences\nDracup, J. F., 1975: Use of Doppler positions to control classical geodetic\nnetworks. Presented to XVI General Assembly of International Association\nof Geodesy, International Union of Geodesy and Geophysics, Grenoble,\nFrance, August, 12 pp. National Ocean Survey Reprints 1975, National\nOceanic and Atmospheric Administration, U. S. Department of Commerce,\nWashington, D. C. (in press).\nMeade, B. K., 1974: Doppler data versus results from high precision traverse.\nProceedings of International Symposium on Problems Related to the\nRedefinition of the North American Geodetic Networks. The University of\nNew Brunswick, Fredericton, N. B., Canada, May 20-25. The Canadian\nSurveyor (Ottawa, Canada), Vol. 28, No. 5, pp. 462-466.\nMeade, B. K., (National Ocean Survey, National Oceanic and Atmospheric\nAdministration, U. S. Department of Commerce, Washington, D. C.) 1976:\nReport on evaluation of horizontal control in southwestern Alaska.\nReview prepared to ascertain the need for readjustment of control to meet\nchanging requirements (unpublished manuscript).\nMoose, R. E., and Henriksen, S. W., 1976: Effect of Geoceiver observations\nupon the classical triangulation network. NOAA Technical Memorandum\nNOS-66-NGS-2, 65 pp. National Ocean Survey, National Oceanic and Atmos-\npheric Administration, U. S. Department of Commerce, Washington, D. C.\nVincenty, T. (National Ocean Survey, National Oceanic and Atmospheric\nAdministration, U. S. Department of Commerce, Washington, D. C.), 1975\n(personal communication on experiments with adjustments of geodetic\nnetworks and related subjects).\nVincenty, T. Determination of NAD 1983 coordinates of map corners. NOAA\nTechnical Memorandum NOS-NGS-6 (submitted for publication 1976).\nNational Ocean Survey, National Oceanic and Atmospheric Administration,\nU. S. Department of Commerce, Washington, D. C.","675\nADJUSTMENT OF TERRESTRIAL NETWORKS\nUSING DOPPLER SATELLITE DATA\nMark G. Tanenbaum\nNaval Surface Weapons Center\nDahlgren Laboratory\nDahlgren, Virginia 22448\nForeword\nThis paper is an attempt to give further dissemination to results presented\nin 2 previously released government reports:\n\"\nNWL TR-3129 (Oct. 1974) \"Simultaneous Adjustment of Terrestrial\n11\nNSWC TR-3368 (Aug. 1975) \"Error Model for Geodetic Positions\nwritten by Mr. R. Anderle of NSWC Dahlgren Laboratory. Much of the other\nwork reported herein was performed in the Astronautics Division of NSWC/DL\nunder the direction of Mr. Anderle.\nCorresponding to the above reports, this paper is divided into 2 major\nsections. In the first, the Doppler 9D system is analyzed so as to permit\nrecommendation of the form of Doppler normal equations which might contribute\nto combined satellite-survey adjustments. The second section gives results\nof preliminary experiments testing the consistency of satellite and survey\ndata in joint adjustments.\nAbstract\nA discussion of systematic and random errors in Doppler determined posi-\ntions is given as a basis for writing the proposed Doppler normal equations\nfor geodetic uses. It is shown that these equations are most naturally\nexpressed by simulated observations of station positions.\nExperiments presented in combined adjustment of geodimeter survey results\nand Doppler positions demonstrate the consistency of these data types even\nwhen the Doppler positions are weighted according to the accuracy of reposi-\ntioning (approximately 70 cm in each coordinate).\nIt is recommended that datum refinement be based on simultaneous adjust-\nment of terrestrial and Doppler satellite data in order to obtain the most\nbenefit from both the precise relative terrestrial measurements and the accurate\nabsolute positions established by the Doppler system. The vertical adjustment\nshould be made prior to or concurrently with the horizontal adjustment so\nthat the strong Doppler height determination can be used to prevent distortion\nof the vertical datum at edges or along spurs which could transfer errors into\nthe horizontal positions.","676\nDoppler Satellite-Derived Positions\nIntroduction\nDoppler observations of Navy Navigation Satellites have been used by the\nDepartment of Defense for over 10 years to determine the geodetic positions\nof isolated sites. This effort has resulted in the establishment of a highly\nconsistent geodetic system with global accuracy of the order of a few meters.\nRecently the Doppler station network has been used to connect and determine\nthe origins of a large number of terrestrial datums in the development of the\nDepartment of Defense World Geodetic System 1972 (Seppelin, 1974). Doppler\ncontributions to national survey datum definition or refinement has also\nbeen considered for the United States (Meade, 1974; Anderle, 1974), Canada\n(McClellan, 1974), and elsewhere.\nComputations in the Doppler 9D System\nThe detailed mathematical methods for computing the precise satellite\nephemeris and station positions are given by Anderle (1976) and Beuglass\n(1975). To summarize the usual procedure briefly, on alternate days, 48 hours\nof current Doppler observations, collected by about 20 semi-permanent stations,\nof a polar Navy Navigation Satellite were first used in a batch estimation\nprocedure determining the precise orbit, allowing adjustment of satellite\ninitial conditions, an atmospheric drag force multiplier, 2 components of pole\nposition, and, for each pass of the satellite tracking data, a frequency bias\nand a tropospheric refraction multiplier, (observed to vary 10% from nominal).\nThe observing stations and the remainder of the force model, including 480\nterms in a harmonic expansion of terrestrial gravitation, solar and lunar\ngravitation and induced tidal attraction, and direct solar radiation pressure,\nwas held fixed. Numerical integration and interpolation were used to solve\nthe orbit and variational differential equations in the UTC time system.\nClassical rigid-earth theory with polar motion and U.S. Naval Observatory\npredicted UT1-UTC values related the station and satellite at observation\ntimes. Precise positions for new integrated Doppler stations were determined\nindependently by an iterative adjustment for the 3 station coordinates and 2\nbias parameters for each of 20 or more passes of satellite data, holding fixed\nthe precise satellite positions, and terminating when consistent rejection\nof passes occurred. Treatment of historical sites at which sampled Doppler\ndata was collected was similar (until January 1976) except for the omission\nof the tropospheric refraction multiplier and the retention of a standard\nrefraction model typical of winter conditions at the APL site. After cali-\nbration of station clocks in the UTC system, Doppler tracking data to be used\nabove was corrected for first order ionospheric refraction by the 2-frequency\nmethod, and weighted, for inclusion in the normal equations, in an iterative\nprocedure, according to the consistency of accepted observations with the\ntrial orbit and station after adjustment for systematic pass orbit and obser-\nvational biases. Computations according to these procedures (since 1971) using\nspecific earth-gravitational fields and permanent tracking station positions\ngave the satellite and new station coordinates in the 9D satellite-geodetic\nsystem.","677\nInternal Consistency\nFormal standard errors, obtained by inversion of the normal equations, of\n20-50 cm in each coordinate are computed for Doppler tracking stations based\non 20 or more satellite passes. However, such 5-day coordinate solutions are\nrepeatable only to 70 cm (rms) over time spans of 1 year, and only to 1.6 meters\n(rms) over 9-year spans (see Tables 1 and 2, Fig. 1, references: Anderle (1973),\nBeuglass (1974)) even after allowance for coordinate drift rates, many of\nwhich (especially the heights) are both statistically significant and unphysi-\ncally large. While there is no reason to believe that such long-term trends\nwill continue, periodic short-term variability (see Fig. 2, assembled from\nAnderle 1976) at the 1-meter level (possibly due to defective gravitational,\ntidal or earth-motion models) is occasionally observed even with modern data.\nSignificant auto-correlations of \"actual\" errors in coordinates, defined by\ndeviation of 57 independent 5-day solutions using 1974 data from the yearly\nmeans, often persisted (see Table 3) for lags of 25 days. Therefore, data\nspans longer than 1 month would be needed to reduce the standard error of\npositioning much below the 70 cm level.\nFormal error correlations between coordinates of a station are mostly\n.1 or less except for unexplained height-latitude correlation (see Fig. 3)\nwhich varies progressively, from about .3 in the north to +.3 near the south\npole. Correlations of the actual errors of 5-day solutions have not followed\nthis pattern (see Table 4) but appear to be driven by a few anomalous results\nfor small numbers of passes in which higher correlations would be expected.\nAbout half of the cross-correlations of actual errors were statistically\nsignificant and in the ranges of (-.6, .2) and (.2, .6). In many cases the\ncorrelations were positive for neighboring stations and negative for distant\nstations (see Fig. 4) although there were many exceptions. Systematic tracking\nnetwork errors could explain these correlations.\nIn a previously unreported study, simultaneous determination of all station\npositions and orbit constants was attempted for 89 2-day spans of polar satellite\ntracking data. Although station coordinate excursions, from values believed\naccurate to 2 meters, of 10 meters or more (excluding longitude shifts) were\nnoted, they were satisfactorily resolved into random coordinate movements\n(rms 2.5 meters) with systematic (principally AZ) network shift. The unexpected\nAZ network weakness was echoed, although at a reduced level, in the formal\ncovariance matrix for network motions developed from the tracking data normal\nequations. A parallel experiment with 18 sets of non-polar normal equations\nsuggested that network Z-axis weakness is associated with polar satellite data\nonly.\nExternal Comparison\nComparison to external systems may be made for estimation of random errors\nor calibration of systematic errors. Comparisons of precise geodimeter survey\nnetworks, which are currently the only available standards having sufficient\ndensity and precision, confirm the 70 cm internal accuracy estimate of Doppler\n9D coordinates (see Part II of this paper for example).","678\nAlthough its source is still a subject of current study, the existence\nof a 1 ppm Doppler scale bias is a well documented fact. Table 5 presents a\ndetailed summary of Doppler with geodimeter and VLBI results, prepared in 1973.\nRecent comparisons (Strange et al, 1975 and Part II of this paper) continue\nto support this observation.\nBecause of the high correlation, in Doppler satellite tracking normal\nequations, with orbit-plane orientation and (for pole position only) gravity\nfield terms, tracking system orientation must be established by external means.\nPole re-orientation (holding fixed the NWL 9B gravity field) was last performed\nin 1971 to establish the 9D system (Beuglass & Anderle, 1972) so as to minimize\ndeviations of Doppler-defined and BIH pole computations at 4 sample times\nduring that year. Although Doppler and BIH computations have since agreed to\nabout 50 cm, comparison of the 9D system with other astrometrically established\nsatellite and survey systems (Fig. 5) shows a possible bias of up to 6 meters\nthat is further substantiated by comparison with an unpublished Doppler general\ngeodetic system (NWL 10G) in which BIH pole positions for contributing satellite\ntracking data spans were observed with standard error 50 cm. In 1973, NSWC\nfound the longitude error of the 9D system to be 0.26 by comparison with gravi-\nmetric NAD datum shift, which it now seems (personal communication, White,\n1976) incorporated an 0.51 local datum offset relative to the Greenwich Mean\nMeridian.\nThe origin of the Doppler system is defined to be the center of mass of\nthe Earth. This assumption was tested by allowing adjustment of an origin\noffset and scale minimizing height deviations between the geometric geoid,\ndefined by mean-sea-level subpoints (below the solution point according to\nthe surveyed height of the antenna electrical center) of Doppler 9D stations,\nand a dynamic geoid. Use of the SAO-II, or Vincent & Marsh '73 geoids resulted\nin origin offsets of the order of 1 meter and rms height residuals of 7 to 9\nmeters which are consistent with neglected high frequency geoid undulations.\nNormal Equations\nTaking into account all of the foregoing, a preliminary recommendation\nwould be to derive the normal equations for Doppler-defined survey points\nfrom observations of uncorrelated coordinates and admit system scale,\norientation, and origin errors with standard errors as follows:\nValue\nStandard Error\nQuantity\n9D-survey\n.7 meter\nCoordinate: 0, l\n9D-survey\n7 meter\nh\n:\n0.77\nOrientation: l\n8\n0\n.5 urad.\n: pole\n0\n1.0 meter\nOrigin: equator\n0\n1.0 meter\n: pole\n-1.1 ppm.\n.2 ppm.\nScale","679\nwhich is equivalent to ignoring long-term internal accuracy estimates, and\nassuming that Doppler coordinate correlations derive from changing systematic\nnetwork errors. While there may be uncertainty as to the standard errors\nassigned to systematic errors, retention of these parameters into the final\nsolution stages of the combined Doppler and survey normal equations will allow\ninexpensive experimentation.\nPART II\nCombined Satellite-Survey Adjustments\nBackground\nDuring 1974, Meade of the U.S. National Geodetic Survey presented a\ncomparison of Doppler satellite determinations of the positions of survey\npoints with positions resulting from a preliminary adjustment of terrestrial\ndata obtained during an extensive geodimeter traverse. Meade found the mean\ndeviation to be slightly over 1 m for 38 sites distributed over the entire\ncontiguous United States (Fig. 6, Table 6). While this is a satisfying result,\nsystematic differences were present in the residuals. This section presents\nthe results of one adjustment, based on the residuals presented by Meade,\nintended to be representative of results which would be obtained from simul-\ntaneous adjustment of the source satellite and terrestrial data. The study\nwas conducted to further evaluate the degree of consistency between the\nterrestrial and satellite data in order to obtain better bounds on the\naccuracy of each data type.\nProcedure\nThe nominal coordinates shown in Table 6 were orbitrarily assigned as\ngeodimeter positions obtained from Meade's preliminary adjustment, for purposes\nof this study; Doppler solutions were taken to be at locations displaced from\nthe geodimeter positions by the amounts given by Meade, Table 6. Distances,\nazimuths and elevation angles were computed between the assigned geodimeter\npositions around loops A, B, C and D and along spurs a and b shown in Fig. 7\nand listed below:\nLoops and Spurs\nLoop A Stations 3, 7, 10, 11, 12, 13, 16, 15, 14,\nLoop B Stations 8,9,21,8\nLoop C Stations ,21,20,19,18,17, 16, 13, 12, 11, 10,8\nLoop D Stations 9,20,21,22,34, 33, 32, 31, 30, 29, 28, 27,26,19\nSpur a Stations 3,4,5\nSpur b Stations 22,23,24,25\nThe loops and spurs follow Meade's diagram reasonably well except for\nthe omission of the intermediate stations and the resulting distortion in the\nsmall loop, B. Results for the last four stations listed by Meade were","680\nomitted since the stations were not on the traverse; therefore the study was\nbased on data for 34 stations.\nNormal equations were formed on the basis of the Doppler positions and\nthe geodimeter distances, azimuths and elevations for the best fitting sets\nof coordinates for the 34 station and relative origin, scale and orientation\nbetween the coordinate systems.\nWeights for the Doppler positions were initially taken to be the reciprocal\nsquares of 1.2 m, 1.5 m and 1.6 m in latitude, longitude and height, the esti-\nmated accuracy of Doppler positions given by Anderle (1974a). Weights for the\ngeodimeter \"measurements\" were initially taken to be the reciprocal squares\nof 1 ppm, .8 sec, and .4 sec in distance, azimuth and elevation. The distance\nand azimuth accuracies were given by Meade; the elevation angle accuracy is\noptimistic compared to Bomford's (1971) accuracy estimate for a geoid profile\nshorter than 500 km, but this formulation of the problem does not consider\nthe contribution to the geoid accuracy from profiles parallel to the geodimeter\ntraverses. Standard errors were recomputed for each solution with the coor-\ndinates of station 20 held fixed in order to separate the uncertainty in\nsystem origin from uncertainty in relative station positions.\nWhile the foregoing model omits detailed treatment of each geodimeter\nstation, it is felt that, in practice, the solution can be extended to include\neach site using one of the techniques designed for sparse networks (Ashkenazi,\n1974) without affecting the consistency of the results obtained in the pilot\nstudy.\nAlthough the use of adjusted terrestrial data in this experiment masks\nthe misclosure of the traverse, it does highlight discrepancies between\nterrestrial and satellite data. In an operational reduction, unadjusted\nterrestrial data should be used so that maximum utilization is made of the\nDoppler data in distributing the misclosure.\nAdjustment Based on a A-Priori Weights\nIn the first experiment, the nominal weights for the observations were\nused in a solution for site coordinates and the scale for the Doppler system.\nA scale solution of -1.002 ppm and the site coordinates gave the Doppler and\ngeodimeter residuals shown in Figs. 8a and 8b and also in Tables 7a and 7b.\nThe standard error of the solutions are given in Table 7c. For the observation\nweights used, the Doppler residuals were only about 70% of the assumed standard\ndeviaiton of observation and the geodimeter residuals were only about 30% of\nthe assumed standard deviations. The differences in North Western U.S. are\nof particular interest. Preliminary comparisons of Doppler and terrestrial\ndata gave anomalous results in this area, and Fig. 8 also appears to show\ninconsistencies in the area. However it is not apparent from the data that\nthe differences are primarily in the terrestrial azimuths, residuals for which\nare well within the uncertainty of measurements. Detailed Doppler results\nfor this area are as follows:","681\nResiduals\nLongitude\nHeight\nStation\nLocation\nLatitude\n-1.2 m\n30\nCentral Calif.\n-.1 m\n.6 m\n.4\n29\nNo. California\n.3\n-.5\n28\nWashington\n-.2\n-.4\n.1\n-.6\n27\nNebraska\n-.3\n.3\nThe remarkably good results for the terrestrial distances and quite satis-\nfactory results for terrestrial azimuths and elevations are given below:\nResiduals\nElevation\nLine\nDistance\nAzimuth\n30\" = 1.0 m\n.17\"\n= .6 m\n31-30\n.00 ppm = .00 m\n39\"\n.04\"\n.7 m\n=-.1 m\n30-29\n.01 ppm = .00 m\n=\n33\" = 1.9 m\n.05\" = .3 m\n29-28\n.24 ppm = .21 m\n-.50\" =-2.8 m\n.08\"\n.5\n28-27\n.01 ppm = .01 m\n=\nm\n.70\" = 3.8 m\n.16\" = .9 m\n21 ppm = .17 m\n27-26\nThe rms of the distances of all lines, given as .13 ppm in Fig. 8b,\ncorresponds to 9 cm for the length of lines involved, while the maximum\nresidual distance of any line was -33 cm, corresponding to - -.38 ppm on that\nline from Texas to New Mexico. Even considering that a scale parameter was\ndetermined in the adjustment, the rms scale residuals are remarkably good.\nThere is also evidence that improved Doppler processing procedures might\nimprove the Doppler residuals, which are shown to be 65 to 100 cm in Fig. 8a.\nA substantial portion of the contribution to the Doppler residuals arises\nfrom a few inconsistent results such as station 22 and 32 in New Mexico and\nsouthern California, where neighboring stations have latitude residuals with\nopposite signs. The positions of these stations were computed using different\nprocedures for calculating the effect of tropospheric refraction. Fig. D5\nof Defense Mapping Agency Report 0001 shows that such differences in latitudes\nwill occur according to whether a tropospheric refraction parameter is con-\nsidered a parameter of each satellite pass. (The cause of the difference is\nnot fully understood, nor is there a consensus on which procedure is more\nlikely to be correct.)\nExperiments Varying Weights for the Observations\nSince both Doppler and terrestrial residuals were below the a-priori\nstandard deviations assigned to the observations, the a-priori standard\ndeviations were varied in an attempt to find the minimum values equivalent\nto the residuals. Results for a series of cases given in Table 8 show that\nterrestrial residuals remain below their a-priori levels for reductions in\na-priori standard deviation of Doppler or terrestrial date by 70% or more.\nDoppler residuals, although not strongly sensitive to changes in a-priori\nestimates of terrestrial data in this range, exceed their own a-priori\nestimate when the latter are reduced by about 50%. Standard deviations of","682\n61, 53, and 83 cm in Doppler latitude, longitude and height are consistent\nwith the Doppler residuals of fit when the terrestrial data are assigned stan-\ndard deviation of 1.0 ppm, .8\" and .4\" in distance azimuth and elevation.\nUnder these conditions, the terrestrial residuals are .35 ppm (or 19 cm),\n.38\", and .21\" in distance, azimuth and elevation. The detailed residuals\nare shown in Figs. 9a and 9b for Doppler and terrestrial data, respectively,\nand the standard errors of the solutions for station position are given in\nTable 9. The Doppler residuals compare favorably with the consistency of\nDoppler solutions across five day time periods in 1973 which was 72, 74 and\n73 cm (Beuglass, 1974). Using the same standard errors of observation except\nincreasing those for stations 22 and 32 by a factor of 10 reduced the Doppler\nresiduals to 38, 36 and 76 cm in latitude, longitude and height, showing the\nimportance of a consistent reduction of the Doppler data.\nRecommendation\nNational survey datum readjustment should be based upon a combination of\nDoppler satellite and terrestrial data in order to make the best use of the\nprecise relative distances measured by the geodimeter and the accurate absolute\npositions established by the Doppler system. The vertical adjustment should\nbe made prior to or simultaneously with the horizontal adjustment in order\nthat the strength of the Doppler determinations of absolute height can be used\nto prevent distortion of the vertical datum at the edges or along spurs which\nwould transfer errors into the horizontal adjustment. Certain Doppler posi-\ntions should be recomputed to remove inconsistencies produced by different\ncomputational techniques.\nReferences\nAnderle, Richard J., \"Determination of Polar Motion from Satellite Observations\",\nGeophysical Survey 1 (1973).\nAnderle, Richard J., \"Transformation of Terrestrial Survey Data to Doppler\nSatellite Datum\", Journal of Geophysical Research, 1974a.\nAnderle, Richard J., \"Role of Artificial Earth Satellites in Redefinition of\nthe North American Datum\", The Canadian Surveyor, 1974b.\nAnderle, Richard J., \"Point Positioning Concept Using Precise Ephemeris\",\npreprint of paper to be presented at the International Symposium on\nSatellite Doppler Positioning, Las Cruces, New Mexico, 1976.\nAshkenzai, V., \"An Assessment of the Proposed Readjustment of the North\nAmerican Horizontal Geodetic Control Networks\", preprint of paper presented\nat the International Symposium on Problems Relative to the Redefinition of\nNorth American Geodetic Networks, Fredericton, Canada, 1974.\nBeuglass, Larry K., \"Pole Position for 1973 Based on Doppler Satellite Obser-\nvations\", NWL Technical Report, 1974.","683\nBeuglass, Larry K. , and R. J. Anderle, \"Refined Doppler Satellite Determinations\nof the Earth's Polar Motion\", Geophysical Monograph Series, Vol. 15, AGU,\n1972.\nBeuglass, Larry K., , \"Computation of Positions of Doppler Satellite Observing\nStations\", NSWC/DL Technical Report TR-3173, 1975.\nBomford, G., Geodesy, 3rd Edition, p. 367, Claredon Press, Oxford, 1971.\nMcClellan, C. D. \"Geodetic Networks in Canada\", presented at the International\nSymposium on Problems Related to the Redefinition of North American\nGeodetic Networks, 1974.\nMeade, Buford, \"Doppler Data versus Results from High Precision Traverse\",\nPreprint of paper presented at the International Symposium on Problems\nRelated to the Redefinition of North American Geodetic Networks, Frederiction,\nCanada, May 1974.\nSeppelin, Thomas 0. , \"The Department of Defense World Geodetic System 1972\",\npaper presented at the Symposium on Problems Related to the Redefinition\nof North American Geodetic Networks, 1974.\nStrange, W. E. et. al., \"Results of Doppler Station Positioning in the United\nStates\", presented at the 56th annual AGU meeting, June 1975.\nVincent, Samir and James G. Marsh, \"Global Detailed Gravimetric Geoid\",\nMay 1973.","Residuals\n142\n135\n118\n159\n155\n188\n206\n242\n143\n132\n186\nCM\n164\n142\n158\n127\n92\n266\n114\nHeight\nStd Err\nCM/YR\n12\n17\n8\n18\n13\n16\n16\n28\n11\n11\n13\n12\n13\n9\n19\n24\n8\nCM/YR\n42\n23\nRate\n40\n109\n63\n10\n13\n12\n28\n61\n2\n-11\n47\n50\n-1\n-71\n13\nCONSISTENCY OF SOLUTIONS FOR STATION POSITIONS\nResiduals\n95\n93\n141\n149\n162\n141\n151\n108\n141\n203\n113\n196\n134\n148\n77\n103\n196\n182\nCM\nLatitude\nStd Err\nCM/YR\n12\n16\n12\n13\n9\n12\n6\n16\n11\n24\n9\n11\n12\n6\n22\n18\n13\nCM/YR\nFROM 1964 - 1972\n-8\n-16\nRate\n-8\n6\n-9\n-20\n-15\n-25\n-9\n-31\n5\n-26\n-30\n-17\n0\n-7\n11\nTable 1\nResiduals\n140\n146\n152\n167\n213\n189\n228\n223\n146\n153\n157\n207\n149\n129\n125\n121\n188\n174\nCM\nLongitude\nCM/YR\nStd Err\n18\n16\n11\n19\n10\n26\n12\n15\n11\n17\n12\n11\n9\n26\n17\n13\n17\nCM/YR\n46\n-1\n11\n-19\nRate\n-27\n49\n20\n-20\n-6\n-26\n54\n-4\n4\n38\n33\n19\n0\nAvg No\nPasses\n35\n48\n29\n26\n45\n43\n42\n37\n34\n45\n88\n115\n88\n35\n38\n38\n61\nNo. Spans\nof Data\n34\n39\n26\n49\n33\n43\n37\n32\n36\n32\n36\n39\n36\n20\n36\n63\n39\nNew Mexico\nPhilippines\nMinnesota\nGreenland\nSeychelles\nSo. Africa\nCalifornia\nStation\nMcMurdo\nMaryland\nAustralia\nAverage\nEngland\nHawaii\nSamoa\nAlaska\nMaine\nBrazil\nJapan","Residuals\nCM\n70\n84\n55\n73\n78\n74\n78\n74\n71\nHeight\nStd Err\nCM/YR\n36\n30\n34\n34\n33\n29\n37\n23\nCONSISTENCY OF SOLUTIONS FOR STATION POSITIONS FOR 1973\nCM/YR\n54\n-102\n-36\n-35\n-11\nRate\n-95\n-2\n35\nResiduals\nCM\n99\n59\n82\n82\n54\n85\n56\n49\n71\nLatitude\nStd Err\nCM/YR\n39\n23\n50\n27\n34\n36\n23\n21\nCM/YR\nRate\n34\n-78\n-3\n14\n85\n25\n-55\n-21\nTable 2\nResiduals\n70\n48\n69\n64\n67\n72\nCM\n71\n81\n101\nLongitude\nStd Err\nCM/YR\n32\n20\n30\n36\n30\n33\n45\n28\nCM/YR\nRate\n-8\n-7\n12\n-25\n27\n38\n88\n-23\nPasses\nMean\nAvg.\nNo.\n13\n18\n18\n35\n20\n15\n12\n17\nSpans\nNo.\n69\n69\n45\n66\n70\n66\n70\n71\nSouth Africa\nNew Mexico\nStation\nMcMurdo\nAustralia\nEngland\nBelgium\nBrazil\nJapan","","5-DAY. SOLUTIONS FOR JAPAN\nMODERN DATA\n687\nFIGURE 2\nLONGITUDE 91.2 cm RMS\n3\n2\n1\n0\n-1\nL\n-2\n-3\n13 27\nL\n85.8 cm RMS\n3\nLATITUDE\nFF\nFF\n2\nFF\nF\nF\nFF\n#F\nF\nF\nFF\nF\n0\nFFFF\nFF\nFFP)\nF\n-1\nFFF\nF\nF F\nFF\nFFF\nFF\nF\n-2\nF\nF\n-3\nHEIGHT\n105.5 cm\nRMS\nH\n3\nH\nH\nH\nH\nH\nH\nH\n2\n144\nHH\nH\nH\nHH HH\nH\nHM\nH\nH\nH\nH\n1\nHIH\nH\nH\nH\nH H\nHH\nor\nHH\nHH\n34\nH\n134\nH\nH\nH\n0\nH\nHIH\nH\nH\nH\nRUN\nHH\nH\nHHH\nH\nHH\nHIH\nH\nH\nKIH\nHH\nH\n-1\nH\nHH\nH\nH\nH\nHHH\nH\nH\nH\nH\nH\nH\n-2\nH\nH\n-3\nH\n1976\n1973\n1974\n1973","","689\nTable 3\nCORRELATIONS\nSTATION HEIGHT CORRELATION DISTANCE IN 5-DAY SPANS\nAUTO\n5\n3\n4\n2\nNO\n1\n.688\n.627\n.524\n.588\n.657\n8\n.346\n.571\n.550\n.512\n14\n.661\n-.054\n.019\n-.028\n.196\n.136\n16\n.197\n.330\n.132\n.204\n.176\n15\n.063\n-.192\n-.016\n-.151\n19\n-.264\n.054\n.170\n.156\n.233\n20\n.221\n.267\n.270\n.395\n.212\n21\n.401\n.204\n.574\n.318\n.061\n22\n.098\n.209\n.370\n.502\n.444\n23\n.593\n.113\n.162\n.316\n.164\n24\n.114\n.083\n.098\n.121\n.332\n.260\n27\n.020\n-.086\n-.000\n.270\n,017\n103\n-.067\n-.096\n.328\n.309\n-.001\n105\n.161\n.076\n.301\n.258\n.085\n111\n, 150\n.225\n.503\n.469\n.365\n112\n.277\n.290\n.219\n.227\n.448\n192\n.214\n.263\n.405\n.406\n.492\n311\n-.037\n.202\n.347\n.080\n321\n.506\n-.050\n.176\n.205\n.093\n323\n.111\n.105\n.147\n,419\n.535\n.496\n332\n.200\n.442\n.318\n.161\n.445\n340","690\n4\nTABLE\nCORRELATION BETWEEN ACTUAL ERRORS\nFOR PAIRS OF STATION COORDINATE COMPONENTS\nCORRELATIONS BETWEEN COORDINATES\nZ TEST VALUES\nNO\nCORRELATIONS\nSTATION\nLAM-PHI PHI-HT LAM-HT LAM-PHI PHI-HT LAM-HT -\nSPANS\nNO\n-.08\n54.\n.022\n-.011\n.41\n.15\n.058\n8\n.26\n57.\n-1.25\n.94\n.035\n-.170\n.128\n14\n-6.22\n57.\n4.10\n-3.44\n.507\n-.437\n-.689\n16\n-1.55\n56.\n1.19\n-2.94\n-.210\n.162\n-.384\n18\n55.\n.32\n6.25\n-.39\n.045\n.700\n-.054\n19\n.66\n56.\n-1.49\n-.202\n.090\n-1.40\n-.190\n20\n57.\n-.59\n.43\n.86\n.116\n-.080\n.058\n21\n-2.31\n54.\n1.40\n-.78\n-.313\n22\n.193\n-.109\n54.\n-.57\n2.45\n.51\n.330\n.072\n23\n-.079\n57.\n.13\n-2.26\n-2.22\n-.298\n-.294\n24\n.018\n57.\n-.19\n-1.01\n-.137\n-2.19\n-.026\n27\n-.289\n-5.15\n57.\n.91\n.123\n-.to\n1.42\n.191\n103\n-1.59\n1.47\n-4.23\n53.\n.204\n-.535\n105\n-,221\n-2.42\n57.\n-.318\n.04\n1.34\n.005\n.131\n111\n-.67\n57.\n-.091\n-.42\n-.29\n-.057\n-.039\n112\n51.\n-.003\n3.59\n-2.89\n-.06\n.477\n-.394\n192\n2.53\n.67\n57.\n-.258\n.331\n.091\n-1.94\n311\n-.25\n.68\n46.\n.104\n-.40\n-.061\n-.039\n321\n-.97\n33.\n-.237\n-.175\n.73\n-1.32\n323\n.132\n54.\n-.163\n1.40\n.37\n-1.17\n.051\n332\n.194\n-2.40\n3.60\n57.\n-.155\n-.315\n.454\n-1.15\n340","----------------\nMc MUR DO\n120\nCORRELATION COEFFICIENTS FOR HEIGHT\nDIFFERENCE IN LATITUDES OF SITES\nALASKA VS OTHER SITES\nAFRICA\nSEYCHELLES\nAUSTRALIA\n90\nPHILIPPINES\nFIGURE 4\nSAMOA\n60°\nGUAM\nNEW MEXICO\nHAWAII\nCALIFORNIA\nGREENLAND TEXAS\nMINNESOTA\nMINNESOTA\nJAPAN\n30°\nMAINE\nENGLAND\nMARYLAND\n.6 BELGIUM\n0\n4\n.2\n0\n-.2\n-.4\n- .6","692\nTable 5\nSCALE BIAS OF NWL-9D POINT POSITIONING RESULTS\nComparison to Geodimeter Scalars (Worldwide BC-4 Network)\nNWL-9D Minus Survey\noDifference\nParts Per\nChord\n(PPM)\nLength\nMeters\nMillion (PPM)\nChords\nNAD 27:\n1.09\n3.5\n1.0\nB002 B003\n3485 km\nED:\n1.08\n6.5\n1.8\n3545\nB006\nB016\n1.59\n3.0\n1194\n3.6\nB016\nB065\n1.17\n1.7\n2457\n4.1\nB006\nB065\nAGD:\n1.19\n-2.2\n1.0\nB023\nB060\n2300\n1.10\n1.3\n0.4\nB032\nB060\n3163\nAfrica:\n1.09\n4.2\n1.2\nB063 B064\n3485\n0.44\nWeighted Mean/Standard Error of Mean\n1.05\nComparison to VLBI Chords\nNWL-9D Minus VLBI\noDifference\nChord\nParts Per\n(PPM)\nMeters\nMillion (PPM)\nChords\nLength\n0.46\n0.6\nHaystack -> Goldstone\n3900 km\n2.5\n0.48\n2.6\n0.7\nAlaska Goldstone\n3800\n0.36\n1.6\nHaystack Alaska\n5000\n7.8\n0.36\nWeighted Mean/Standard Error of Mean\n1.09\nComparison to Geodimeter Networks (Seven Parameters Transformations)\noDifference\nAreal\nNWL-9D Minus Survey\n(PPM)\nExtent\nParts Per Million (PPM)\nNetworks\nUnited States:\n16° X 30°\n0.21\n1.19\nCCD 18 stations\n16° X 43°\n0.17\n1.55\nCCD 19 stations\n16° X 43°\n0.23\n1.05\nCCD 20 stations\n15° X 22°\n0.41\n1.31\nMR-72 6 stations\n15° X 22°\n0.44\n1.08\nMR-72 8 stations\n0.91\n0.60\nAustralia 3 stations\nUnder AGD\n(First Table)\n0.16\nWeighted Mean/Standard Error of Mean\n1.17\n0.13\nWeighted Mean/Standard Error of Mean\n1.14\n*\nFrom all Table 5 sources.","X (m)\n10\n18 Geodimeter Sites on CCD\n6 STNS\nComparison Of Orientation Of Z Axis\nSAO III\nMR-72\nB-N\nGSFC 73\nNWL 10G\n+\n+\n+\nY (m)\nFIGURE 5\n5\n+\n5\n+\nSAO II\n+\nMEADE 21 STNS\nWith NWL 9D\n+\nMEADE 32 STNS\n+\nBC-4\n-5\nSAO III\n+ BC-4\n-10","----------\n-\nO 2 of E\nMETERS\nVECTOR\nSCALE\nGEODIMETER TRAVERSE TO DOPPLER NWL 9 D\nPOSITION SMIFT\n(MEADE, 1974)\nFIGURE 6","5\na\n2\n4\nREPRESENTATION OF TRAVERSE DATA BY DISTANCES,\nI\nAZIMUTHS, ELEVATIONS ALONG LOOPS A, B, C, D,\n3\n14\nA\n7 6\nO\n15\n13\n12\n€\nSPURS a, b THROUGH 34 STATIONS\n16\n011\n00\n8\n17\n9\nL\nB\n18\nFIGURE 7\n20\n19\n21\n26\n23\nb24\n27\n22\ne\nD\n34\n33\n0\n32\n28\n31\n30\n29","696\nTABLE 6\nPOSITION DIFFERENCES AND NOMINAL POSITIONS\nTraverse Minus Doppler\nNominal Position\nSite Doppler\nHeight Latitude Longitude Height\nLongitude\nLatitude\nNo\nNo\n-2.6m\n-.5m\n283.17419°\n.9m\n39.02772°\n5.7m\n20001\n1\n.2\n1.0\n2.2\n0\n34.07\n281.85\n51008\n2\n-4.0\n-1.6\n2.8\n30.94880\n278.31881\n-26.5\n3\n20015\n.1\n0\n2.8\n28.00\n279.55\n0\n4\n51014\n-.3\n.3\n2.8\n0\n25.82\n279.71\n51015\n5\n-.4\n.8\n3.4\n0\n30.77\n274.25\n6\n51012\n-1.5\n.5\n4.0\n41.0\n30.56787\n273.78363\n10028\n7\n-2.3\n-.8\n1.8\n78.1\n31.21252\n270.25418\n20016\n8\n.1\n-1.6\n1.2\n33.47855\n268.99731\n8.3\n9\n10003\n.9\n-.5\n1.2\n104.1\n33.56527\n270.83431\n10023\n10\n.5\n-2.0\n1.2\n34.78771\n271.75816\n213.3\n11\n10022\n-2.5\n-1.5\n1.2\n266.8\n37.55189\n273.91955\n10021\n12\n-1.8\n-1.7\n.6\n38.58914\n274.35197\n177.5\n13\n10020\n-.9\n0\n.3\n40.08655\n278.26103\n361.5\n14\n30025\n-2.2\n-.9\n.3\n277.2\n40.16428\n275.39063\n15\n30027\n-1.2\n-.7\n.9\n224.0\n40.23528\n274.17403\n16\n10019\n-1.1\n-.9\n-.3\n212.8\n40.82233\n270.71099\n17\n30028\n.6\n0\n-.9\n0\n264.25\n41.48\n18\n51033\n1.0\n-.7\n0\n39.22406\n261.45763\n567.5\n10006\n19\n1.6\n-.9\n-.3\n0\n35.85\n262.12\n51030\n20\n.1\n.8\n-.3\n294.0\n262.02101\n30.44691\n10018\n21\n1.5\n-.3\n-3.1\n1171.7\n32.27887\n253.24596\n20002\n22\n-.8\n2.3\n-.6\n1345.1\n33.02673\n253.86159\n10045\n23\n1.2\n1.8\n-1.8\n253.63667\n1235.4\n33.12006\n10046\n24\n-1.0\n1.2\n-3.1\n1318.2\n38.97899\n249.88905\n25\n30030\n2.6\n.7\n255.13181.1\n1860.9\n0\n41.13332\n10000\n26\n4.4\n.2\n1.5\n251.36877\n1007.2\n47.78542\n30099\n27\n.1\n5.7\n-1.8\n240.66199\n340.3\n47.18515\n28\n30029\n.7\n4.5\n-1.1\n39.74572\n237.84940\n69.7\n30098\n29\n1.0\n2.9\n-.3\n13.9\n37.49808\n237.50138\n10055\n30\n-1.6\n2.8\n.9\n759.1\n34.96410\n242.08640\n31\n10032\n.4\n1.0\n-2.8\n2259.7\n34.38182\n242.31930\n32\n20003\n-2.6\n3.5\n1017.3\n-1.2\n243.11138\n35.42773\n33\n10031\n-.7\n3.3\n-2.2\n35.19674\n245.95988\n1149.1\n34\n20208","Residuals\n60\nRESIDUALS OF DOPPLER DERIVED STATION COORDINATES\n1.02\n.69\n.65\nRMS\nWere Scaled By - -1ppm\n5\nNWL 9D Coordinates\nFROM JOINT DOPPLER' are GEODIMETER ADJUSTMENT\nSCALE OF METERS\nMETERS\n4\n65\nAssumed\nStd. Dev.\n3\nLatitude (m) 1.2\nLongitude (m) 1.5\nHeight (m) 1.6\n2\nI\n70\nO\n75\n#\n1.1\n.9\n.5\n80\nO -3\nC\nb\n@\n2.7\n1.0\n85\n5\n-.6\nO\n9\no\nO\n.7\n.5 o -1.5\n1.4\n-1.2 O\n90\nO\no\nCASE 5\n.2\n1.7\nHeight Residuals\nC -.4\nFIGURE 8a\n95\n-1.0\n.0\n(meters)\nO\nO\n100\n-.4\n105\n- 1.3 O\n-.9\n1.\no\nO\n.3\n1.2\n5\nO\n110\nf\n-\nO\nO -.0\n115\n128.8\nO\nO\n120\nO\n4\nO\n-1.2\n125\n130\n25\n20\n45\n40\n35\n30\n50","8\nResidals\nShown In Meters Around Spurs a, b\nRMS\n.13\n26\n.11\nDistance And Azimuth Residuals\nRESIDUALS OF GEODIMETER DERIVED STATION COORDINATES\nAnd Loops A, B, C, D To Scale:\n20 -125 -120 - -115 -110 -105 -100 -95 -90 -85 -80 -75 -70 -65 -60\no I 2 3 4 5\nMETERS\nAssumed\nStd. Dev\n1.0\n0,8\n0.4\nFROM JOINT DOPPLER* ENTA GEODIMETER ADJUSTMENT\nDistance (ppm)\nAzimuth (sec)\nElevation (sec)\ng -4\n53.3\n.K\nI\n20-20\nD\nA\no\n.0\n.4\n.5\nOF\n.0\no\nO\n25\n1\nO\n-.0\n-06\nGDD\n2\nO\n00\n-.0\nis\n0\n-.3\nC\n8\nFIGURE 8b\nCASE 5\n.6\nB\nFC\nResiduals (mm)\nElevation\n-1.10\n0-4\n0-0\n.0\n2\n.3\n-\n-.7\n7.7\nb\n.0\n-1.0\n9\nD\nTE\n0.1\nG\n.5\n.6\n3R\n-.00\n-130\n30\n25\n40\n35\n45\n50","699\nTABLE 7a\nDOPPLER RESIDUALS\nCASE 5\nResiduals\nHeight\nLongitude\nLatitude\nSTATION\n1.1m\n-.4m\n.5m\n1\n-1.1\n-.7\n-.5\n2\n2.7\n1.5\n-.2\n3\n-.9\n.0\n.1\n4\n-.5\n-.2\n.3\n5\n-.6\n-.6\n-.3\n6\n.5\n-.3\n-.9\n7\n1.7\n.2\n-.2\n8\n-.5\n.7\n.0\n9\n-1.5\n-.6\n.3\n10\n-1.2\n.8\n.2\n11\n1.4\n.5\n-.3\n12\n.7\n.7\n.2\n13\n-.3\n-.9\n.2\n14\n1.0\n.1\n.3\n15\n.0\n.0\n-.2\n16\n.2\n.3\n.2\n17\n-.4\n-.2\n-.1\n18\n-.4\n.6\n-.7\n19\n-1.0\n-.1\n.6\n20\n.0\n-.4\n.5\n21\n-1.2\n1.5\n1.3\n22\n1.1\n-1.1\n-1.3\n23\n-.9\n-.6\n-.1\n24\n.5\n-.1\n.2\n25\n-1.3\n.3\n.2\n26\n.3\n-.3\n-.6\n27\n.1\n-.4\n-.2\n28\n.4\n-.5\n.3\n29\n-1.2\n.6\n-.1\n30\n.8\n-.2\n-1.9\n31\n-1.2\n1.5\n1.8\n32\n1.8\n-.9\n-.1\n33\n.0\n-1.0\n.5\n34\n1.02\n.69\n.64\nRMS","700\nTABLE 7b\nTRAVERSE RESIDUALS\nCASE 5\nStation Pair\nAzimuth\nElevation\nLoop\nDistance\n.21\"\n(.49m)\n3 4\n.09\n(.03m)\n-.034\n(-.07m)\na\nppm\n(-.13)\n.05\n(.09)\n4 - 5\n.05\n(.01)\n-.08\na\n(-1.27)\n.14\n(.56)\nA\n1 - 2\n-.23\n(-.13)\n-.33\nA\n2 - 3\n.00\n(.00)\n.25\n(.81)\n-.11\n(-.35)\nA\n3 - 6\n-.19\n(-.07)\n.20\n(.53)\n.13\n(.35)\n-.03\n(-.01)\n.00\n(.00)\nA\n6 - 7\n-.01\n(.00)\n-.67\n(-1.98)\nA\n7 -10\n-.23\n(-.10)\n.12\n(.37)\nA\n10-11\n-.04\n(-.01)\n-.04\n(-.04\n-.03\n(-.04)\nA\n11-12\n-.05\n(-.02)\n.12\n(.30)\n-.18\n(-.44)\nA\n12-13\n-.02\n(.00)\n.87\n(.07)\n-.02\n(-.02)\nA\n13-16\n-.03\n(-.01\n.19\n(.24)\n-.01\n(-.01)\nA\n16-15\n.08\n(.01\n.10\n(.07)\n-.05\n(-.04)\nA\n15-14\n.20\n(.05)\n.06\n(.10)\n-.02\n(-.03)\nA\n14- 1\n.17\n(.07)\n-.28\n(-.86)\n-.08\n(-.25)\n(.00)\nB\n8 - 9\n.01\n-.25\n(-.45)\n.11\n(.21)\n9 -21\nB\n-.05\n(-.03)\n-.31\n(-1.55)\n.12\n(.59)\n21-8\n-.18\n(-.15)\n-.27\n(-1.48)\nB\n-.13\n(-.70)\n-.18\nC.\n8 -21\n(-.15)\n-.28\n(-1.55)\n.15\n(.81)\nC\n21-20\n.13\n(.07)\n-.16\n(-.66)\n.11\n(.46)\nC\n20-19\n.15\n(.06)\n.07\n(.19)\n.01\n(.03)\nC\n19-18\n.10\n(.03)\n.08\n(.19)\n-.14\n(-.33)\n18-17\n.06\n(.03)\n-.24\n(-.88)\nC\n-.29\n(-1.10)\nC\n17-16\n.06\n(.02)\n-.35\n(-.73)\n-.13\n(-.27)\n16-13\n.20\nC\n-.03\n(-.01)\n(.25)\n.01\n(.02)\nC\n13-12\n-.02\n(.00)\n.08\n(.07)\n.02\n(.02)\n12-11\n.10\n(.26)\nC\n-.05\n(-.02)\n.18\n(.45)\n11-10\nC\n-.04\n(-.01)\n-.04\n(-.05)\n.04\n(.04)\n10 8\nC\n.00\n(.00)\n-.25\n(-.47)\n.01\n(.01)\nD\n19-20\n.15\n(.06)\n.07\n(.19)\n.00\n(-.01)\nD\n20-21\n.13\n(.07)\n.03\n(.14)\n-.10\n(-.41)","701\nTABLE 7b\n(continued)\nStation Pair\nElevation\nLoop\nDistance\nAzimuth\n21-22\n-.38\n(-.33)\n-.30\n(-1.80)\n.04 (.25)\nD\n22-34\n-.25\n(-.19)\n.09\n(.47)\n-.18 (-.95)\nD\n34-33\n.03\n(.01)\n.26\n(.46)\n-.06 (-.13)\nD\n33-32\n.01\n(.00)\n(.06)\nD\n.31\n(.29)\n.06\n32-31\n.09\n(.01)\n.19\n(.09)\n.00\n(.00)\nD\n31-30\n.00\n(.00)\n.30\n(1.02)\n.17\n(.59)\nD\n30-29\n.01\n(.00)\n.39\n(.68)\nD\n-.03\n(-.05)\n29-28\n.24\n(.21)\n(1.94)\nD\n.33\n.05\n(.32)\n28-27\n.01\n(.01)\n-.51\n(-2.79)\nD\n.09\n(.49)\n27-26\n.21\n(.17)\nD\n.70\n(3.81)\n.16\n(.90)\n26-19\nD\n.03\n(.02)\n.32\n(1.26)\n-.17 (-.69)\nb\n22-23\n.12\n(.07)\n.08\n(.05)\n-.03 (-.02)\nb\n23-24\n.00\n(.00)\n.01\n(.00)\n.01\n(.00)\nb\n24-25\n-.12\n(-.09)\n-.12\n(-.61)\n-.14 (-.73)\n.13 ppm (.09m)\n.26\"\n(1.07m)\n.12\" (.43m)\nrms","702\nTABLE 7c\n(1)\nSTANDARD ERRORS\nCASE 5\nStation 19 Fixed\nOrigin Free\nZ\nY\nX\nZ\nY\nStation\nX\n.91m\n1.07m\n.67m\n1.55m\n2.07m\n1\n.67M\n.94\n1.07\n1.02\n1.52\n2.07\n2\n1.03\n.77\n.97\n.69\n1.34\n.72\n2.07\n3\n.81\n1.05\n1.00\n1.35\n2.12\n4\n1.02\n.84\n1.11\n1.15\n1.37\n2.15\n5\n1.18\n.80\n.94\n.66\n1.42\n2.01\n6\n.69\n.79\n.93\n.66\n1.43\n2.01\n7\n.69\n.69\n.84\n.71\n1.42\n1.95\n8\n.72\n.75\n.95\n.81\n1.45\n9\n.84\n2.01\n.64\n.80\n.64\n1.36\n.66\n1.95\n10\n.66\n.81\n.70\n1.94\n1.39\n11\n.71\n.66\n.78\n.66\n1.89\n1.45\n.67\n12\n.65\n.77\n.62\n1.45\n.62\n1.89\n13\n.92\n.97\n1.62\n.55\n.56\n1.95\n14\n.73\n.82\n1.51\n.52\n1.89\n.53\n15\n.65\n.77\n.51\n1.89\n1.45\n16\n.53\n.94\n.97\n1.66\n.55\n1.95\n17\n.58\n.67\n.76\n.53\n1.57\n.64\n2.01\n18\n1.58\n.78\n1.86\n---\n---\n19\n.46\n.54\n1.57\n1.04\n1.87\n20\n1.15\n.66\n.79\n1.58\n.67\n1.90\n.71\n21\n.81\n.67\n.91\n1.46\n1.92\n.84\n22\n.91\n.79\n1.46\n.71\n.87\n1.91\n23\n.91\n.79\n1.46\n.71\n1.92\n24\n.87\n1.12\n1.25\n1.69\n1.34\n1.43\n2.08\n25\n.96\n1.02\n.71\n1.89\n1.85\n26\n.96\n1.13\n1.11\n1.86\n1.84\n1.07\n1.22\n27\n1.13\n1.23\n1.01\n1.91\n1.83\n1.19\n28\n1.08\n.94\n1..81\n1.65\n1.03\n1.27\n29\n.91\n.95\n1.63\n.87\n1.11\n1.79\n30\n.87\n.80\n1.49\n.76\n1.07\n1.79\n31\n.87\n.80\n.73\n1.04\n1.79\n1.49\n32\n.90\n.80\n1.86\n1.46\n.70\n.98\n33\n.98\n.97\n.78\n1.92\n1.52\n34\n1.04\n(1) Corresponding to a-priori standard observations of 1.2, 1.5 and\n1. 6m in Doppler determinations of latitude, longitude, and height and\n1.0 ppm, .8\" and .4\" in traverse distance, azimuth and elevation angle.","RESIDUALS\nRMS\n.79\n1.05\n.71\nWere Scaled by - 1.01 ppm\no I 2 3 4 5\n-60\nASSUMED\nSTD. DEV.\nMETERS\nRESIDUALS OF DOPPLER * DERIVED STATION COORINATES\n* *NWL 9D Coordinates\n1.04\n.97\n.78\nScale Of Vectors:\nFROM JOINT DOPPLER * - GEODIMETER ADJUSTMENT\n-65\nLongitude (m)\nLatitude (m)\nHeight (m)\n-70\n- 75\n2\n1.2\nC\n-1.0\nQ\n.5\n-80\n-3\n&\nO\na\n2.7\nI.I\n-85\n-.6\nO\n0\nO\no\nO\n.7\n-1.5\n1.4\nO\nO\n-90\n1.2\nCASE 14\n.2\n1.7\nO\n-.5\nFIGURE 9a\n-4\n-95\nHeight Residual\nO\nO\n(meters)\nO\nO\nQ\n-100\n-.5\n-1.1\n-105\n1.0\n- 1.4 O\n10\nO\nO .3\n-\n-1.2\n-110\nO\n.5\nC 1.8 O -0\n-115\n8\nO .2\nO\n1.2\n-120\n.4\nO\n1.3\n-125\n-\n130\n25\n35\n50\n30\n20\n45\n40","Residuals\nRMS\n.19\n.10\n.28\nShown In Meters Around Spurs a, b\nDistance And Azimuth Residuals\nAssumed\nAnd Loops A, B, C, D To Scale:\nStd. Dev\n-60\no I 2 3 4 5\n.24\n.24\nRESIDUALS OF GEODIMETER DERIVED STATION COORINATES\n1.0\nMETERS\n-65\nDistance (ppm)\nFROM JOINT DOPPLER* - GEODIMETER ADJUSTMENT\nElevation (sec)\nAzimuth (sec)\n-70\n-75\nE .3\n.5\n-80\n.4\n.10\nC\n.3\nA\no\n.O\n.4\n-85\n4.0\nO\nC\na\nO\ne\n.0\no\n-.0\n.2\n-\n-\nG\nCASE 14\nG\n-90\n-.0\nO\n@\n-.3\nO\n.8\na\n.6\nB\nFIGURE 9b\nC\n-95\n0-.3\nO\n7\n-.0\nResidual (m)\n-1.0\n3\nQ\n-100\nElevation\n.0\n.2\n-.3\n-.6\n-105\nb\n.0\n-.6\n-.03\n.7\n-110\nD\n-.I\nQ\n-115\nO\n.5\n6\n5\n-120\n-\n4@\nG\n-0\n-125\n-130\n20\n25\n30\n35\n45\n40\n50\n55","A-priori observation errors computed as the root sum square of the geoid height error given by\nElevation\n.4\"/.11\"\n.12/.05\n.12/.05\n.08/.03\n.24/.10\n.21/.13\n.4/.16\n.4/.37\n.4/.21\n.4/.21\n.2/.11\nBomford (1971) and 0.5 m yielded weighted residuals which were 0.29 times the a-priori error.\n(2)\n.8\"/.35\"\nAzimuth\n.24/.17\n.24/.12\n.24/.17\n.24/.19\n.38/.33\n.8/.26\n.38/.27\nTraverse\n.8/.31\n.8/.46\n.8/.38\n.8/.37\nLow weight was given to Doppler results for two inconsistent stations\n1 ppm/.13 ppm\nDistance\n1 /.13\n.1/.006\n.35/.09\n.36/.21\n.3/.03,\n.3/.05\nSolution A-Priori Observation Error/Residuals of Fit\n1/.22\n1/.58\n1/.28\n1/.35\n1/.37\nRESIDUALS OF FIT\nTABLE 8\n1.6m/1.02m\n1.04/1.02\n1.04/1.30\n1.04/1.05\n.86/1.03\nHeight\n1.04/.89\n.77/.94\n1.6/.03\n.86/.83\n.86/.76\n1.6/1.3\n.48/.6\n1.5m/.69m\nDoppler\nLongitude\n.97/.83\n.97/.62\n.97/.84\n.97/.79\n1.5/.69\n.59/.53\n.59/.36\n.59/.66\n.36/.43\n1.5/.96\n.45/.5\nLatitude\n1.2m/.64m\n.78/.69\n.78/.61\n.78/.76\n.78/.71\n.66/.61\n.66/.38\n.66/.67\n.37/.41\n1.2/.65\n1.2/.85\n.36/.6\nScale\n1.003\n1.134\n1.189\n.934\n.831\n1.169\n1.013\n.926\n1.06\n1.04\n1.00\n1.09\nfor\n(1)\n(1)\nCase\n(1)\n(2)\n5\n6\n7\n8\n11\n13\n14\n15\n16\n17\n18\n19","706\nTable 9\n(1)\nSTANDARD ERRORS\nCASE 14\nStation 19 Fixed\nOrigin Free\nZ\nY\nX\nY\nZ\nStation\nX\n.57m\n.65m\n1.41m\n1.09m\n.46m\n.47m\n1\n.57\n.67\n.53\n1.44\n1.03\n2\n.55\n.47\n.60\n.41\n1.44\n.93\n3\n.44\n.50\n.65\n.51\n1.48\n.93\n4\n.54\n.54\n.69\n.94\n.59\n.62\n1.50\n5\n.47\n.58\n.96\n.40\n1.41\n6\n.41\n.47\n.58\n.96\n.40\n7\n.41\n1.41\n.43\n.51\n.41\n1.38\n.99\n8\n.41\n.48\n.59\n1.41\n1.01\n.48\n9\n.48\n.40\n.49\n.34\n1.36\n.97\n10\n.35\n.40\n.49\n1.35\n.98\n.34\n11\n.35\n.40\n.47\n.33\n1.33\n1.01\n12\n.33\n.40\n.47\n1.32\n1.02\n.32\n13\n.32\n.49\n.55\n1.07\n.35\n1.35\n14\n.37\n.41\n.48\n1.03\n.31\n1.32\n15\n.32\n.40\n.47\n1.02\n.30\n1.32\n16\n.31\n.50\n.54\n.36\n1.09\n17\n.37\n1.34\n.41\n.45\n1.10\n.34\n1.35\n18\n.45\n1.08\n---\n---\n19\n.47\n1.32\n---\n.30\n.34\n.41\n1.33\n1.06\n20\n.57\n.42\n.47\n1.04\n.47\n.48\n1.37\n21\n.49\n.57\n1.00\n.45\n1.35\n22\n.58\n.49\n.57\n1.35\n1.00\n.45\n.58\n23\n.49\n.57\n1.00\n.45\n1.35\n24\n.58\n.73\n.81\n1.17\n.77\n25\n.86\n1.43\n.61\n.60\n1.22\n.50\n1.33\n26\n.61\n.72\n.71\n.64\n1.27\n1.30\n27\n.74\n.73\n.77\n1.29\n.64\n1.27\n28\n.79\n.58\n.64\n1.24\n1.13\n.56\n29\n.79\n.61\n.57\n.53\n1.24\n1.11\n30\n.77\n.49\n.55\n.45\n1.03\n1.25\n.71\n31\n.49\n.54\n1.03\n.45\n1.25\n.71\n32\n.49\n.55\n1.02\n.45\n1.26\n.70\n33\n.54\n.59\n1.04\n.49\n1.29\n34\n.71\n(1) Corresponding to a-priori standard deviations of observation of .78,\n97, and 1.04 m in Doppler latitude, longitude and height and 1ppm, .24\"\nand .24\" in traverse distance, azimuth and elevation angle.","707\nAN ORB DOPPLER PROGRAM ANALYSIS\nAND ITS APPLICATION TO EUROPEAN DATA\nJ. Usandivaras\nUniversite de Tucuman\nConicet, Argentine\nP. Pâquet\nR. Verbeiren\nObservatoire Royal de Belgique\nBruxelles, Belgium\nSummary\nThe basic formulas for a Doppler program are given. They are deduced\ndirectly from the Guier's equations generally used for data filtering.\nDepending on their availability, either point positionings or net adjustments\nare possible, whether the ephemeris are precise or not. For the net adjust-\nments orbital corrections are along track, range and crosstrack displacements\nwhich are considered as constant over a limited area. Special attention is\npaid to the frequency unknown. Both single point positioning and net adjust-\nment are applied to EDOC (European Doppler Campaign) data with precise\nephemeris, but with simulated perturbated ones net adjustments are computed.\nRefraction corrections taking into account actual meteorological parameters\nare applied and the relativistic effect as well. The translation parameters\nof ED50 are given for five stations.\nForeword\nSince several years the Doppler data analysis is largely used to solve\nproblems such as the satellite orbit determination, detection of the polar\nmotion and variation in the rotation of the earth, adjustment of geodetic\nnetwork, etc.\nThe principles of the mathematical methods developed to study these\nvarious problems are well known and often appropriated to a well defined\nproblem. In a first approach and to perform the adjustment of a geodetic net-\nwork, for example, the most often adopted solution proceeds in two steps\nbased on a precise ephemeris delivered by DMATC or generated by the broadcast\norbital parameters. These two steps are:\na) a data filtering using the Guier elements (frequency, range,\nalong track),\nb) the wrong data being eliminated, a differential solution is\ndeveloped in a earth fixed cartesian coordinates system.\nThe purpose of this paper is to mix a network adjustment with a determina-\ntion of local orbit errors. By local errors we mean errors that remain\nconstant along a short arc, for example, one pass above a set of European\nground stations. The observation equations will be directly deduced from the\nGuier elements.","708\nThe next main notations are used:\nFG = the high frequency reference,\nEG = the low frequency reference,\n= the high frequency received by the station,\nFR\nfR = the low frequency received by the station,\nthe high frequency transmitted by the satellite,\nFS\n=\na first approximation of F's'\nFos\n=\nis such that\n=\noS\nAFS = the offset of the satellite high frequency,\nC = the light velocity,\nthe wave length in function of FG'\nAG\n=\n= the wave length in function of Fs'\nAs\n= the Doppler effect of Fs'\nF d\nN = the number of integrated cycles as reported by each station,\np = a scaling factor,\n= epoch of signal generation at the true satellite position,\nti\nTi = the time of propagation between the station and satellite.\nThe General Doppler Formula\nThe Doppler measurement consists to integrate the frequency difference\nFG-FR\nduring a prefixed time interval or to get a prefixed number of cycles pN:\n(FG - ER) dt.\n(1)\nTaking into account that\n- each cycle received in the time interval (ti+1\nhas been transmitted during (ti+1 - t1) allows to write\n,\n- the transmitted frequency is stable during one pass,\n- the time of propagation is related to the distance \"station-satellite\"\nby the relation","709\nthe integration of eq. 1 gives\nGPN\n(2)\nThe integration of Eq. 1 can be expressed in another form than Eq. 2. If the\nintegration limits are noted (t ti+1), these limits being the local time,\nthe integration gives the relation\nsPNs\n(3)\nThe main difference between Eq. 2 and Eq. 3 is the expression of the wave\nlength. In Eq. 2 this quantity is defined as a function of the ground refer-\nence frequency while in Eq. 3, the frequency transmitted by the satellite is\nused.\nIn practice as an error of one cycle in the high frequency induces a\nwave length error of about 2.10-9 meters, the choice between Eq. 2 and Eq. 3\nis not very important. In the Transit system the high frequency used to\ndefine the wave length can have an offset as large as 40 Hertz without\ndeterioration of the station coordinates.\nHowever, we shall use the relation (Eq. 2) and we can already here\nmention that in our network analysis the reference frequency of each station\nwill be adjusted with respect to the reference frequency of a main station.\nThis will be obtained numerically during the computations of the observation\nequations.\nBy this procedure and remembering that a ground frequency must be precise\nbut not necessarily accurate, a frequency error in a particular station will\nbe eliminated in the general solution of the system. Only the offset in\nregards to the main station will be introduced in the final system.\nIn the relation (Eq. 2) we only know a first approximation Fos of FS\nwhile the reference frequency is considered as defined. We also know a\nfirst approximation of the station coordinates. Taking these remarks into\naccount, Eq. 2 becomes\nGPN1 - -\n(4)\n= -\nwhere\nX, Y, Z are the station coordinates,","710\nthe terms with mark o are computed with a first approximation of the\nstation coordinates (X, Yo, Zo) .\nTo the unknowns AFos, , AY, AZ of Eq. 4 often a term considering the\nsatellite drift is also included. As the instantaneous values of FS will be\ncomputed we do not need to introduce this drift as unknown. This Eq. 4 is\nalso the most generally used to adjust a geodetic network.\nPerturbation of the Measurements\nThree corrections are applied to the integrated quantity N. The signal\ntransmitted by the satellite and picked up at the station is travelling\nacorss the atmosphere.\nFor the low part of the atmosphere, a tropospheric correction is applied.\nThe methods used to remove this perturbation are well known and mainly\nexplained in Hopfield [1971] and Saastamoiner [1973]. The limits of the height\nof the low part of the atmosphere used in our computations are:\n- 40.082 km + 0.14898 Tc for the dry component, Tc being the\ntemperature (K)\n- 12 km for the net component.\nFor the upper part of the atmosphere the ionospheric refraction is corrected\naccording the general law that the ionospheric perturbation can be expanded\nas a series of the form:\n8\na\ni\ni\nF\ni=1\nS\nIf this development is limited to its first order, the mixing of two received\nfrequencies transmitted in coherence by a satellite is used to remove the\nionospheric perturbation.\nThe mixing of these two received frequencies gives a frequency output F\nE\nat first order free of ionospheric effects and called the effective frequency.\nFor the EDOC campaign the observed satellite was transmitting the\nfrequencies of 400 MHz and 150 Mhs minus as offset of about 80 ppm. As the\nmethods used to combine the two received frequencies are not uniform, the\neffective integrated frequency can be different from one station to another.\nThe five stations for which we received the Doppler data apply the\ncorrection according the next relations:\nBARTON/STACEY - BRUSSELS\n192\n1\nF\nF\nF\n=\n,\nR\n55\nE","711\nGRASSE\nFREE\nFREE\n=\n=\nFIRENZE - WETTZELL. The correction is computed and the resulting\neffective frequency is scaled to FR Thus\nFREEFE\n.\nAs in our computations, the equations (Eq. 2) is scaled to FR, the\nnumber of integrated cycles N reported by each station must be corrected by\na scaling factor P deduced from the preceding relations. The values of p\nare for\nBARTON STACEY - BRUSSELS\n192/55\nFIRENZE - WETTZELL\np = 1\nGRASSE\np 64/55\n.\nOn the first member of Eq. 2, a correction for the effect of relativity\nis also applied according the relation demonstrated by HARKINS [1973].\n(1/2\n)\n1\nvG2)\n+1/2\n(5)\nAN\nAT\nGM\n=\n2\nwhere\nAT is the integration time interval,\nEG are the scalar values of the vectors \"center of mass-satellite\"\n's'\nand \"center of mass-station. \"\nVs' VG are the absolute velocities of the satellite and station.\nThis quantity AN must be subtracted from N.\nThe GUIER Equation\nThe GUIER plane is defined by the first approximation of the station\nposition and the along track component of the satellite motion at time\nof closest approach (TCA).\nTo express the station displacement GUIER uses a reference system with\nits origin at the satellite position at TCA while the axes are:\nR : the range axis from station to satellite,\nL : along track component in the sense of the satellite\nmotion,\nZ : the third axis perpendicular to the plane (R, L)\n.","712\nIn this reference system and writing the left member of Eq. 4 in the\nform:\n(6) titi\nwhere 1j is the residual frequency term at time,\nthe\nGUIER [1963] proposes to represent 1 by the equation:\nj1tc2 (tm-tc) +\n(7)\n+\nwhere\n82£\nAF\n=\n= the time of closest approach,\ntc\n1, a\nthe independent term,\n=\nthe error term,\n=\n\"a,o sin (AM(t_))\n(8) 02c()c(\n(AM) sin AM\nC (AM)\nIn these relations the subscript C identifies quantities computed at\nTCA, and\n-\n= the mean angular motion of the satellite in its orbital plane,\nn\ndistance from station to satellite,\nr =\nr\ndistance from center of mass to satellite,\np =\nC(AM) = 1 - cos (AM),\n0 = being the angle between the vectors","713\nThe relation (Eq. 7) is well known for its efficiency to filter the\nDoppler data.\nIntroducing a new reference system (p, L, 5) by a rotation of angle 0\naround the L axis (Fig. 1), , at first order, the quantity L, RO are defined\nas:\n(9)\n= (1 0) sl sat-8lsta\n(10)\ncos 0 85 sat sinO dr sta\nwhile according to our hypothesis on the local error the second order terms\nare of the form:\n(11)\nL2=0\n(12)\nR2 = 8r\nsta cos 0 - SZ sta sin 0 + Sp sat (1 - c\nwhere Slsta, orsta and 8Zsta are the components of the station displacement\nin the GUIER system, (Spsat, Slsat, 85sat) are the errors of the satellite\nposition at TCA in the new geocentric system.\nSingle Station Positioning\nIf the precise ephemeris are at the disposal of the users the relation\n(Eq. 7) can be used to determine the station coordinates. In this particular\ncase the relations (Eq. 9), (10) and (12) become:\nTo Slsta\n(13)\nSrsta\nsta\nR2 or cos 0 - SZ sta sin 0.\nBy a transformation of the coefficients us o' \"a,o and ua 2 of Eq.\n7\nthe station displacement can be directly expressed in the earth fixed refer-\nence system. Let (f1, f3) and (e1, e2, e3) be the vectorial basis in\nGUIER and in the earth reference systems. If the station and satellite\nthe\ncoordinates at TCA are designated respectively by (X0, Yo, Zo) and (x, y, z), ,\nif (x, y, z) are the components of the satellite velocity V, the transforma-\ntion is given by:\na,0 - 0) + us,o 2 - \"a,2 sin 0 E = e e1+fe2 + ge3\n(14)\nwhere e, f, g are given by:","714\n(Y -y) z - (2 -z)\nX\ny\n-X\ncos 0\ne\no\na,o a,2\n-\nrv\nr\nV\n(Z x - (x -x) N°\nY -y\n(15)\nf\n=\ny\no\ns ,0\nr\nV\nrv\n(x-x) y - (X -y) - X\nZ\n-Z\nsin 0\n-u\ng\no\na,2\nrv\nr\nV\nThe new observation equations are of the form:\n82f. + e AX + f AY + 81 AZ = + Vi\n(16)\nwhere\nS 22, l and V i have the same signification than in Eq. 7,\ni\n, , AZ are the corrections to a first approximation of the station\ncoordinates,\nj is the pass number, while i is an index for observations of the pass j.\nIn the earth reference system this last Equation (16) allows us to\nanalyze several passes in a same system of normal equations. For the computa-\ntions, the observed quantities being cycles and not frequency the Equations\n(16) are multiplied by the time interval of integration. This is in the aim\nto avoid abnormal weighting of the observation equations in the case of fixed\nnumber of integrated cycles. Also, to reduce the number of parameters in the\nnormal equations, one reduction by the GAUSS procedure is performed to\neliminate 82. f. The coefficients of the first normal equations, particular\nfor each pass, must be stored in the aim to determine the satellite frequency\noffset after the final deduction of the position unknowns.\nThe next table shows how the second order terms increase the convergence\nof the solution. Each mean coordinate (X, Y, Z) of Brussels being initially\nshifted of plus 50 meters, passes acquired on a one week period (days 121 - 127,\n1975) were analyzed with and without the second order terms.\nWith Second Order\nFirst Order Only\nIteration\nAY\nAZ\nAY\nAZ\nAX\nAX\n- 48.87\n- 56.09\n- 71.30\n- 49.90\n- 50.49\n1\n- 66.81\n+ 0.06\n0.36\n2\n+ 22.57\n6.77\n+ 30.28\n0.70\n+\n-\n+ 0.20\n0.26\n3\n8.84\n1.44\n- 11.19\n+ 0.06\n-\n4.02\n0.00\n0.00\n0.00\n4\n3.76\n+\n+\n0.70\n+\n1.32\n5\n1.51\n0.39\n-\n-\n-\n6\n+ 0.52\n0.22\n0.32\n7\n0.18\n0.23\n+\n0.10\n-\n-\n8\n0.02\n0.01\n0.02\n+\n+\n+\n9\n0.00\n0.00\n0.00","715\nRemarks on the signs of sin 0 and cos 0\n0 being the angle between the vectors \"station, satellite\" and \"center of\nmass, satellite\", the cos 0 is always positive.\nHowever to determine the sign of sin 0 the geometry of the pass must be\nconsidered. It is induced by the rotation between the reference systems\n(R, L. Z) and (p, L, 5) which can be clockwise or counterclockwise depending\non the horizontal coordinates of the TCA and the direction South-North (SN)\nNorth-South of the satellite motion. According this geometry the next\nor\nfigure resumes the sign of sin 0.\nN\nNS : sin 0>0\nNS : sin 0<0\nSN : sin 0<0\nSN : sin 0>0\n&\nW\nE\nNS : sin 0>0\nNS : sin 0<0\nSN : cos 0<0\nSN : sin 0>0\nS\nCoordinates of Five EDOC Stations by the Single Positioning Method\nDoppler Results\nAs the observed satellite has a polar orbit and as the EDOC stations are\nin mid-latitude (40-50) the (X, Z) components of the along track and range\ndisplacements expressed in the earth system have a strong correlation. To\nwork with a less correlated system and for the computation the coordinate\nvariations were expressed in spherical coordinates.\nThe resulting coordinates are given in Table 1. In Fig. 2 a comparison\nof the coherence between the satellite frequency offset deduced by this pro-\ncedure and the values published in the USNO circular letters (series 17)\nis\npresented. A typical error on the satellite frequency determination is about\n0,002 Hertz.\nRemarks on Table 1\nFor good passes the two last rows give the total number of equations and\nthose eliminated. These numbers are to be associated with the average inte-\ngration period which is for\nBARTON STACEY, BRUSSELS\n30 sec,\n20 sec,\nFIRENZE, GRASSE\nand the number of passes eliminated during processing (Table la).","716\nDue to computer size, for Wettzell data, the initial integration period\nof about 4 seconds has been converted in an integration period of about 24\nseconds.\nThe coordinates and errors are in meters.\nThe errors attributed to the mean coordinates are obtained considering\neach weekly value as independent measurement.\nThe global coordinates are the results of a system including all the\nobservations performed from day 121 until day 151.\nThe mean internal error is about, on each coordinate, 20 cm.\nComparison with Geodetical Coordinates (ED50)\nThe geodetical coordinates furnished by station are reproduced in\nTable 2. The global Doppler solutions are compared to these values in Table 3.\nIf the corrections, proposed by ANDERLE (1974), are applied that is\nor = 0\"26\nand\nAH = -5.3 m\nthe values of Table 4 are obtained.\nIt clearly shows that two different regions can be considered:\na) the northern one (BRUSSELS and BARTON STACEY) : AX = 88.5m;\nb) the southern with AX = 81.1 m;\nsmaller differences are existing for AY and AZ.\nThe mean of these values agrees fairly well with those obtained by\nSEPPELIN (1974) :\nAX = -84 m,\nAY = -106 m,\nAZ = -130 m,\nand also by WEIGHTMAN (1975) :\nAX = -84 m,\nAY = -103 m,\nAZ = -129 m.\nNetwork Adjustment and Introduction of the Local Orbit Error\nIf the precise ephemeris is not available a less efficient ephemeris has\nto be used. With some limitations the relations (Eq. 9) to (Eq. 12) allow to\ntake into account an orbital error. To express this orbital error the GUIER's\ncomponents are projected in the (p, L, 5) geocentric reference system while\nthe stations coordinates remain in the earth fixed reference system (x, Y, Z) .\nMoreover we suppose that the orbital error may be considered as a constant\nfor one pass over a limited area such as Europe.","717\nIt is important to remember that the (p, L, 5) system has its origin at\nthe point of TCA of each station. Although the space positions of the satellite\nat TCA are different from each other, the circular characteristic of the TRANSIT\norbit allows us to suppose that the components of the satellite displacement\nare the same for all the stations. Another point is that it can be thought\nthat this procedure increases largely the number of parameters in the final\nsystem. However if (a) the earth potential driving the satellite motion is\nrepresented with an error lower than the observation error, or (b) the models\nadopted to remove the tropospheric and ionospheric perturbations are realistic,\nthe orbital error between each passes can be considered as poorly correlated.\nUnder these hypotheses the problem to determine station coordinates and\norbital errors can be solved in the classical block adjustment computation.\nIndeed the observation equations have the form:\na Dl + b i Ap + C AS + (AF s ) + e AX k + f AY k + gi AZ k = l i + Vi\n(17)\nwhere - the subscripts (i, j, k) are related to the observation i performed\nduring the pass j by station k\n(1\nfrom Eq. 7 and Eq. 9,\na\n=\ni\n(1\n0)\nfrom Eq. 7, Eq. 10 and Eq.\n12,\nQ.\nbi\ncos\n-\na,0\nS\nfrom Eq. 7 and Eq. 10,\nsin 0\nC\nCi\n-u\na,0\nfi, 8 are defined by the Eq. 15,\ne\ni'\nl and Vi have the same signification than in Eq. 7.\nAs already mentioned for the single station positioning, to avoid abnormal\nweighting, the Equations (17) are multiplied by the time interval of integration.\nIf all stations are equipped with a frequency standard the unknowns (Fos) j,k\ncan be considered as a common unknown of the system. However, this condition\nbeing generally not satisfied the offset corrections (AFos)j,k can be analyzed\naccording two different methods:\na) by station, a value of the offset is computed at a prefixed epoch\nand a common linear drift of Fs will be considered. In this\nproposal the number of unknowns in the final system is four times\nthe number of stations plus one frequency drift;\nb) in our analysis frequency problems are solved following the next\nprocedure. Before to be introduced in Eq. (17) the observations\nof pass j are filtered by Eq. (7) the offset\n(18)\n= -\nmeasured by station k is obtained.","718\nIf the reference frequency produced by the ground station k has an error\nof (AFG)k, the independent term Lj,k will have the form:\n(19)\nwhere l should be the value computed with (AFG)k=0.\nAlso to save homogeneity of reference frequency in the network one\nstation M, with acceptable reference standard, is used to determine the true\nvalue of the satellite frequency offset:\n(20)\nThis offset determined by the reference station M is now used to define the\nemitted frequency\n(21)\nand combining Eq. (18) and Eq. (21) to deduce\n(22)\nNow the true value lj,k of the independent term of station k, in a\nhomogeneous reference system, is obtainable by\n(23)\n=\nIn practical data analysis this solution presents the advantage to avoid\nnumerical problems particularly when stations have very similar systems of\nreference - (cesium beam tube for example).\nFor the pass j and for each station it is possible to form a system of\nnormal equations. All of them having as common unknowns the orbital\nparameters and the satellite frequency, the matrix of the whole being computed\ndirectly as addition of the individual ones.\nOnce this matrix obtained the reduction procedure of GAUSS allows us to\nrestrict the number of parameters, conserved for the multipass solution, to\nthree times the number of satellites.\nThe stations coordinates obtained, a backward solution gives the pass\nunknowns: the orbital parameters and the satellite frequency offset.\nThe coordinate variations obtained as solutions of this reduced system\nare the most probable values in the mean square sense. The inverse weight\ncoefficients represent the correlation between stations as introduced by\norbital parameters.","719\nNet Adjustment\nIn order to avoid an ill-conditioned system as it results from an adjust-\nment without constraints, a variable number of stations coordinates can be\ntaken as fixed.\nThis fact can be interpreted as a scale determination of the terrestrial\nnet.\nThe results of Table 5 (days 131-151) were obtained with the BRUSSELS\ncoordinates taken from its global analysis. It means that the scale is\nconserved as a Doppler scale for this point.\nA good agreement is found between the coordinates resulting of the single\npositioning and net adjustment. It is also the case for the satellite\nfrequency as determined by both methods. The transmitted frequency is obtained\nwith a typical precision of about 0.005 Hertz. The determination of the\norbital parameters is realistic for mean elevations greater than 20 degrees;\nfor lower elevations the matrix is ill-conditioned, nevertheless, it must not\naffect the station parameters determination.\nA simulation of an erroneous orbit was made by introduction of a constant\ndelay of 05006. It can also prefigurate a time error at the main station.\nThe condition, BRUSSELS coordinates fixed, produces the conservation of the\ncoordinates of the net within acceptable values. The difference between\nsingle positioning and net adjustment coordinates can reach one meter. We\nhave no criteria to decide which is the best solution but in any case the\nuse of different analysis and data selection or correction can give greater\ndifferences than one meter; NOUEL [1975], PIUZZI [1976], USANDIVARAS, PAQUET\n[1976].\nRemarks on Some Computational Problems\nThe European stations being very close from each other it exists in such\na system a very strong correlation between the coefficients (aj, bi ci) and\n(ei, fi, gi) The value of the determinant is very near a true zero.\nTo reduce these relations between coefficients and deduce an acceptable\nvalue for the determinant it has been necessary to fix one station.\nThe minimum elevation at TCA is fixed at 15 degrees while the minimum\nelevation for the observations is 10 degrees.\nCriteria to Reject Doubtful Passes\nThe initial coordinates being already well known a maximum of 10\nmeters for the station displacement must be satisfied;\nthe mean error for a pass adjustment being about 0.01 Hertz, a maxi-\nmum error of 0.03 Hertz is allowed;\na minimum of 25 percent of the data of a pass are to be recorded before\nor after TCA;\nby pass, a minimum of 10 good data must be recorded.","720\nConclusions\nThe Doppler analysis proposed mathematical model agrees with the obser-\nvations up to 0.01 Hz and allows a more rapid convergence.\nThe results obtained by DMATC with the observations of the Tranet Network\nand those computed here with the data of Firenze, Barton and Brussels only do\nnot show systematic deviation for what concerns the station coordinates.\nThe campaign data spanning over four time intervals, the individual\nresults of each time spare having good consistency among themselves, are also\nconsistent with the global analysis.\nIt must be noted that the precisions of the mobile equipment are as good\nas those obtained with fixed stations. (Wettzell).\nConcerning the network analysis as no particular method was used to solve\nthe determinant of the system although its small value, we think that improve-\nments are possible by using a more appropriate method (UOTILA - 1973).\nObviously, nothing can be concluded about the translation parameters for\nthe ED50 ellipsoid provided the evident regional variations, but special\nemphasis must be laid on the determination of these \"anomalies\" for the\nfuture.\nAcknowledgement\nJ. C. Usandivaras is greatly indebted to the director of the Royal Obser-\nvatory of Belgium, Prof. Velghe, who allowed him during two years, to feel\nhimself as a member of the Observatory and also to the Consejo Nacional de\nInvestigaciones Cientificas y Tecnicas of Argentine that supported this stage.\nReferences\nAnderle, R., \"Role of Artificial Earth Satellites in Redefinition of the North\nAmerican Datum.\" The Canadian Surveyor, Vol. 28, No. 5, Dec. 1974.\nGuier, W.H., \"Studies on Doppler Residuals-I/Dependence on Satellite Orbit\nError and Station Position Error.\" The Johns-Hopkins Univ.-Appl. Phys.\nLab. TG-503, June 1963.\nMr. Harkins, \"Relativistic Effects in Satellite Dynamics & Doppler Tracking. \"\nNWL, Dahlgren, VA., AD-762400, May 1973.\nHopfield, H.S., \"Tropospheric Effect on Electromagnetically Measured Range -\nPrediction From Surface Weather Data.\" Radio Science, Vol. 6, No. 3, 1971.\nNouel, F., \"Campagne EDOC.\" Rapport Presente Aux 27Emes Journees Luxembourgeoises\nde Geodynamique, 1975.","721\nPaquet, P. \"L Observation Radioelectrique des Satellites Artificiels et\nSon Role in Astronomie Fondamentale.\" Ciel Et Terre, Vol. 89, No. 4,\n1973. Obs. Roy. Belg.-Comm. B No. 82-S, Geoph. 118, 1973.\nPaquet, P. \"Effet Doppler Integre - Correction Des Mesures.\" Journees Lux.\nde Geodynamique, Nov. 1974.\nPiuzzi, A. , \"EDOC Campaign - Complementary Results.\" Presented at the 29th\nJournees Luxemb. de Geodynamique, 1976.\nSaastamoinen, J., \"Atmospheric Correction for the Troposphere and Stratosphere\nin Radio Ranging of Satellites.\" Bull. Geodesique, No. 105-106-107 AIG,\n1973.\nUotila, U. \"Generalized Inverse as a Weight Matrix.\" The Canadian Surveyor,\nVol. 28, No. 5, pp. 698-701, 1974.\nUsandivaras, J., , \"An Orb Doppler Analysis and It's Application to European\nData.\" 29th Journees Luxembourgeoises de Geodynamique, 1976.\nWeightman, J.A., \"On the Interaction of Satellite Geodesy and Classical\nGeodesy.\" Paper for the IAG Assembly, Section 2, Grenoble, 1975.","722\nZ\n5\n-p\nSatellite\nAlong Track\nR\nFig. 1","----\na\n150\nUSNO\nUcale of.\nFIG. 2 SATEULITE OFFSET OBSERVATORY AND UCCLE; OBSERVATORY\n140\n120\n009\n0,05\n0.01\n0.01\n0.","724\nTABLE 1\nBARTON STACEY\nMI\nNO\nDEL\nY\nMY\nZ\nDAYS\nx\nMX\n363\n31\n-96581,72\n0,53\n4946540,24\n0,37\n121-128\n4004960,81\n0,38\n4946539,84\n0,34\n428\nis\n128-135\n4004961,27\n0,42\n-96581,36\n0,51\n0,36\n4946539,78\n0,24\n1160\n111\n135-145\n4004961,34\n0,29\n-96581,59\n0,52\n4946540,95\n0,33\n478\n53\n145-150\n4004961,06\n0,40\n-96580,78\n0,24\n-96581,36\n0,42\n4946540,20\n0,54\nMEAN\n4004961,12\n240\n-96581,38\n0,23\n4946540,16\n0,15\n2435\nGLOBAL\n4004961,06\n0,18\nPRUXELLES\nZ\nMZ\nNO\nDEL\nY\nMY\nDAYS\nX\nMX\n0,44\n4919534,33\n0,27\n588\n70\n121-128\n4027835,64\n0,29\n306999,71\n0,38\n4919533,85\n0,25\n668\n74\n128-135\n4027836,60\n0,28\n307001,03\n4919533,34\n0,20\n0,21\n306999,99\n0,32\n976\n93\n135-145\n4027836,00\n0,28\n585\n47\n145-150\n4027836,57\n0,33\n307000,71\n0,49\n4919534,89\n4027836,22\n0,46\n307000,36\n0,61\n4919534,10\n0,66\nMEAN\n4027836,13\n0,14\n307000,31\nn,20\n4919533,99\n0,13\n2817\n284\nGLOBAL\nFIRENZE\nDAYS\nMY\nI\nMZ\nNO\nDIL\nX\nMX\nY\n4392483,01\n0,22\n567\n85\n121-128\n4572410,30\n0,31\n897983,87\n0,35\n01,17\n1047\n154\n128-135\n4522409,61\n0,19\n897983,76\n0,26\n4392483,26\n135-145\n4522499,46\n0,18\n897984,28\n0,26\n4342482,94\n0,15\n1471\n171\n834\n94\n145-150\n4522410,10\n0,25\n897985,07\n0,37\n4392483,68\n0,22\n4522409,87\n0,40\n897984,30\n0,55\n4392483,22\n0,33\nMEAN\n0,10\n3969\n526\nGLOBAL\n4522409,74\n0,11\n897984,20\n0,15\n4392483,21\nGRASSE\nY\nMY\nZ\nKZ\nNO\nDFL\nDAYS\nX\nMX\n1,67\n151\n76\n121-128\n4581911,64\n1,57\n556565,31\n3,32\n4389085,83\n0,90\n556566.86\n1,18\n4389089,12\n0,70\n243\n67\n128-135\n4581913,01\n556566,05\n237\n135-145\n4581910,99\n0,55\n0,76\n4389090,54\n0,45\n773\n1,38\n4389089,73\n0,85\n150\n34\n145-150\n4581910,20\n0,97\n556564,70\n4581911,46\n1,19\n556565,73\n0,93\n4389088,85\n2,10\nMEAN\n1317\n414\n4581911,18\n0,41\n556566,04\n0,58\n4389089,89\n0,34\nGLOBAL\nWETTZELL\nDAYS\nX\nMX\nY\nMY\n2\nMZ\nNO\nDEL\n121-128\n4075543,08\n2,16\n931802,58\n1,89\n4801606,48\n1,63\n123\n5\n128-135\n4075540,83\n0,29\n931804,44\n0,44\n4801606,65\n0,24\n521\n28\n135-145\n4075540,23\n0,21\n931805,47\n0,31\n4801605,24\n0,19\n917\n53\n145-150\n4075540,28\n0,33\n931805,47\n0,49\n4801605,49\n0,29\n461\n22\nMEAN\n4075540,45\n0,33\n931805,13\n0,59\n4801605,79\n0,75\nGLOBAL\n4075540,35\n0,15\n931805,25\n0,21\n4801605,65\n0,13\n2022\n108","725\nTABLE 1A\nBALANCE OF PASSES\nP3\nP4\nTOTAL\nSTATION\nP1\nP2\n4\n43\n5\n22\n2\n107\n13\nBARTON STACEY\n19\n2\n23\n27\n31\n3\n43\n4\n2\n130\n12\nBRUXELLES\n29\n3\n14 0\n26\n0\n40 6\n23\n4\n103\n10\nFIRENZE\n15\n68\n31\n10\nGRASSE\n6\n11\n4\n32 10\n11\n16\n1\n83 13\n8 3\n24\n5\n35 4\nWETTZELL\nTABLE 2\nGEODETIC COOODINATES /FD.50/\nSTATION\nX\nY\nZ\n4 005 046,565\n-96 469,883\n4 946 662,413\nBARTON STACEY\n4 027 920,755\n307 112,284\n4 919 656,186\nBRUXELLES\n4 522 485,418\n898 097,275\n4 392 605,244\nFIRENZE\n4 581 988,375\n556 679,914\n4 389 212,092\nGRASSE\n4 075 618,244\n931 917,179\n4 801 723,482\nWETTZELL\nTABLE 3\nGLOBAL SOLUTIONS-ED.50 COOPDINATES\nDZ\nSTATION\nDX\nDY\n-122,25\n-85,51\n-111,50\nBARTON STACEY\n-84,62\n-111,97\n-122,20\nBRUXELLES\n-75,67\n-113,02\n-122,04\nFIRENZE\n-77,20\n-113,87\n-122,20\nGRASSE\n-79,69\n-112,34\n-119,95\nWETTZELL","726\nTABLE 4\nGLOBAL SOLUTIONS WITH ANDERLE CORRECTIONS MINUS ED 50 COORDINATES\nSTATION\nDY\nDY\nDZ\nBRUXELLES\n-88,36\n-107,16\n-126,31\nBARTON STACEY\n-88,70\n-107,38\n-126,38\nFIRENZE\n-80,56\n-108,06\n-125,70\n-108,57\nGRASSE\n-81,70\n-125,87\nWETTZELL\n-34,23\n-107,99\n-123,96\nTABLE 5\nNLT ADJUSTEMENT-0.5D COORDINATES\nSTATION\nDX\nDY\nDZ\nBARTON STACEY\n-86,17\n-111,24\n-122,62\nBRUXFLLES\n-84,62\n-111,97\n-122,20\nFIRENZE\n-76,12\n-114,63\n-121,02\nGRASSE\n-76,55\n-115,07\n-122,04\n-80,44\nWETTZELL\n-112,80\n-120,32\nTABLE 6\nSIMULATED DISTURBED ORBIT NET ADJUSTIMENT-ED.50 COORDINATES\nSTATION\nDX\nDY\nDZ\nBARTON STACEY\n-86,19\n-110,68\n-122,58\n-84,67\nBRUXELLES\n-111,97\n-122,20\nFIRENZE\n-75,86\n-113,08\n-121,48\n-75,84\n-114,80\nGRASSE\n-121,88\n-80,26\n-112,28\n-120,45\nWETTZELL","727\nCONCEPTS OF THE COMBINATION\nOF GEODETIC NETWORKS\nD. B. Thomson\nE. J. Krakiwsky\nDepartment of Surveying Engineering\nUniversity of New Brunswick\nFredericton, N. B.\nCanada\nAbstract\nThis paper discusses the concepts of combining a Doppler satellite net-\nwork with one or more terrestrial networks. It is shown that the solution\nto the problem does not, in all instances, resolve itself to the use of a\nstraightforward \"seven-parameter similarity transformation.\" Even when using\na model containing seven parameters, the authors show that there are at least\ntwo different interpretations of such a model which yield different results.\nAmong the more complex approaches (relative to the seven-parameter solution),\nthe authors discuss two models having two sets of rotations which are meant\nto separate coordinate system rotations from network rotations. A model is\ndescribed in which the parameterization of possible systematic errors, beyond\noverall rotations and a scale change in the terrestrial network, is given.\nFinally, an approach is discussed for combining a Doppler satellite system\nwith several Geodetic systems; this model also has two sets of rotations but\nare different from those of other models. By presenting the concepts of\ncombining networks, the authors have attempted to show that the solution to\nthe overall problem is not based on any one simplified model, but must be\nbased on a complete model which corresponds closely with the underlying\n\"laws of nature.\"\nIntroduction\nThis paper concentrates on the concepts of the combination of three-\ndimensional Doppler satellite and terrestrial geodetic networks. The emphasis\nis placed on models in which there is a parameterization of the relation\nbetween the satellite and terrestrial datums (coordinate systems) these\nquantities are treated as unknown parameters to be solved for.\nThe motivation for combining satellite and terrestrial goedetic networks\nis a desire to determine, as accurately as possible, the relative positions\nof terrestrial points. In addition, the position and orientation of the datum\nto which the coordinates of the aforementioned points refer is of paramount\nimportance. Accurate and homogeneous Doppler satellite networks provide an\nindependent source of inherently three-dimensional coordinate data which can\ncontribute significantly in attaining the above mentioned goals.\nSome Definitions and Assumptions\nTo ensure that the concepts and theory presented in this paper are placed\non a solid foundation, some definitions are in order. The word datum is\ndefined as \"something known or assumed as fact, and made the basis of reasoning","728\nor calculation\" [Oxford English Dictionary, 1971]. Thus, a geodetic datum is\nthat \"something\" to which geodetic computations are referred. The term\n\"coordinate system\" is also used in this paper to refer to a \"datum\". A\ngeodetic network is a geometric object in which the various network points are\nuniquely defined by a triplet of coordinates. These coordinates are not\ndirectly obtainable but are derived, using appropriate functional relation-\nships, via some observables. Geodetic networks are intricately related to\ntheir geodetic datums. The coordinates of network points do not define a\ndatum but are utilized to recover the parameters which define the relative\nposition and orientation of the datum. The definitions of the Average Terres-\ntrial (AT), Geodetic (G) and Local Geodetic (LG) coordinate systems referred\nto in this paper are the same as those given in previous papers by the authors\n[e.g., Krakiwsky and Thomson, 1974; Thomson and Krakiwsky, 1975], and can be\nfound elsewhere in the literature [e.g., Veis, 1960].\nThe concepts presented in this paper are based in part on some assumptions\nregarding the state of the data that would be used in a practical and useful\ncombination of networks. Herein, the following assumptions are made:\na) It is assumed that the satellite network is represented by a homo-\ngeneous set of three-dimensional coordinates and associated covariance\nmatrix as computed via Doppler satellite techniques [e.g., Brown,\n1970; Brown, 1975; Kouba and Boal, 1975];\nb) The reference frame (datum) to which the Doppler coordinates refer\nis assumed to be the Average Terrestrial coordinate system. The\nDoppler system is only one \"estimate\" of this ideal coordinate\nsystem [Anderle, 1974];\nc)\nThe three-dimensional terrestrial network coordinates and associated\ncovariance matrix are assumed to be the results of rigorous compu-\ntations involving terrestrial observables (e.g., directions, distances,\nelevation differences) and astronomic latitudes, longitudes, and\nazimuths [e.g., Vincenty, 1973]. In the case where practical con-\nsiderations have necessitated the traditional splitting of terrestrial\ncoordinates into horizontal and vertical components, it is assumed\nthat the coordinates, and their respective covariance matrices are\ncombined to yield a set of homogeneous three-dimensional terrestrial\nnetwork coordinates [e.g., Krakiwsky and Thomson, 1974; Thomson, 1976];\nd) The terrestrial coordinate system is assumed to be a Geodetic coor-\ndinate system that has been positioned and oriented in the earth\n(relative to the Average Terrestrial coordinate system) using rigorous\nstandard procedures [e.g., Hotine, 1969];\nFinally, a requirement of each of the models presented herein is\ne)\n.\nthat several coordinated points of the Doppler and terrestrial net-\nworks be coincident.","729\nParameterization\nWhen combining Doppler and terrestrial networks, the choice of unknown\nparameters in the formulation of a mathematical model is extremely important.\nOne must be confident that there is reasonable evidence to suggest that\ncertain parameters should be included as unknowns to be solved for. Further-\nmore, it is essential that the role of the unknown parameters in a model be\nproperly interpreted.\nIn this paper, two types of unknown parameters are considered. The first\nare those that relate the Doppler and terrestrial network coordinate systems.\nSince the Doppler system can be considered as a good approximation of the\nAverage Terrestrial coordinate system, such information could assist in\nattaining the desired position and orientation of the terrestrial geodetic\nsystem. The second type of unknown parameters considered herein are the\nunresolved systematic errors in terrestrial networks. Such errors are the\nresult of a misoriented (relative to the Average Terrestrial) Geodetic system\n[e.g., Hotine, 1969; Thomson, 1976], unknown and unmodelled systematic\nerrors in terrestrial horizontal direction measurements [e.g., Kukkamaki,\n1961; Bomford, 1971], distance measurements [e.g., Jones, 1971], zenith\ndistance measurements [e.g., Heiskanen and Moritz, 1967; Hradilek, 1972],\nand astronomic latitude, longitude and azimuth determinations [e.g., Merry,\n1975; Mueller, 1974]. In contrast, it is assumed that Doppler network\ncoordinates are comparatively free of the effects of systematic errors; thus,\nin combination with terrestrial network coordinates, they can be used to\nmodel the effects of unresolved systematic errors in the terrestrial network\ncoordinates.\nStandard Concepts\nThe most straightforward and most often used approach in combining\nDoppler satellite and terrestrial networks is via a seven parameter similarity\ntransformation. The seven parameters normally consist of three components of\na translation vector, three rotation elements, and a scale difference.\nDepending on the formulation of the transformation model (e.g., the express\nrelationship between the chosen observables and the seven unknown parameters),\nsome interpretation as to the meaning of the seven parameters is possible.\nThree mathematical models of the aforementioned type are in common use.\nThe so-called \"Bursa\" model [Bursa, 1962] is given by Fig. 1:\n(1) (Fo)D+ (1+K) R1 (E R2 R3 ( E ) (TPC iG - (pi) i'D ,\nX\ny\nZ\nwhich the unknown parameters are: ro, the translation vector between the\nin\norigins of the Doppler (D) and Geodetic (G) coordinate systems; K, the scale\ndifference parameter relating the scales of the two reference frames; and\nEx, Ey, and three differentially small rotations about the Geodetic\ncoordinate system axes. The observables in this model are the position\n* R1, R2 and R3 are the well known three-dimensional rotation matrices.","730\nvectors (Fi)G and (Pi)D. A second model attributed to Molodensky [Molodensky\net al., 1962] is given by Fig. 2:\n(2) (1+K) R1 (4x) R2 (4/) R3 (42) -\nThere are, to the author's knowledge, two interpretations of this model. The\nfirst, which has been used by several investigators [e.g., Badekas, 1969;\nMueller et al., 1970] as well as the authors [Krakiwsky and Thomson, 1974;\nThomson and Krakiwsky, 1975; Thomson, 1976], is that there is an a priori\nassumption of parallelity of the Doppler (= Average Terrestrial) and Geodetic\ncoordinate systems (Fig. 2). In this case, the scale difference parameter\nK and the differentially small rotations 4x, Yy, and 42 are interpreted as\npertaining to the terrestrial network represented by the observables (FKi)G.\nFurther, the translation vector, (Fo)D, expressed in the Doppler (D) system,\nrepresents the translation between the origins of the two reference frames.\nComparing the models attributed to Molodensky and Bursa, one obtains the\ndifference [Thomson, 1976]:\n(3) rom - rob + (OM QB)rki - OB k + - =\nin which\nQB=Re - I,\nand the subscripts M and B refer to the Molodensky (2) and Bursa (1) models\nrespectively. If one were to assume that the two models would yield identical\nresults (i.e., QM QB; KM = KB), = then one obtains:\n(4)\nThis expression (4) is satisfied if and only if = 0 and KB=0.\nThere are other ways of expressing the difference between the models\nattributed to Molodensky and Bursa. The authors pointed out the difference\nin stating that one should use the sum of the position vector of the initial\npoint with respect to the datum origin, and the position vector of an\narbitrary point with respect to the terrestrial network initial point, as\nthe observable in place of (rki)G [Krakiwsky and Thomson, 1974]. In this\ninstance, the term (rk)G in Eq. 2 would be removed. Having done this, the\nBursa and Molodensky models would be mathematically equivalent. Leick and\nvan Gelder [1975] confirmed this in stating that one should use (1+K) R1\n(4x) R2 (vy) R3 (42) (FK)G in place of (rk)G in Eq. 2.\nA second interpretation of the Molodensky model is one in which there\nis no a priori assumption of parallelity of Doppler (= Average Terrestrial)\nand Geodetic systems [Leick and van Gelder, 1975; Soler, 1976], but it is\nassumed that a local geodetic coordinate system at the terrestrial network\ninitial point is parallel to the Geodetic coordinate system [Soler, 1976].","731\nUsing this interpretation of the Molodensky model, it has been shown [Soler,\n1975] that it is equivalent to the Bursa model.\nA third model of this type, the Veis model [Veis, 1960], is given by\nFig. 3:\n(5) = + (EK)G + (180-)R2 P2R1 (dv) R2 (du) R3 (dA)\nP2R2 (qk-90) 23(12-180) -\n.\nThis model, in which (ok, K) are the geodetic coordinates of the terrestrial\nnetwork initial point (k), and dv, du, dA are three differentially small\nrotations about the axes of the Local Geodetic coordinate system at k, is\nmathematically equivalent to the Molodensky model and thus the interpretations\nof the latter also apply here. The rotations and dv, du, dA are\nrelated by:\nsin\nsin\ndA\ny\n-COS\ncos\nX\n(6)\nsin\nu\n-cos k\nsin\nsin\n1k\ndu\n=\n-cos\ny\n0\ndv\n4\n-sin OK\n-cos\nZ\nAll three models given here contain a maximum of seven unknown trans-\nformation parameters. A solution for each of the models is easily obtained\nvia a combined case least squares estimation procedure. As has been\nindicated, there are differences between the Bursa and the Molodensky (or\nVeis) models. Further, there are different interpretations of the Molodensky\n(or Veis) models. When using any of these models (1), (2) or (5), one\nobtains identical values for the rotation parameters (Ex = 4x, Ey = Yy, EZ =\n47) and scale difference [Krakiwsky and Thomson, 1974; Leick and van Gelder,\n1976; Thomson, 1976]. The difference that occurs is a subtle one of inter-\npretation of the rotation and scale parameters. With the Bursa model (1),\nthe geodetic position vector of each point is scaled and rotated, while with\nthe Molodensky (2) and Veis models (5), only the interstation vectors, expressed\nin the Local Geodetic system at k, are scaled and rotated.\nFor the purposes of practical geodetic computations, this difference\nhas been expressed in another way. Mueller and Kumar [1975] state that the\nmodel attributed to Bursa \"deals primarily with the case when the two systems\ninvolved have \"global\" coverage\" (e.g., two global satellite networks). They\ngo on to say that for a coordinate transformation where one of the systems\nis non-global in coverage (e.g., a national terrestrial network), then the\nmodel attributed to Molodensky should be used in which case the rotations\n\"are to be considered about the origin (initial point) on the geodetic datum,\nrather than about the origin of the Cartesian coordinates.\n\"\nThe basic assumption underlying each of these similarity transformations\nis that the differences in coordinates can be resolved via seven parameters.\nIt is likely that more parameters are required - a set to resolve the differ-\nences between the Doppler and Geodetic coordinate systems and another set to","732\nmodel the unknown systematic errors in the terrestrial network. Hotine [1969]\nstated it as follows:\n\"In addition to the initial choice of discordant system of\ngeodetic coordinates, the network itself may have systematic\nerrors of scale and orientation for which an allowance should\nbe made before we adjust the network to adjacent work or into\n\"\na fixed system of a worldwide triangulation.\"\nIf there is only one set of rotations (e.g., Bursa, Molodensky, and Veis\nmodels):\n\"\nthe effect of a systematic orientation error in the\n.\nnetwork could be concealed by evaluating false values of\n\"\n[Hotine, 1969].\nthe rotation parameters\nRecently, some work has been done in an attempt to overcome the problems\nmentioned above.\nRecent Concepts\nHotine [1969] formulated a model in which the rotation parameters\n(Ex, Ey, Ez) for the discordant Geodetic coordinate system were separated\nfrom two other parameters - da, a change in azimuth, and dB, a change in\nzenith distance - which represent the systematic errors in the terrestrial\nnetwork. The azimuth change, da, is a rotation of each interstation vector\nrki about the z-axis of the Local Geodetic coordinate system at the terrestrial\nnetwork initial point k. The zenith distance parameter, dB, is a constant\napplied to all network difference vectors rki. A scale difference parameter,\nK, is included to model the systematic errors in scale in the terrestrial\nnetwork. The model (Fig. 4), containing nine unknown parameters, is given\nas:\n(7) = (Fo)D+' R2(Ey) +\nRHP2R2 (-90) R3(-180)\n,\nin which\ndB\n1\n-da\ncos\na\n(8) RIH =\nda\n1\nsin\ndB\n,\n-dB/cos 0\n1\nwhere aki is the geodetic azimuth from the terrestrial network initial point\nto an arbitrary network point i. Hotine [1969] also mentioned the possibility\nof including in his model a parameter da representing a change in length of\nthe semi-major axis of a reference ellipsoid. However, as he pointed out,\nthe inclusion of this parameter would tend to eliminate the systematic error","733\nin the scale of the terrestrial network since the ellipsoid would be\nrescaled to absorb any scale errors.\nSince there are only two networks involved in this combination model,\nthe estimation procedure for its solution is not easily formulated. Hotine\n[1969] did not propose any estimation procedure but stated:\n\"This procedure assumes that the parameters are independent and\nthat second-order effects can be either neglected or removed\nby some process of iteration, although in some cases, the\nparameters, especially the rotations, will be strongly correlated. 11\nAnother model, termed UNB-1 herein, based on the same general concepts\nas those used by Hotine, is given as Fig. 5 [Krakiwsky and Thomson, 1974;\nThomson and Krakiwsky, 1975; Thomson, 1976]:\n+ R2(90-)2\n(9)\nIn the above, six parameters (3 translations, 3 rotations) are included for\nthe discordant Geodetic coordinate system and four parameters - one scale\ndifference K and three rotations dv, du, dA - are included to model the\nsystematic errors in the terrestrial network.\nAs with the previous model (88), a special estimation procedure is\nrequired to obtain a solution. The least-squares estimation procedure\nproposed, in functional form, is:\nF1(X1,L1) =\n(10)\nF2 (X1, X2, L2) = 0\nwhere X 1 are the coordinate system transformation parameters (xo, yo, 20,\nEx' Ey, Ez);\nX2 are the rotation and scale differences parameters pertaining to\nthe second network (K, dA, du, dv) or (K, da, dB);\nL1 are the observables (coordinate differences (xik) yik, Zik)G and\ncoordinates (X, Y, Zi)D of the \"inner zone\")\nL2 are the observables (coordinate differences (xik, Yik, Zik)G and\ncoordinates (X, Yi, Zi)D of the \"outer zone\").\nThe reason for the splitting of the coordinates of common points into\n\"inner\" and \"outer\" zones is to make the solution possible for the two sets\nof parameters in each of the models ((8) and (9)). The inner zone contains\nsufficient observables (L1) to solve for the unknown parameters (X1). The\ncommon network points of the inner zone should be sufficiently close to the\nterrestrial initial point so that the observables (coordinates) of the","734\nterrestrial network will not contain significant systematic errors. The\nouter zone then contains the remaining common network stations. Linear\nTaylor series expansions of F1 and F2 yields the matrix equations:\nA11X1 + BILVI + =\n(11)\nA21X1 + A22X2 + B22V2 + W2 = 0,\n(12)\nwhere\nOF1\nA11\nL1\nOF2\nA21\n=\n2X2/X2,\nL2\n= W2 = F(X°, L2)\n.\nThe least squares normal equations equations relating the unknown quantities\n(X1, X2, 1, ) to the known quantities (A11, B11, W1, A21, A22, B22, W2,\nEI) are obtained via the variation function [Krakiwsky, 1975]:\n-\nCOV\nEL2\nV2\nW1) 2K(A12X1 + A22X2 + B22V2)\n(13)\n.\nThe solution vectors are obtained using:\nA21\nX2\n(14)\n-1\nT\nW1\nW2\nIn the two aforementioned models ((8) and (9)), the basic concept is to\nseparate the parameters that relate the Doppler and terrestrial datums from\nthose few (a maximum of 4), that are used to model the overall effects of\nthe systematic errors in the terrestrial network. An alternate approach,\nin which the systematic errors in the terrestrial network may be modelled","735\nmore completely is to use the method of least-squares approximation [Vanicek\nand Wells, 1972]. In this case, the systematic errors are represented by a\nthree-dimensional polynomial of n th order. The coefficients of the polynomial\nare determined using least-squares approximation in which the quantity to be\nminimized is the sum of the squares of the weighted discrepancies between a\nmathematically defined vector field and the vector field represented by the\ncoordinate differences (i.e., (xi)G-(Xi)D; Two\nmodels that utilize this approach are given here.\nThe first, in which the total discrepancy in coordinates\nis modelled by an algebraic polynomial, is given as:\n(15)\nCijk\n,\nor, in a more expanded form:\nn\nP*(T)\nX\ni,j,k=0\n1n(x)\nPY(T)\ny\n=\n=\n=\ni,j,k=0\n(16)\nn\nZ\nG\nD\ni,j,k=0\ny\nX\nin which cijk (or cijk' cijk' cijk) are the unknown polynomial coefficients\nto be solved for. Having defined the mathematical vector field in this way,\none may then compute the expected vector difference (F1) G- (11) D for any\narbitrary point (ri) of the terrestrial network. An unfavorable aspect of\nthis approach is that all unknown information - translation components,\noreintation parameters of the Geodetic coordinate system, and systematic\nerrors in the terrestrial network - are lumped together. This can create\ndifficulties in interpreting the results.\nA second approach that utilizes the concepts of the Hotine (8) and\nUNB-1 (9) models plus the least-squares approximation methodology is given\nby:\np\n(17)\nNow, in (17), the translation and rotation parameters for the discordant\nGeodetic coordinate system appear explicitly. The systematic errors in the\nterrestrial network are modelled by the vector field represented by Pn(rki).\nAs with the Hotine (8) and UNB-1 (9) models, a special estimation procedure\nis required to obtain a solution. In functional form, analogous to (10),\none may write:\nF1 (X1, L1)=0,\n(18)\nF2 (X1, C, , L2) = 0\n,","736\nin which C are the coefficients of the three-dimensional polynomial. The\nsolution is given by an equation similar to (14).\nThe final situation dealt with in this paper is one in which we consider\nthe relationships between the Average Terrestrial, Doppler, and several\nGeodetic coordinate systems. This can be accomplished using a model - termed\nUNB-2 herein - developed by Vanicek and Wells [1975]. The stated objective\nof this model is to enable one \"to examine numerically the parallelism of\ngeodetic systems (based on terrestrial observations) and satellite systems\n(based on satellite observations) and the average terrestrial system\" [Wells\nand Vanicek, 1975]. The model is given by Fig. 6:\n- r S + R1(E))R2(E,)Rg(E2) to\n(19)\nwhere rG is the translation vector between the Average Terrestrial and\nGeodetic systems, rs is the translation vector between the Average Terrestrial\nand the Doppler systems, K is the scale difference in the Geodetic system,\nRA is a rotation matrix (see below), and Ex, Ey, EZ, rk' rki, and Pi are as\npreviously defined.\nThe originators of this model have proven that under certain conditions\nonly four datum position and orientation parameters exist (three translations,\none azimuth rotation) [Vanicek and Wells, 1974]. This occurs when the\norientation and position of the datum is defined at a terrestrial initial\npoint, at which point the equations:\n(20)\nare accepted by definition. Under this condition, the required zenith\ndistance condition at the initial point is satisfied. This then leaves only\nthe azimuth orientation condition to be satisfied. Thus, the rotation\nmatrix, RA, pertaining to the Geodetic coordinate system contains only the\nazimuth orientation unknown and is given by [Wells and Vanicek, 1975].\n-A cos sin AK\n1\nA sin ok\n1\nRA =\n-A\nsin k\nA\n1k\ncos\ncos\n1\n(21)\nA\nsin\n1k\n-A\ncos\ncos\ncos\nThere are eight unknowns to be solved for using this model - Ex' Ey,\nEz, A, K, rsg The last quantity, the difference vector rsg replaces rs\nand rG since the center of gravity (origin of the Average Terrestrial\nsystem)\nis unknown. One satellite coordinate system and several geodetic datums,\nhaving several associated common points, are combined in one parametric\nleast-squares solution.","737\nConclusions\nAccurate, homogeneous satellite networks, such as those established\nusing Doppler positioning, combined with terrestrial networks, can provide,\nthrough the use of a properly conceived mathematical model, essential\ninformation for:\na) the desired positioning and orienting of a terrestrial datum;\nthe modelling of systematic errors in terrestrial networks;\nb)\nc) the establishment of accurate three-dimensional terrestrial\ngeodetic networks;\nd) the relationships between the Average Terrestrial, Doppler and\nseveral Geodetic coordinate systems.\nTo accomplish the above, a straightforward \"seven-parameter similiarity\ntransformation\" in general is not adequate, and a model corresponding more\nclosely to the underlying \"laws of nature\" is desirable.\nReferences\nAnderle, R., (1974). \"Transformation of Terrestrial Survey Data to Doppler\nSatellite Datum.\" Journal of Geophysical Research, Vol. 79, No. 35.\nBadekas, J., (1969). \"Investigations Related to the Establishment of a World-\nwide Geodetic System.\" Reports of the Department of Geodetic Science,\nNo. 124, The Ohio State University, Columbus, Ohio.\nBomford, G., (3rd. ed. 1971). Geodesy. Oxford University Press, London.\nBrown, D.C., (1970). \"Near Term Prospects for Positional Accuracies of 0.1\nto 1.0 Meters from Satellite Geodesy.\" DBA Systems, Inc., Melbourne,\nFlorida.\nBrown, D.C., (1975). \"A Test of Short Arc Versus Independent Point Positioning\nUsing the Broadcast Ephemeris of Navy Navigational Satellites.\" Presented\nto the 1975 Spring Annual Meeting of the American Geophysical Union,\nJune 16-19, Washington, D.C.\nBursa, M., (1962). \"The Theory of the Determination of the Non-parallelism\nof the Minor Axis of the Reference Ellipsoid, Polar Axis of Inertia of\nthe Earth, and Initial Astronomical and Geodetic Meridians from Obser-\nvations of Artificial Earth Satellites.\" Translation from Geophysica et\nGeodetica, No. 6.\nHeiskanen, W.A. and Moritz, H., (1967). Physical Geodesy. W.H. Freeman and\nCompany, San Francisco.\nHotin, M., , (1969) Mathematical Geodesy. ESSA Monograph No. 2, U.S.\nDepartment of Commerce, Washington, D.C.","738\nHradilek, L., (1972). \"Refraction in Trigonometric and Three-Dimensional\nTerrestrial Networks.\" The Canadian Surveyor, Vol. 26, No. 1.\nJones, H.E., (1971). \"Systematic Errors in Tellurometer and Geodimeter\nMeasurements.\" The Canadian Surveyor, Vol. 25, No. 4.\nKouba, J. and J.D. Boal (1975). \"Program GEODOP. \" Geodetic Survey of\nCanada, Ottawa.\nKrakiwsky, E.J. and D.B. Thomson, (1974). \"Mathematical Models for the\nCombination of Terrestrial and Satellite Networks.\" The Canadian\nSurveyor, Vol. 28, No. 5.\nKrakiwsky, E.J., (1975). \"A Synthesis of Recent Advances in the Least\nSquares Method.\" Department of Surveying Engineering, Lecture Notes\nNo. 42, University of New Brunswick, Fredericton.\nKukkamaki, T.J., , (1961). \"Lateral Refraction on the Sideward Slope.\"\nAnnales Academiae Scientiarum Fennicae, Serie A, III, Geologica-\nGeographica, 61.\nLeick, L. and B.H.W. van Gelder, (1975). \"On Similarity Transformations\nand Geodetic Network Distortions Based on Doppler Satellite Observa-\ntions.\" Reports of the Department of Geodetic Science, No. 235, The\nOhio State University, Columbus, Ohio.\nMerry, C.L., (1975). \"Studies Towards an Astrogravimetric Geoid for\nCanada.\" Department of Surveying Engineering, Technical Report No. 31,\nUniversity of New Brunswick, Fredericton.\nMolodensky, M., V. Yeremeyev, M. Yurkina, (1962). Methods for Study of the\nExternal Gravitational Field and Figure of the Earth. Israel Program\nfor Scientific Translations, Jerusalem.\nMueller, I.I., C.R. Schwarz, J.P. Reilly, (1970). \"Analysis of Geodetic\nSatellite (GEOS I) Observations in North America.\" Bulletin Geodesique\nNo. 96.\nMueller, I.I., (1974). \"Review of Problems Associated with Conventional\nGeodetic Datums.\" The Canadian Surveyor, Vol. 28, No. 5.\nMueller, I.I. and M. Kumar, (1975). \"The OSU 275 System of Satellite Tracking\nStation Coordinates.\" Reports of the Department of Geodetic Science,\nNo. 228, The Ohio State University, Columbus, Ohio.\nOxford English Dictionary (1971). The Compact Edition of the Oxford English\nDictionary. Oxford University Press.\nSoler, T., (1976). \"On Differential Transformations Between Cartesian and\nCurvilinear (Geodetic) Coordinates.\" Reports of the Department of\nGeodetic Science, No. 236, The Ohio State University, Columbus, Ohio.","739\nThomson, D.B. and E.J. Krakiwsky, (1975). \"Alternate Solutions to the\nCombination of Terrestrial and Satellite Geodetic Networks.\" Energy,\nMines and Resources Canada, Publications of the Earth Physics Branch,\nVol. 45, No. 3.\nThomson, D.B., (1976). \"Combination of Geodetic Networks.\" Department\nof\nSurveying Engineering Technical Report No. 30, University of New\nBrunswick, Fredericton.\nVanicek, P. and D.E. Wells, (1972). \"The Least-Squares Approximation and\nRelated Topics.\" Department of Surveying Engineering Lecture Notes\nNo. 22, University of New Brunswick, Fredericton.\nVanicek, P. and D.E. Wells, (1974). \"Positioning of Geodetic Datums.\" The\nCanadian Surveyor, Vol. 28, No. 4.\nVeis, G., (1960). \"Geodetic Uses of Artificial Satellites.\" Smithsonian\nContributions to Astrophysics, Vol. 3, No. 9. Smithsonian Institution,\nWashington, D.C.\nVincenty, T. , (1973). \"Three-Dimensional Adjustment of Geodetic Networks.\" \"\nDMAAC Geodetic Survey Squadron, F.E. Warren AFB, Wyoming.\nWells, D.E. and P. Vanicek, (1975). \"Alignment of Geodetic and Satellite\nCoordinate Systems to the Average Terrestrial System.\" Bulletin\nGeodesique, No. 117.","740\nZ\nD\nZG\nG\nTERRAIN\nPOINT\nEZ\n1i\npi\ney\nGEOMETRIC\nYG\nCENTRE OF THE\nREFERENCE ELLIPSOID\nYD\nEx\nX\nG\nX\nD\nfif = (Fo'D + (1+K) R1 (E__) X R2 2 (E\") Ey R3 (EZ) (Fi) G - (Pi'D = to\nFIG. 1","741\nZD,\nZG\nZ\n4\nZ\nTERRESTRIAL\nINITIAL\nk\nPOINT\nTki\ny\n4x\nTERRAIN\nx\nPOINT\npi\nk\nGEOMETRIC CENTRE OF THE\nYG\nREFERENCE ELLIPSOID\nYD\nXG\nXD\n= (Fo) + (K'G + (1+K) R1 (4 X ) R2 (y y' ) R3 (4) Z (r ki'G - (Pi'D =\nto\nFIG. 2","742\nTERRAIN POINT\nZLG\nAi\ndA\nZG\nYLG\nki\nXLG\nZ D\nD\ndv\ndu\nTERRESTRIAL\nk\nINITIAL\nPOINT\nYG\n4k\nk\nYD\nXG\nXD\nFi = (Fo'D + (IK'G + (1+K) R3 (180-k) R2 (90- P2R1 (dv) R2 (du) R3 (dA)\nP2R2 ( -90)R3(Ak-180) (rki's ki G - =\nFIG. 3","743\nTERRAIN POINT\nZIG\nrki\nda\ndB\nZG\nYLG\nG\nXLG\nZ\nD\nTERRESTRIAL\nk\nINITIAL\nPOINT\nEZ\nA\nYG\n4k\nEy\nro\nVD\n1k\nEx\nXD\nXG\n14 = o'D + R1 (Ey) X R2 2 (E y ) R 2 3 (EZ) Z {(KK'G + (1+K)R3 (180-> k' R2 (90-)\ndB\n1\ncosa\n-a\nki\nP2R2 ( -90) R3 (XK -180) ( - =\n1 sina, ki dB\nP2\na\n1\n-dB/cosa\n0\nki\nFIG. 4","744\nTERRAIN POINT\nAi\nZIG\nrki\ndA\nYLG\nZG\nXLG\nZD\ndv\ndu\nTERRESTRIAL\nk\nINITIAL\nPOINT\nYG\n4k\nEy\nYD\n1k\nXB\n14i = o'D + R1 (E X ) R2 2 (E y' ) R2 3 (EZ) Z { (*K'G + (1+k)R3 (180- 'k) k R2 (90-)\n-90) R3 (XK 180) =\nFIG. 5","745\nELLIPSOIDAL\nNORMAL\ni\nZAT\nZ G\nZs\nA\nrki\nINITIAL\nk\nPOINT\nr\nk\nE\nZ\nYG\nSG\nORIGIN OF REFERENCE\nSATELLITE\nELLIPSOID\nORIGIN\nGe\nYs\ny\nis\nYAT\nGEOCENTRE\nEx\nXs\nXG\nXAT\n1\n-Acoso sin)\nAsino\nk\nk\nk\n1q = (GGAT K\n-Asino\n1\nAcoso cos)\nk\nk\nAcoso sin)\n-Acoso cos\n1\nk\nk\nk\nk\n(FK +r ki'G - (ra) S AT + R1 1 (E X ) R2 (E y. ) R. 3 (E2) (Pi's = to\nFIG. 6","746","747\nINTRODUCTION TO THE WORKSHOP\nON POLAR MOTION\nPaul Melchior\nRoyal Observatory of Belguim\nUccle-Bruxelles\nAs an introduction to this workshop on polar motion determination by the\nmeasurement of the Doppler effect on the frequencies transmitted by satellites,\nI propose to show in a very simple way how an incorrect positioning of the\nreal instantaneous pole of rotation of the Earth affects the measurements.\nLet us consider (Fig. 1) on the celestial sphere the approximate position\nof the pole which is adopted for the orbit computations and the predicted\nephemeris. I will suppose that one has just taken the CIO itself as the pro-\nvisional position (in fact, one takes a better approximate position).\nCIO, the Conventional International Origin, is a direction defined by\nadopting mean constant latitudes at five selected stations as exact (Carloforte,\nKitab, Mizusawa, Ukiah and Gaithersburg).\nThese latitudes are used in a least squares process to provide the so-\ncalled ILS polar motion which should play the role of a calibration or standard\nreference for other more precise (international precision) systems.\nWe can not overlook that these 5 stations were not all operating in 1900-\n1905 (they are only 4 amongst the 6 operating at that time) and this definition\ndoes not give any information concerning a mean pole or inertia pole at the\n1900-1905 epoch.\nWe can trace the CIO equator on the celestial sphere. Now the true\ninstantaneous pole is at P and the true P equator is also drawn on the sphere.\nThrough CIO we define X and Y axis in the tangent plane to the sphere.\nThe CIO/X meridian plane cuts the CIO equator at o which is the origin of the\nlongitudes defined by the BIH.\no is the Conventional Zero longitude point defined by adopting as exact\nmean longitudes at about 60 stations participating in the BIH operations.\nIt is a point on the CIO equator and the meridian defined by CIO and X\nis not passing through Greenwich Transit Circle but is not far from it.\nTherefore, the expression \"Greenwich Meridian\" is incorrect when one\nclaims for precisions of the order of 0\"1.\nThe position of P with respect to CIO and X axis is given by the ampli-\ntude of the displacement 4 and the azimut A. These parameters correspond to\nthe classical coordinates of the pole as given by IPMS or BIH in the following\nmanner:\n(1)\n= y cos A\ny = 4 sin A","748\nWe will still define on CIO equator the vernal equinox Y.\nNow let us consider a polar satellite orbit observed as SRP.\nThe errors made by considering erroneously CIO as the pole in the compu-\ntations are an along track error Au and an orbital inclination error Ai.\nFrom the figure we can immediately write:\n(2)\nMT = 90°\nYO = tsid\nYR = So\nMO = A\nThus:\nRO = YO - sid\nMR = MO - RO = A - tsid + = - So\n(3)\nRT = MT - MR = 90° + t sid - A\nMR = -\nand from the triangles TRS and TMN:\n(4)\nAu = ycos - A)\nwhile the triangle S - CIO - P gives:\nAi = - usin .\nFor a non polar orbit (dashed line on the figure), one should write:\nAu' = Au cosec i\nbut Ai remains unchanged.\nExpressions (4) and (5) show that the period of the perturbation is very\nclose to the sidereal day as So varies only very slowly for polar orbits while\nA has a period of about 400 days.\nThis also shows that theoretically a single station observing six or\nmore satellite passes per day could determine 4 and A, thus both polar coordinates.\nThis being stated, let me remind you shortly that it was in 1899 that the\nInternational Association of Geodesy established the first international coop-\nerative service in the story of astronomy and it was devoted to the determination\nof\nthe polar coordinates (x, y) This Service has the immense merit of having\nnever stopped despite the many troubles created by the several wars dividing\nhumanity.\nWe must pay a great tribute to this spirit and perserverance. It is thus\nwith\nmuch caution that we have now to update the Service by the introduction\nof the new techniques now available.","749\nThis Service, like the BIH which also derives the polar coordinates,\nbut in the frame of another solution of astronomical optical observations\nis a member of FAGS (Federation of Astronomical and Geophysical Services).\nFAGS was founded by the three International Unions of Geodesy-Geophysics,\nof Astronomy and of the Radio Sciences.\nFAGS brings together ten such services among which several are of direct\ninterest to space navigation and satellite orbit computations: the International\nGravimetric Bureau, the International Centre for Earth Tides, the Geomagnetic\nindices Service, the Solar activity Service, and evidently the International\nPolar Motion Service and the Bureau International de 1'Heure.\nFAGS covers a small part of the expenses of these services from Unesco\nand ICSU subsidies but the main part is supported by the host countries which\nof course, consider the FAGS support as a label of quality for the work\nperformed by these centres.\nAt present nine of the centres are located in Western Europe, the tenth\none, IPMS, being at Mizusawa, Japan.\nOn this basis we can try to investigate which steps should be taken now\nto update the Service and improve the precision with which the pose coordinates\nare determined.\nScientific and Other Applications Benefits for\nImproved Determination of Polar Motion and UT1\nBasically such an improvement should provide a better knowledge of inter-\nnal processes in the Earth in relation with\na) the core-mantle coupling; and in that case precession-nutations\nphenomena, which are due to the tidal torques exerted by the\nMoon and Sun on the non rigid Earth, have to be considered and\nreinvestigated jointly with polar motion,\nb) the excitation and damping processes of the free Chandler\ncomponent,\nc) the existence or non-existence of a forced secular motion of the\npole.\nHowever, many other effects (secondary in size in such measurements) will\nappear and should not be overlooked: earth and oceanic tides, tidal dissipa-\ntion, mean sea level changes and general circulation of the oceans and the\natmosphere, ocean-continent interactions, tectonic movements, time variations\nin the geopotential and surely others.\nBenefits for Science and human life are difficult to estimate.\nBut if there should really be a relation with earthquake activity, the\nbenefit would be immense: either if the polar motion has a triggering effect\non earthquakes or if both phenomena result from the same internal process.","750\nOur first goal should be definitely to solve this major question.\nNevertheless other benefits appear:\na) higher accuracy in Geodesy needs better determination of polar\nmotion,\nb) better knowledge of the polar motion would permit a higher precision\nin point positioning in geometric Geodesy and an improvement of\nsatellite orbit computations in dynamic Geodesy, and\nc) a precise knowledge of the polar motion and UT1 is obviously needed\nfor space navigation but the question may be raised here whether\nthe Space Agencies will prefer to determine the needed parameters\nby themselves just for the duration of a mission or whether they\nwill prefer to use the parameters currently derived by an improved\ninternational permanent service.\nIn my opinion, it would be a great pity if the purely scientific interest\nof a better knowledge of polar motion and UT1 and its application to space\nnavigation were treated separately, each ignoring the other.\nThe cheapest procedure will be finally to derive the parameters describing\nthe earth's rotation on a permanent basis. It may result in finally discovering\nthe correct mechanism responsible for the observed fluctuations, which should\npermit then fairly precise predictions.\nThis was indeed the goal of the IAG when founding the ILS in 1899 for a\nduration of six years, which has been extended now to 80 years because obviously\nthe precision of the determination by the optical instruments has not been suf-\nficient to solve the problem.\nThis introduces the question of\nAccuracy and Precision of Determinations\nAccuracy is related to absolute precision (external errors) and to\ncalibration.\nIn Doppler measurements it is considered to be + 0\"05, compared to IPMS\nand BIH.\nPrecision is related to internal errors and is considered to be + 0\"02\nin latitude and + 0\"08 in longitude from one pass.\nHowever, comparing different techniques to estimate their accuracy has\na meaning only if these techniques have a comparable precision.\nOnly then shall we be able to determine their systematic differences,\nanalyze them and perhaps find an explanation.","751\nTherefore, the ILS solution for the polar motion (that is, the solution\nrestricted to the old 5 stations) cannot be compared any more to any one of\nthe other solutions.\nI think that a reasonable goal should be to reach a precision of 0\"003\n(10 cm) in latitude and possible the same level of accuracy. Probably the\n0\"001 or better will be reached only when VLBI becomes continually available.\nOne could perhaps propose a system based upon many precise determinations\nand a few accurate determinations to calibrate repeatedly the system of\nparameters.\nA Question Raised is the Time Period Over Which\nAveraging Can Be Carried Out\nIt is obvious that the procedure of monthly averaging of the ILS is now\nold fashioned, that even 5 days averaging is no longer satisfactory.\nI would prefer to avoid any averaging of independent determination of\n(, X) and recommend keeping in a data bank instantaneous values, that is,\nvalues obtained within 2 to 4 hours measurement.\nThis time interval is compatible with individual groups of stars as\nobserved with astrolabes, VZT or PZT, with one satellite pass in Doppler measure-\nments, and with lunar laser determinations.\nIt should allow new investigations on short period components.\nUpdating of Equipment and Minimum Length of Time\nOver Which Homogeneous Measurements Must be Continued\nThe ILS has never been updated in 80 years. It seems however, that a\n12 years cycle of homogeneous data must be preserved and updating the methods\nand equipment should be carried out, bearing this in mind.\nGeographic Location of the Stations\nI should recommend a limited number of main permanent stations situated\nas far as possible from the boundaries of tectonic plates.\nThese stations should be equipped with all possible instrumentation for\nmonitoring the geophysical local parameters which are variable with time\n(vertical direction, value of g, height, underground water level, etc.).\nA number of temporary substations should be established and measurements\nrepeated there from time to time for specific aims (oceanic interactions,\nboundaries of tectonic plates, geological features like faults and graben,\nseismic activity) .\nIn this respect, I would like to point out the possibilities of some of\nthe developing countries which are not really poor countries but are seeking\nto develop their scientific capabilities. I have heard from some of them a","752\ndesire to develop some astronomical activity associated with a small observa-\ntory. It seems to me that a Doppler station associated with a time service\ncould offer them a good opportunity to introduce their students in a practical\nway to celestial mechanics, geodetic reference systems, geophysical applications\n(high atmosphere and ionospheric research for example).\nTheir contribution should help us to build up a very well geographically\ndistributed net of stations and in exchange we should support them with our\nexperience.\nA short pamphlet could be prepared to explain the many advantages of such\nan activity in the developing countries.\nSpeed With Which Data Becomes Available\nMust be increased by the use of teleprocessing. I think that our goal\nshould be to have the parameters available after one day by 1983.\nThis is a condition for space and civilian transsonic navigation as well\nas for possible seismic applications.\nFinally my Position with Respect to the\nDifferent Techniques now Available is as Follows\nVisual Optical methods will disappear within a short time just because\nit becomes extremely difficult to find people to make night observations.\nMoreover the excessive effort requested from them for a very low final effi-\nciency is disappointing.\nDoppler method is by far the cheapest and therefore accessible for prac-\ntically all countries in the world, including developing ones. It has all\nweather capability which is of great importance in countries with bad weather,\nwhich is the case in general at high latitudes.\nUntil 1990 this method is sure to be the one which will give us the\npolar motion on a continuous basis.\nLunar laser seems most promising and includes many interesting problems\nto be solved for the Earth as well as for the Moon.\nIt looks to us to be an intermediate solution for the Earth rotation\nand should continue as a system for monitoring the Moon's rotation.\nVLBI is the final solution to be reached.\nIt has two basic advantages that no other method has simultaneously:\na) all weather capability; b) astronomical fundamental reference system,\nbut it is presently very expensive to ensure a permanent service with it and\nI do not envisage this solution within the next 10 years.","(BiH)\n0\nT\nEquator\ncio\nX (BiH)\nFIG. 1\norbit\ncio\nAu /Du'\nA\ni\nR\nDi\nP\nN\nM\n&\nr","754\nReference\nICSU (1972) , The Federation of Astronomical and Geophysical Services (FAGS) :\nObjectives and Activities, ICSU Information Bulletin\nParticipants\nName\nOrganization\nFunction\nB. Guinot\nBureau int. de 1'Heure\nDirector\nB. R. Bowman\nDMATC\nGeodesist\nR. J. Anderle\nNSWC/D2\nAnalyst\nS. Takagi\nILS/Mizusawa\nAstronomer\nDEMR/Ottawa\nJ. Orosz\nAnalyst\nS. Yumi\nIPMS\nDirector\nP. Melchior\nORB\nAstronomer\nJ. Popelar\nDEMR\nGeophysicist\nA. C. Schultheis\nSystem Planning Corp.\nDirector\nC. Solloway\nCALTECH-JPL\nMathematician\nD. Mc Carthy\nUSNO\nAstronomer\nF. Nouel\nGRGS-CNES\nAnalyst\nJ. Luck\nDiv. Nat. Mapping, Australia\nAstro/Geod.\nL. Aardoom\nDELFT Univ., , Tech, Netherlands\nLecturer/Geodesy\nB. Schutz\nAerospace Engr, Univ. of Texas Assoc. Prof.\nD. Short\nLogetronics Inc.\nR. Sullivan\nSystem Planning Corp.\nAnalyst\nNational Geodetic Survey/NOAA\nW. Strange\nChief, Gravity,\nAstronomy and\nSatellite Branch\nG. Veis\nNation. Tech. Univ., Greece\nP. Wilson\nInst. F. Angewandte Geodaesie,\nFrankfort, F.R.G.","755\nMINUTES OF THE WORKSHOP SESSION ON POLAR MOTION\nJ. Popelar\nDepartment of Energy, Mines & Resources\nOttawa, Ontario, Canada\nThe workshop discussion was opened by Professor Melchior who\ninvited the representatives of the three major services IPMS, BIH\nand DPMS to express their opinion on the main points he had raised\nearlier in his presentation to the plenary session. He also\nencouraged all the other participants to ask questions and/or state\ntheir opinion on all the subjects related to polar motion.\nHe\nemphasized that only by serious, coordinated effort of all involved\ncan the present service be improved to reflect the state-of-the-art\nin the polar motion studies. It is necessary to modernize the polar\nmotion service now or else it might lose its credibility and support\nfrom the scientific unions. The time has come to re-examine and\nre-define the points of reference for the polar motion service and\nmake the necessary instrumental and organizational changes to\nprovide the best service for the scientific community.\nAgrees with Prof. Melchior and supports early introduction of the\nYumi\nDoppler, VLBI and LLR techniques to improve the polar motion results.\nHe suggests the use of VLBI and LLR to measure the distances between\nthe astronomical observatories in order to separate station movements\nfrom the effects of polar motion. The Doppler satellite technique\nis superior because numerous observations are possible. The VLBI\nand LLR is still too expensive for polar motion applications.\nPopelar\nHow do you propose to include the results of the new techniques in\nthe IPMS?\nI am against mixing the results of optical astronomical observations\nMelchior\nwith the Doppler results since the former relate to the local vertical\nwhereas the latter do not.\nI think that the astronomical and Doppler systems should run in\nYumi\nparallel for a period of time to better understand their relationship.\nAgrees in general with Prof. Melchior but caution must be exercised\nGuinot\nduring the actual implementation. One must be careful when phasing\nout the classical observations because they currently provide UT1\non a routine basis.\nThis is a very important service.\nMelchior\nIn order to derive the best UT1 one is fully justified to combine\nGuinot\nthe astronomical and Doppler pole determinations. After all, consider-\ning the number of observatories contributing to the BIH the effect of\nlocal verticals should cancel out and it is well known that there\nare greater differences between some astronomical pole determinations\nthan between the mean astronomical and Doppler satellite results.","756\nFor scientific analysis the astronomical and Doppler satellite results\nshould be treated separately but for the operational service they\nhave to be combined to obtain best possible results in short time.\nIt is difficult to define the absolute accuracy of the systems and\nany new service must not introduce additional noise or more impor-\ntantly drift in the results.\nSecular drift is of particular importance to the new techniques which\nMelchior\nshow superior internal precision over short time.\nThe Doppler results do not show more drift than the BIH, IPMS and\nAnderle\nILS results.\nCan Prof. Melchior specify the need for precise pole determinations\nGuinot\non a daily basis?\nThis need might arise if some geodynamical hypothesis relating the\nMelchior\nsources of Chandler wobble and earthquakes prove to be true. Then\npolar motion results might be used for earthquake predictions for\nexample.\nIt would be very difficult to maintain accuracy of such service with\nGuinot\nour present system.\nThe Doppler technique can provide very precise pole positions for\nAnderle\n24 hour intervals. Presently the polar positions are obtained for\nevery 2 days with about 5 day delay. The 48 hour interval seems to\nseparate better the correlation between the polar motion effect and\nthe atmospheric drag term in the solution.\nWe should try to obtain a one day resolution rather than a 1 day\nMc Carthy\nturn-around in polar determination.\nWeather dependent observations do not have this capability.\nGuinot\nThe best independently obtained results of the different techniques\nAnderle\nshould be kept separately until their differences are understood\nand explained in detail. There is a definite need and justification\nto combine the available results for operational purposes.\nIs it reasonable to try to derive the polar coordinates from\nMelchior\nDoppler observations at one station as I have suggested in my\npresentation? It would be very useful at stations like Brussels,\nOttawa and others for direct comparison between the astronomical\nand Doppler satellite results.\nIt is possible particularly for stations at higher latitudes.\nAnderle\nThe precise satellite ephemeris have to be transformed from the\nterrestrial system back to the inertial system true of date.\nDMATC can provide the short transformation subroutines which\nBowman\nbesides the rotation also include a translation; this is\nnecessary to align the Doppler satellite and astronomical systems.","757\nAnderle\nThis procedure must not be expected to provide the same pole\ncoordinates as obtained from the bi-daily solutions due to the\ncorrelation between the effect of polar motion and the atmospheric\ndrag effect. Our pole positions are the best the Doppler system\ncan presently provide. There are some significant trends in Tranet\nstation coordinates which are difficult to explain (set of graphs\ndemonstrated systematic drifts in station latitudes, longitudes\nand heights sometimes exceeding 50 cm/year based on 2.5 or 3.5\nyears of data). These systematic effects can be possibly attributed\nto the changes in the Tranet network configuration, reflection of\nsome periodical variations, etc. But it seems the longer the data\ninterval the smaller the secular drift.\nYumi\nSecular drift is difficult to determine. After 10-20 years the\nresiduals might increase again.\nAnderle\nSome of the periodical variations will be eliminated as we improve\nthe force model. Heights used to show annual variation due to\nneglecting the refraction effect but it should have no effect on\npolar motion.\nGuinot\nAll astronomical observations show strong annual variations.\nMelchior\nWhat information is needed for solid earth tides?\nAnderle\nNominal changes of station coordinates due to appropriate earth\ntide model will improve the present force model. The actual phase\nlag is relatively small to have any significant effect.\nMelchior\nDo not mix together the solid earth and ocean tides.\nAnderle\nThe improved force model will include models for solid earth,\nocean and atmospheric tides. We believe it will reduce the drift\nof station coordinates.\nProf. Melchior opened a general discussion at this moment.\nMc Carthy\nWhat will be the role of GPS (Global Positioning System) in future\npolar motion studies?\nAnderle\nSome limited simulations using range-rate only have provided poor\nresults. It is expected that improvements in instrumentation,\ngravity field and particularly the elimination of clock related\nerrors will lead to the same precision for polar motion results.\nMc Carthy\nUSNO considers VLBI as potentially the most suitable for polar\nmotion studies and expects significant progress in radio-astrometry\nin the next 2-3 years. In cooperation with NRO experiments with\ndedicated interferometer are planned using a 5 km baseline; the\nexpected precision is approximately 0.01. The PZT program will\ncontinue using new instrumentation which permits to increase the\nnumber of observed stars.","758\nSchultheis What are the prospects of using satellite laser ranging for\npolar motion?\nLaser systems are very expensive, weather dependent and the\n?\ngreatest problem is data continuity.\nGaposhkin obtained good results using laser ranging at LAGEOS\nAnderle\nsatellite, so the potential is there.\nIs there any possibility that a satellite based system will\nPopelar\nprovide UT1 in the future?\nSatellite systems cannot provide UT1 with sufficient accuracy.\nAnderle\nTime derivative UT1 can be determined reliably but not UT1 on\na routine basis.\nIndependent determination of UT1 can be very useful to BIH.\nGuinot\nNew PZT and also a new Doppler station have been recently installed\nTagaki\nat Mizusawa and the preliminary results look good. Comparisons\nbetween the results will be carried out.\nWhat is the progress with the PZT installation in Carloforte?\nMelchior\nThe PZT is ready to be shipped but there are some delays in\nTagaki\nsigning of the contract.\nAt this point the morning workshop session was adjourned. The\nafternoon session was opened by brief review of the morning\ndiscussions for the new workshop participants by Prof. Melchior,\nJ. Popelar and F. Nouel. Then the discussion continued examining\nthe availability and cost of new instrumentation.\nContinuity of polar motion service demands that all ILS stations\nMelchior\nare equipped with PZT and Doppler satellite stations. The polar\nmotion service must introduce new instrumentation and techniques\nwhich can presently operate on a routine basis. It is also\ndesirable that the observatories participating in the IPMS and\nBIH update their instrumentation; from the optical astronomical\ninstruments the PZT is apparently the best choice. But most\nPZT have been built as individual instruments and there are large\ndifferences between them. Zeiss Jena in DDR discontinued production\nof PZT. FGR Zeiss may start production of its own PZT.\nThe Doppler satellite system in its present form will probably\nWilson\nbe phased out after 15 years. Would it not be better to use\nLaser ranging to Lageos or the Moon as a basis for polar motion?\nHigh performance Laser system costs about US $1,300,000, a mobile\nunit of the same characteristics is about $1,000,000 and if 10\nunits are built the price of a unit may drop to about $400,000.","759\nWe must update the equipment now with working systems. Laser\nMelchior\nsystems have still a number of problems and are more expensive.\nPZT and Doppler guarantee the best results for a new service in\nthe immediate future.\nAny new service must provide higher precision. The network should\nGuinot\ninclude all PZT and Doppler stations without the special treatment\nof the ILS stations.\nMelchior\nBut we must not abandon the ILS stations to which the CIO is\nrelated. A separate solution only for PZT stations would be\ndesirable to increase the precision of the results.\nThere are other astronomical instruments which provide data of the\nGuinot\nsame quality as PZT and they should not be ignored.\nWilson\nThe Laser system is very useful for polar motion and has much\nlonger life time than the Doppler is expected to have.\nThe present Doppler system will be replaced by GPS only if GPS\nBowman\nwill provide results of geodetic accuracy and that implies\naccurate determination of polar motion.\nThe installation of PZT at the ILS stations is important for\nVeis\nincreasing the precision of observations while still maintaining\ntheir relationship to the local vertical. It will take a long\ntransition period (12-24 years) to phase in the new techniques\nand to establish the relationship between the astronomical and\ngeodetic systems.\nVLBI is potentially the most suitable technique for polar motion\nSchultheis\nstudies and its viability has already been established. It would\nbe better to concentrate on developing VLBI for routine observations\nand avoid two lengthy transition periods.\nThe Unions cannot afford the expenses of setting up a VLBI system\nMelchior\nand all the existing facilities are too busy with other programs.\nThe VLBI is still in the research stage and it has to be brought\nto the application stage before it can be used for regular service.\nSchultheis There is no need for high performance large antennae for polar\nmotion so the cost does not have to be very high.\nMost people agree that Doppler should be part of the polar motion\nMelchior\nservice now and VLBI is the future technique. We have to have\npositive recommendations for the IUGG General Assembly in 1979.\nDevelopment of a VLBI system for polar motion should start now\nWilson\nand laser can be used for the transition period.\nThe optical and Doppler systems are presently working, laser in\nVeis\nconnection with LAGEOS has yet to prove itself and VLBI is still\nin development.","760\nWhen establishing the new service more regular distribution of\nMelchior\nobserving stations should be sought. More consideration should\nbe given to developing countries which should be made aware of\nthis need; a brochure describing the requirements would be most\nsuitable.\nHistorically observatories have been providing services based on\nVeis\ncontinuous observing programs. It is important that people in\nresponsible positions are made aware that the need for such\nservices and continuous observations still exists and that they\nreceive the necessary support.\nA lot of money is spent on establishing or re-definition of\nStrange\nhorizontal and vertical control networks. A part of these funds\nshould be allocated to monitoring the stability of such networks\nwhich represents a continuous observing at certain stations.\nConsideration should be given to certain facilities such as\nLuck\nexisting radio-telescopes, Doppler stations, etc. which can be\nsuitable for future polar motion service before they are phased\nout\nbecause of the termination of their present program. In some\ncountries such facilities are controlled by foreign organizations\noperating world wide networks without a direct involvement of\nthe local scientific community.\nThe local observatories should be encouraged to collaborate and\nPopelar\nif possible operate stations of such world-wide networks in\ncooperation with the central agency.\nIt is sometimes difficult to get the observatories interested in\nVeis\nmainly service-type operations without a possibility of an active\nscientific participation. Most of these operations require\ncentralized data processing by computers and there is very little\na local scientist can do.\nSuitable data processing facilities are available to most observa-\nPopelar\ntories and the cost of computers is constantly declining while they\nare becoming more powerful. Also the data communication facilities\nare becoming more efficient and easy to use so in the near future\nactive participation and independent data processing by a number of\nscientific groups will be possible.\nEROLD and MEDOC are good examples of experiements which provide\nGuinot\napplication of new techniques and active participation of local\norganizations. They should provide information on practical\nproblems of organizing an international service based on new\ntechniques.\nWhat are the requirements on geographical distribution of stations\nMelchior\nin a world-wide network?","761\nIt will be possible to reduce the number of Tranet network stations\nBowman\nfor maintaining the NAVSAT system. GPS will require even fewer\npermanent stations due to the altitude of the satellites. There\nis no need for stations at very high latitudes.\nNouel\nMEDOC experiment will use 10-15 stations in a well balanced network.\nIt is considered to be sufficient for improving the gravity model\nfor polar orbit satellites and provide good solution for polar motion.\nVeis\nGood geographical distribution of stations is always important to\nmaintain the homogeneity of a system.\nStrange\nU.S. Geodetic Survey might establish a Geoceiver station in Alaska\nto contribute to the MEDOC experiment if it is desirable.\nWilson\nHow will the time frame for the MEDOC system be determined?\nNouel\nSix Tranet network stations with their own atomic standards will\nbe part of the MEDOC system and they will be synchronized using\nthe satellite clock.\nTime corrections to the satellite clock are usually under 30 us\nBowman\nwhich does not significantly affect computation of precise ephemeris.\nStrange\nThe ionospheric research at the University of Texas indicates that\ninhomogeneities of ionosphere might affect latitude determinations\nduring a solar cycle.\nYumi\nThe distribution of stations in longitude should be as regular\nas possible.\nMelchior\nWhich is the best way to organize the new polar motion service?\nShould an international steering committee be set up?\nGuinot\nDue to DMA involvement in the Doppler system, there might be some\ndifficulties when eastern block countries would like to participate.\nMelchior\nEast and West commissions can possibly be established but the terms\nof reference for the new polar motion service should be defined\nbefore 1979.\nVeis\nAd-hoc committee can possibly prepare a report on the new service\nbut the terms of reference for the new international service will\nhave to be supported by a truly international group.\nThe S.S.G. 7 can take part in the project.\nStrange\nBy 1979 the directors of the present services should prepare the\nMelchior\nnew terms of reference for the international polar motion service\nacceptable to DMA, IPMS and BIH.","762\nIt will be difficult to prepare any firm proposal for 1979 because\nGuinot\nthe proposed international experiments will not be fully evaluated\nby that time.\nWe must organize the PZT and Doppler international services for\nMelchior\nthe next 10-1 15 years now.\nDoes it mean that a new Doppler network will be organized including\nBowman\nan independent processing?\nDMA presently is and still will be for some time the only organiza-\nPopelar\ntion capable of running a routine Doppler satellite polar monitoring\nservice. It is important that the Doppler station network and any\nof its future modifications assure the best results for polar motion\ndeterminations and at the same time provide sufficient information\non the relationship between the astronomical and Doppler systems to\nmaintain the continuity of the polar motion studies.\nThe optical and Doppler techniques should operate in parallel until\nYumi\nall their differences are fully understood. It is difficult to say\nhow long.\nAre we trying to organize something that already exists?\nGuinot\nWe have to formalize some of the current practices and try to\nMelchior\norganize the best polar motion service based on our present knowledge\nof the problem. We must clearly state what is the best pole position\nand how it is determined. The new terms of reference for the inter-\nnational polar motion service must formally declare the principles\nand procedures to be used.\nAt this point the workshop adjourned. It was generally agreed that\nthe recent development of new techniques and their contribution to\npolar motion studies is significant enough to justify re-organization\nof the current polar motion service. Every effort should be made\nto prepare the necessary changes and seek their formal approval\nduring the next general assemblies of IAU and IUGG in 1979.","763\nDETERMINATION OF GEOPHYSICAL PARAMETERS\nFROM LONG TERM ORBIT PERTURBATIONS USING\nNAVIGATION SATELLITE DOPPLER DERIVED EPHEMERIDES\nBruce R. Bowman\nDefense Mapping Agency Topographic Center\n6500 Brookes Lane\nWashington, D.C. 20315\nDepartment of Geodesy and Surveys\nAbstract\nDefense Mapping Agency Doppler navigation satellite ephemerides are used\nto study long term perturbations of the 1100 kilometer circular polar orbits\nof the Navy navigation satellites (NNS). High quality mean orbital elements\nare computed from several NNS ephemerides for each 2-day data span during\n1974 and 1975. The mean semi-major axis and inclination values are shown to\nbe precise to within 2 cm and 0.016 arcseconds respectively. The semi-major\naxis variations are shown to have high correlations with solar activity and\natmospheric density variations. New geopotential resonance terms of 28th\ndegree and 27th order are determined from the elements, and the ocean tidal\nperturbations in the inclination are analyzed to demonstrate the accuracy of\nthe mean elements.\nIntroduction\nThe study of long periodic and secular orbit perturbations has long\nbeen accomplished using mean values of satellite orbital elements. Mean\nelements have been used to analyze the long term atmospheric density varia-\ntions, to determine geopotential zonal and resonance coefficients, and more\nrecently to solve for the long periodic solid Earth and ocean tidal parameters.\nA limiting factor in the past has been the lack of high quality mean element\nsets for the analyses. The analytical procedures used to compute the mean\nelements were not sufficient to remove completely the high frequency effects\nto obtain only the long periodic and secular variations. However, recently\na method for transforming osculating elements to mean elements has been\ndevised (Douglas, et. al., 1973) that retains the original precision of the\nosculating elements. The purpose of the present analysis was to determine\nthe accuracy of the mean orbital elements that could be obtained using the\nmost accurate satellite ephemeris available. The study also was designed to\ndetermine the usefulness of these mean elements for the solution of geophysical\nparameters producing long term orbit perturbations.\nMean Element Generation and Processing\nMean elements for this study were computed from ephemerides of position\nand velocity vectors converted to osculating elements. The data used were\nthe Naval Surface Weapons Center (NSWC) and Defense Mapping Agency Topographic\nCenter (DMATC) precision ephemerides for the U.S. Navy navigation satellites\n(NNS). The NNS satellites are in near circular, polar orbits with perigee\nheights of approximately 1100 km. Doppler observations of these satellites\nare obtained primarily from a network of 13 permanent and 4 mobile van stations\nof the Defense Mapping Agency TRANET and from 4 Navy Astronautics Group sites.","764\nThe ephemeris of an NNS satellite is computed from Doppler observations\nusing the NSWC orbit determination program CELEST (0'Toole, 1976). A least\nsquares solution is used to find orbit constants, a drag scaling factor, the\nEarth's pole position, and a frequency and tropospheric refraction bias para-\nmeter for each pass which best fit the observations. A 48-hour data span is\nused for the reduction. The CELEST program numerically integrates the equa-\ntions of motion using a 12th order Cowell formulation with one minute time\nsteps. Forces considered in the equations of motion include contributions\nfrom the Earth's gravity field, the direct lunar-solar effects, the solid\nEarth tides, atmospheric drag, and solar radiation pressure. The Earth's\ngravity field is expressed as a spherical harmonic expansion complete through\ndegree and order 19 with many pairs of higher order coefficients for a total\nof 487 terms. The Universal Time (UT1) is used from a weekly extrapolation\nof values published by the U.S. Naval Observatory. Standard deviations for\nsingle-pass fits are 10 to 15 cm for the range differences of the Doppler\ndata. Two-day solutions result in ephemeris accuracies of approximately\n3 to 5 meters as determined by the solution standard deviations and from\ncomparisons of overlapping points at the end of one data span and the beginning\nof the next span.\nThe precision ephemeris is output in Earth fixed coordinates at 1 minute\nintervals. Osculating elements are computed for each ephemeris point by first\nrotating from Earth fixed to inertial coordinates of date, and then converting\nto Keplerian elements. The input UT1 correction and the pole position computed\nfor the 2 day data span by CELEST are used for the transformation of inertial\nspace.\nThe study of long period and secular variations of the orbit can be under-\ntaken by computing mean elements from the osculating elements of each successive\n2-day ephemeris arc. The mean element computation is performed using a\ncomputer program (Goad, 1976) to remove from the osculating elements all\nshort periodic effects, i.e., those with periods equal to or less than the\norbital period, and effects introduced by the rotation of the Earth which\nare the m-daily effects of tesseral harmonics. The tesseral harmonic first\norder short periodic and m-daily effects are analytically removed by using the\nequations of Kaula (1966). The remaining short periodic effects (all less\nthan 50 meter magnitude) due to the Sun and Moon, atmospheric drag, radiation\npressure, second order effects of oblateness, etc., can be removed by filtering\nthe corrected osculating elements using a low band pass filter. The resulting\nosculating elements have only long periodic and secular perturbations present,\nand these are averaged numerically over the 2-day data span to obtain one set\nof mean elements corresponding to the 2-day ephemeris. Special procedures are\nused in the mean element program for long periodic effects of special interest\nthat have periods less than 15 days. If these perturbations are averaged over\nthe 2-day data span the amplitude of the effect would be reduced when computing\nthe total variation of the perturbation from a sequence of mean elements. For\nperiods of 6 days or less the 2-day averaging would be smoothing over 1/3 of\na cycle or more, which greatly reduces the total amplitude being sought. The\nlong periodic tesseral harmonics of interest and the short periodic tesseral\neffects are all removed analytically at the same time. The long periodic\neffect is then recomputed for the epoch time of the 2-day mean elements and\nthe perturbation is added back into the mean elements. This procedure ensures","765\nthat the entire perturbation is present and has not been effected by averaging.\nThe long periodic 14-day direct lunar perturbation is considered also in this\nmanner to insure accurate computations of tidal perturbations with the same\n14-day period, but with amplitudes 1 or 2 orders of magnitude less than the\ndirect effect.\nThe mean elements were tested to determine the minimum number of osculating\nsets that could be used in the 2-day numerical average without loss of preci-\nsion. Analysis of the NNS ephemerides indicated that an interval of 5 minutes\nbetween osculating vectors could be used to obtain the same mean elements\nobtained from using the full 1 minute interval ephemeris.\nThe mean elements were processed with the NASA Rapid Orbit Analysis\nand Determination (ROAD) program (Wagner, et. al., 1974). This program is\na multiple arc/satellite orbit generator which can estimate also a wide\nvariety of geophysical parameters. The orbit generator numerically integrates\nmean element variations with step sizes ranging from a fraction of a day to\nseveral days or more depending upon the long term effects that are selected\nfor computation. The forces that can be specified in the perturbation model\nare geopotential disturbances (to 40,40), direct lunar-solar gravity and\nindirect luni-solar tidal effects, radiation pressure, and atmospheric drag.\nBy either numerically or analytically averaging the full perturbations over\none revolution only the long periodic effects of the forces are considered.\nROAD has the capability of solving for: (1) the six orbital parameters,\n(2) a bias in the semi-major axis, (3) up to 5 element rates and accelerations\nfor each initial Kepler element, (4) a constant drag coefficient and solar\nradiation pressure coefficient, and (5) up to 3 sets of sinusoidal coefficients\nand periods for drag and radiation pressure. The program can solve also for\ngeodetic parameters common to all satellite arcs such as the Earth's gravity\nconstant and radius, geopotential harmonic coefficients, and tidal parameters.\nA least squares process is used to determine the solution parameters from\nthe input data of mean Keplerian elements.\nPrecision of Mean Elements\nThe precision of the mean elements was determined from an analysis of\nshort spans of mean element data processed with the ROAD program. The\nelements analyzed were the semi-major axis and orbital inclination. The\nsemi-major axis is important in determining geopotential resonance perturba-\ntions, atmospheric density variations, and solar radiation pressure perturba-\ntions because there are no first order long periodic gravitational perturbations\npresent in the semi-major axis. The inclination is important for determining\nsolid Earth and ocean tide parameters because only small perturbations are\npresent in the inclination from the other forces. The study of these geo-\nphysical effects was the main emphasis for the application of the mean elements.\nPrecision of the Mean Semi-major Axis (a)\nThe noise level of the a values is extremely difficult to determine because\nof the continual change in orbital period in response to the daily atmospheric\ndensity variations. Several different data spans of 40 to 55 days during\nperiods of low solar activity were selected for the analysis. Variations","766\ndue to the 27-day solar rotation period could not be removed adequately if a\ndata span of more than 2 solar rotation periods was used. The data were\nprocessed in ROAD using the Jacchia 1971 model atmosphere (Diamante and Der,\n1972) with daily geomagnetic index (Ap) and solar flux (F10) values (CIRA,\n1972) input to the program. The long periodic geopotential resonance\nperturbations in a were removed in ROAD by using the best values obtained\n(refer to Section 4.2) for the 13th, 14th, 15th degree 13th, 14th order and\nthe 28th degree 27th order spherical harmonic coefficients. A constant solar\nradiation pressure coefficient was included in the ROAD solution along with\na 27.5-day sinusoidal atmospheric drag coefficient and its corresponding\nphase. The resulting observed minus computed a residuals from ROAD were then\nanalyzed for remaining periodic terms. A spectral analysis of the data\nindicated periods of 4.0 and 11.3 days with amplitudes of approximately 4 cm\neach. The 4-day period corresponds to an aliasing effect of a remaining\ngeopotential resonance perturbation of 1.7-day that is sampled at a 2.0-day\nrate. A least squares procedure was used to eliminate the 4.0 and 11.3-day\nperiod plus any remaining secular trend. The resulting residuals for two\ndifferent data spans for one NNS satellite are shown in Fig. 1. The sa1\nvalues, corresponding to the first data span residuals, have a standard\ndeviation of 3.6 cm but at times show a consistency of approximately 2 cm.\nThe La2 values for the second data span have a lower standard deviation than\nthe sa1 values but still show at times a consistency of approximately 2 cm.\nThe difference between the 2 cm value and the standard deviations is most\nlikely the result of the daily fluctuations in atmospheric density.\nThe noise level can be computed theoretically from the known precision\nof the original 1 minute ephemeris data. The overlapping data points from\none 2-day ephemeris to another are consistent to within 3 to 5 meters, and\nthe 2-day orbit fits have root mean squares of 3 to 5 meters. From Kepler's\nThird Law a change of 1 cm in a will result in a change of 1.27 m/day in the\nmean anomaly for a NNS orbit. Therefore, a difference of 3 to 5 meters in\nmean anomaly will result in a difference of 1.2 to 2.0 cm in a from one\n2-day arc to the next. This precision can be observed in Fig. 1, which shows\nthat the noise level of the mean semi-major axis values can be conservatively\ngiven as 2.0 cm.\nPrecision of the Mean Inclination (i) Values\nThe precision of the mean inclination values was determined in a manner\nsimilar to determining the noise in a. ROAD was used to calculate the i resi-\nduals. Included in the integration were the NSWC [28,27] spherical harmonic\ncoefficients (DMA, 1975), the full NASA Goddard Earth Model (GEM) 8 (Wagner,\net. al., 1976) zonal harmonic coefficients to 29th degree, drag and radiation\npressure coefficients determined from perturbations in a, and solid Earth tides\nusing a Love number of 0.29 and tidal lag of 0.5 degree (Lambeck, 1974).\nSeveral data spans of approximately 50 days and one of 500 days of ROAD\nresiduals were analyzed. Spectral analysis indicated periods in the data of\n4.0, 6.1, 14.0, and 63.0 days with amplitudes of approximately 0.01\", 0.02\",\n0.03\", and 0.04\" respectively. The 4-day period, which was marginally apparent,\ncorresponds to the Nyquist frequency. The 6.1-day period corresponds to the\n[28,27] geopotential resonance period, indicating that the NSWC values for","spans.\n1. TIME 30 40 50 60\no=3.6cm\n0=3.0cm\n20\n10\n0\nFig.\n10\n5\n-5\n-10\n10\n5\n-5\n-10","768\nthe coefficients require modification (refer to section \"Determination of\nGeopotential Resonance Coefficients\"). The 14-day period corresponds to the\nsemi-diurnal lunar tide frequency and is the result of the ocean and atmos-\npheric tide perturbations. The 63-day period was determined from a spectral\nanalysis of over 500 days of residuals (refer to section \"Analysis of Ocean\nTide Perturbations\") and is the result of an error in the even zonal harmonic\ncoefficients with periods of twice the argument of perigee period.\nThe ROAD residuals were used in a least squares solution to remove\nsecular trends and the periods indicated above. Figure 2 shows the results\nfrom two different data spans approximately one year apart. From an analysis\nof 5 spans, each approximately 50 days in length, the average standard devia-\ntion was 0.016\" with no data rejected. There does not appear to be any better\nconsistency in the data in Fig. 2, and the noise level cannot be assumed to\nbe higher than expected due to short term perturbations such as atmospheric\ndrag. The range of residuals was found to be + 0.020\" when 1 or 2 outlying\npoints were removed from each 50-day data span. An error of 0.02\" in the in-\nclination corresponds to an out of plane error of 0.7 meter at 1100 km height.\nThis error bound is in good agreement with the stated accuracy of the ephemeris\nbecause the out of plane component is almost always better determined than\nthe tangential component of the orbit for the 1 minute NNS ephemeris.\nApplications\nAnalysis of Atmospheric Density Variations\nThe very precise semi-major axis values are useful for determining\naccurate atmospheric density variations at NNS heights near 1100 km. The\nsemi-major axis of a NNS orbit decays at a rate of approximately 150 meters\nper year due to atmospheric drag, which means that the total drag perturbation\nover a year can be measured to within 1 part in 10,000, and the minimal decay\nrate allows a chance to study the density variations at nearly the same height\nover very long continuous data spans of several years of more. Use of a long\ncontinuous data span is essential in studying long term density variations.\nA knowledge of these variations increases our understanding of the physical\nphenomenon of atmospheric density and composition variations, and adds to our\nknowledge of the fundamental interaction of solar activity with the Earth's\natmosphere.\nThe most prominent effect in the variation of a, other than the secular\ndecay, is the semi-annual change (CIRA, 1972). The semi-annual effect is a\nfunction of satellite height, and to a lesser extent, a function of the 11-\nyear solar cycle. At 1100 km altitude the atmospheric density changes by\napproximately 100% during the year, producing a semi-annual amplitude of\napproximately 20 meters for an NNS satellite. Since the magnitude of this\neffect is variable from year to year the differences in the observed changes\nand those computed from a model atmosphere can be very useful in studying\nthe physical phenomenon of the semi-annual variation. Figure 3 shows the\ndifference of the observed a values minus computed a values based on the\nJacchia 1971 model atmosphere used in the ROAD program. Solar flux values\nwere input for the 500-day data span in Fig. 3, and constant drag and solar\nradiation pressure coefficients were determined. The sa values show a","Fig. 2. Inclination residuals and standard deviation, (5, for two separate data spans.\n60\n50\n40\nTIME (Days)\n(J = 0.013\"\nO = 0.016\n30\n20\n10\n0\n0.04\n0.02\n0\n-0.02\n-0.04\n0.04\n0.02\n0\n-0.02\n-0.04","predicted Jacchia 3. Semi-major 1971 atmospheric axis residuals, model. Ja, Also of shown observed mean values minus 500\nsemi-annual variation at 1100km height. is the variation in density, computed Jp, values from from the\nooo\nooo\n400\nOO\nO\nooooo\n8\n8\nooo\n300\nooo\nTIME (Days)\nooo\nOO\n8\noo 00000000\n8\n200\n8\n8\n8\n8 8\nooo 8\noooooo\nooooo\nooo\n100\nO\nooo\noooo\nFig.\n0\n0\n0\n-50\n-2.0\n50\n4.0\n2.0","771\nvariation of 6 meters, which is approximately 30% of the semi-annual effect.\nThere is a high correlation of the sa residuals with the semi-annual variation\nalso shown in Fig. 3. The Da residuals are low at maximum density values and\nhigh at minimum density values. This means that the observed semi-annual\neffect is approximately 30% less than the computed variation for this particular\n500-day time span. The 30% figure is only approximate because the sa values\nare probably contaminated with a solar radiation pressure perturbation that\nwasn't entirely removed. Special care must be taken in modeling the solar\nradiation pressure perturbation of semi-annual period with an amplitude of\napproximately 6 meters for an NNS satellite.\nDensity variations correlated with solar activity also have been observed\nfor NNS orbits (Beuglass and Douglas, 1972). Figure 4 shows the sa' residuals\nfrom Fig. 3 after a correction has been made for a semi-annual and annual\nvariation of sa. Also shown in Fig. 4 are the F10 solar flux values measured\nat 10.7 cm, and A geomagnetic index values used to measure solar flares. The\nF10 values show an approximate 27-day period corresponding to one solar rota-\ntion period. There is a good correlation between the first 100 days of sa'\ncorrected residuals and the F10 variations in Fig. 4 even though the Jacchia\n1971 model atmosphere in ROAD used the F 10 values to remove the variation\neffect. The response of Da' to can be observed to be highly variable,\nespecially when comparing the first and last 100 days in the figure. The sa'\nresiduals show much less correlation with solar flares as measured Ap. The\ncorrelations of the residual values with solar flux measurements indicate\nthat better atmospheric models can be determined from using high precision\ndata such as the mean elements obtained for the NNS crbits.\nDetermination of Geopotential Resonance Coefficients\nThe mean elements also can be very useful in solving for long period\ngeopotential resonance coefficients. Resonance occurs when the orbit ground\ntrace repeats the same pattern after an integer number of revolutions of the\nsatellite. For the NNS orbits one particular resonance condition occurs with\na period of 5 to 6 days. This resonance is calculated by using the spherical\nharmonic coefficients [28,27] in the computation of the geopotential orbit\nperturbations. The 5 to 6-day period has a magnitude of approximately 20 cm\nin a and 27 meters along track. Previous determination of the [28,27] coeffi-\ncients (DMA, 1975) have been accurate to only within 100% of the value because\nof the small magnitude of the resonance perturbation in relation to all the\nother variations present.\nData on 3 NNS satellites (numbers 59, 68, and 77) from 1974 to 1976 were\nused for the analysis. An attempt to process 500 days of data in ROAD and\nsolve for the [28,27] coefficients was unsuccessful because of the large daily\natmospheric density variations greatly affecting the orbital elements. Instead\nof using the 500-day data set, the data span was divided into 40 to 50-day\nperiods. Only times of low solar activity were selected in order to minimize\nthe effects of the atmospheric drag perturbations, However, for satellite 59\n(1967-48A) only 100 days of data were available, and one time span during\nhigh solar activity had to be used. The [28,27] coefficients were determined\nwith ROAD for each separate data span. A sinusoidal atmsopheric drag\ncoefficient plus phase with a period of 27 days were computed to minimuze the","250\n8\nFig. 4. Values of 'a that have been corrected for a semi-annual and annual variation. Also\nincluded are the solar 10.7cm radiation F 10 (units of and the geomagnetic\nOOO\n200\nOOO\n150\nTIME (Days)\noo\noo\noooooo\nO\nO\nOOO\noo .\n100\n50\np\nindex A\n8\n00\n.\n0\n50\n0\n-0.5\n125\n100\n100\n75\n0.5\n0\nFo","773\nremaining F10 effects of solar activity. As noted previously, the F10 solar\nactivity of period equal to the solar rotation period of 27 days could be\nadequately eliminated if data spans of less than 2 solar rotation periods\nwere used. A radiation pressure coefficient also was included in the\nsolution.\nThe results of the analysis are shown in Fig. 5. The data spans for the\ndifferent NNS satellites are given at the top of the figure, with the results\nof the coefficient determinations shown below. Normalized values [-1.4 X\n10- 8 , 0.9 X 10 ] were used for the comparison [C, S] coefficients. A standard\ndeviation of approximately 0.3 X 10 8 was determined in each ROAD solution\nfor each coefficient. The bottom graphs of Fig. 5 show the range of F10 values\nand maximum Ap values occurring during each data span. The [28,27] C and S\ncoefficients show no correlation with time or solar activity, indicating that\nthe remaining drag variations within the data spans had little effect on the\ndetermination of the coefficients. There does appear to be a slight difference\nin the C and S values determined from satellite 77 (1973-81A) and those\ndetermined from satellite 68 (1970-67A) This difference is better shown in\nFig. 6, which is a plot of the [28,27] C and S coefficients determined for\neach satellite. The values used for the GEM 8 (Wagner, et. al., 1976) and\nNSWC (DMA, 1975) gravity models are also given. The numerical values of the\ncoefficients are listed in Table 1. The difference in means of each satellite\noccurs because the determined [28,27] coefficients are really \"lumped\" coeffi-\ncients containing higher order terms dependent upon the argument of perigee\nand other factors (Wagner and Klosko, 1975). The average value of Table 1\ncan be used to compute the [28,27] perturbation to an accuracy 100% better\nthan previously obtained. Thus, the use of mean elements in computing long\nperiodic perturbations, such as geopotential resonance effects, can greatly\nimprove the determination of the geophysical parameters currently being used\nfor orbit determination.\nX 10 8\nC\nS\nSource\n-1.27 + 0.2\n0.94 + 0.1\nSatellite 68\n-1.58 + 0.1\n0.98 + 0.2\nSatellite 77\n1.00\nSatellites 59, 68, 77\n-1.45 + 0.2\n+ 0.2\nGEM 8\n-0.43\n0.16\n-2.20 + 1.0\n0.90 + 1.0\nNSWC\nTable 1\nAverage normalized [28,27] coefficients for solutions\nfrom satellites 59, 68, and 77, and values used for\nthe GEM 8 and NSWC gravity models\nAnalysis of Ocean Tide Perturbations\nAnother application of mean elements is the study of ocean tide pertur-\nbations. Only within the last few years have data been accurate enough to","4\nFig. 5. Values of normalized (28,27) geopotential coefficients (C,S) minus (C,S) values of (-1.4, 0.9) X 10-8 for\nsatellites 59, 68, and 77. Also shown are solution data spans, the range of solar radiation F 10 during the\n1976\n47\n2\nS77\nC77\n12\n10\n45\nS77\nC77\nS68\nC68\ndata spans, and the maximum geomagnetic index Ap value for each span.\n8\n33\nC77\nS77\n1975\n28\nC68\n6\nS68\nS77\nC77\n4\nC77\nS77\nS68\n38\nC68\nTIME\n2\n42\nS68\nC68\n12\n10\n1974\nC59\n46\nS59\nS68\nC68\n8\n130\nC59\nS59\n82\n6\nMonth\n125\n100\n75\nto\n(0.3)\n0.\n-0\n(-0.3)\nCoefficients X 108\nMaximum Ap\n68, 1970-67A\n77, 1973-81A\n59, 1967-48A\nNormalized\n28,27\nSatellite\n-(C,S)\nRange\nF10\n(C,S)","775\nSatellites\n59\n68\nC X 108\n77\n0.\n1.0\n2.0\nS X 108\nGEM 8\nX\n-1.0\nI\n10\n-2.0\nx\nNSWC\nFig. 6. Values of normalized (28, 27) geopotential\ncoefficients (C,S) from solutions using satellites 59, 68,\nand 77, and from the GEM 8 and NSWC gravity models.","776\ndetect the ocean tide effects in the variations of the elements (Lambeck,\n1974; Douglas, et. al., 1974; Felsentreger, et. al., 1975). The ocean tide\nperturbation for the NNS orbits is an order of magnitude smaller than the\nsolid Earth tide effect and has the same frequency as the solid tide varia-\ntions. This indicates that the major problem is one of accurate elimination\nof the small solid Earth tide perturbation in order to analyze the even\nsmaller ocean tide effects.\nThe inclination (i) of the orbit is an excellent element to use for\nanalyzing tidal perturbations. There are no drag or geopotential terms\nappreciably affecting the analysis of the tidal perturbations in i. Only\nsolar radiation pressure must be accurately determined when considering the\nlong periodic solar tidal changes. For an NNS orbit the magnitude of the\nvariations in i amounts to approximately 2\" for the solar solid Earth tide\nof 180 to 190-day period, and approximately 0.3\" for the lunar solid Earth\ntide of 14-day period. The magnitude of the solar and lunar ocean tide\nvariations in i amount to only 0.2\" and 0.05\" respectively, showing that\nonly very accurate elements will enable accurate determinations of fluid\ntidal parameters.\nOver 500 days of mean elements of satellite 68 were processed with the\nROAD program to analyze the ocean tide perturbations. Figure 7 shows the\nresulting inclination residuals following the removal of the solid Earth tide\nusing a Love number K2 of 0.29 with a phase lag of 0.5 degree. The full\nGEM 8 zonal geopotential field to the 29th degree was used to eliminate all\nzonal effects, and the NSWC resonance coefficients were used for the 13th,\n14th and 27th order terms. A constant drag and radiation pressure coefficient\nwere also included. These two coefficients were determined in a ROAD solution\nusing the perturbations of the semi-major axis not affected by tidal pertur-\nbations. The results of Fig. 7 show the long term solar fluid tide variations\nplus other effects amounting to periodic changes of 0.6\" in the inclination.\nThe residuals were examined using spectral analysis techniques to\ndetermine the existing frequencies of the perturbations. Because of the long\nperiods of the solar perturbations, only a few cycles were available within\nthe data span. This meant that special care had to be taken in separating\nthe long period variations with spectral analysis methods. The technique\nselected for the analysis was the Maximum Entropy Method (MEM) originally\nproposed by Burg (1967), with improvements made by Ulrych and Bishop (1975).\nThe MEM theory is very useful in studying data of very short spans with regard\nto the low frequencies of interest because the method is maximally noncommittal\nwith regard to the unavailable information outside the span. The algorithm\nlisted by Ulrych and Bishop (1975) was used with a prediction error filter\nlength of 50% of the data span for smoothing. Figure 8 shows the log of the\npower spectrum of the inclination and node for the high frequency range of\n0.05 to 0.20 cycle per day. The node was included for comparison purposes\nto help eliminate confusion over noise spikes in the spectrum. It should be\nnoted that the magnitudes in Fig. 8 are not very accurate values for the power\nof each period since it has been found (Ulrych and Bishop, 1975) that the MEM\namplitudes vary widely for highly peaked spectra. The important information\nis contained in the observable frequencies, and once the frequencies are\nknown the magnitudes and phases of the different periods can be determined\nfrom standard regression analysis.","500\nradiation pressure, atomspheric drag, zonal harmonics, and solid earth solar tides.\n8\nresiduals, 11, after removal of perturbations from\n400\n300\n0000\nTIME (Days)\noooo\n200\noooo\nFig. 7. Inclination\n100\noo\n0\n0.0\n-0.2\n-0.4\n0.4\n0.2","-------------------\n0.20\n10, for the\nFig. 8. Frequency spectrum of inclination residuals, J1, and node residuals,\n6.1\n0.15\nFREQUENCY (Cycles/Days)\n6.9\nfrequency range of 0.05-0.20 cycles per day.\n0.10\n14.0 12.5\nPERIOD\n(Days)\n0.05\n-2.0\n-1.0\n-2.0\n-3.0\n-3.0\n-1.0","779\nThe periods of interest have been labeled in Fig. 8. The 6.1-day period\nis a result of the inadequate [28,27] resonance coefficients of the NSWC gravity\nset. The 6.9-day period, which is marginally apparent in i and not in So, is\nthe result of inadequate [27,27] resonance coefficients. The 6.9-day period\nis not present in So because the theoretical effect is an order of magnitude\nless than for i. The 12.5-day period is an aliasing frequency resulting from\na 2-day sampling of geopotential resonance perturbations of the 13th, 14th,\n15th degree and 13th and 14th order with periods of 1.7 and 2.4 days. The\n14-day period is the semi-diurnal lunar ocean tide variations with a magnitude\nof approximately 0.03\" determined previously from the analysis of the accuracy\nof the mean i values. The value is reasonably consistent with that predicted\nby Lambeck, et. al., (1974). The 14-day period does not show in the So spectrum\nbecause the theoretical amplitude is approximately 0.014\", a value just below\nthe noise level of 0.016\" determined for the orbit plane mean values.\nThe power spectrum of the long period terms is shown in Fig. 9. Three\ndistinct periods of approximately 62, 93, and 192 days are present in the\nspectrum. Corresponding peaks exist in the So spectrum, although the periods\nare shifted slightly. The small shifting of the frequencies from one spectrum\nto the next is a common problem that has been found with using the Maximum\nEntropy Method (Ulrych, et. al., 1973; Graber, 1975). The 62-day period is\nprecisely half the period of the precession of the argument of perigee. This\nindicates that the GEM 8 zonal model is inadequate, and also indicates the\nwell known fact that the mean elements are useful in refining the different\nzonal gravity models. The 192-day period is the semi-diurnal solar ocean\ntide perturbation. The cause of the 93-day period is unknown at this time.\nA regression analysis was performed with the 500 days of inclination residuals\nto determine the magnitudes of the long periodic terms. Amplitudes of 0.04\",\n0.08\", and 0.19\" were obtained for the 62, 93, and 192-day periods, respectively.\nThe 0.19\" solar ocean tide value is in good agreement with the theoretical\nvalue of 0.21\" (Goad, 1976) when one considers errors in the determination\nof the solar radiation pressure perturbation coefficient, and neglect of the\n0.05\" magnitude atmospheric tide perturbation. Further study of the solar\nocean tides must include detailed analysis of radiation pressure effects\n(direct and indirect), the semi-annual atmospheric drag perturbation, the\natmospheric tide variation, plus all other perturbations affecting the inclina-\ntion on a semi-annual bassis.\nConclusions\nThe determination of geophysical parameters affecting satellite orbital\nparameters can be greatly enhanced by using mean orbital elements computed\nfrom precision Doppler ephemerides by the technique of Douglas, et. al, (1973)\nas extended by Goad (1976). It has been demonstrated that precisions of 2 cm\nin the semi-major axis and 0.016\" in the inclination can be achieved when using\nthe NNS ephemerides. The high precision of the changes in the semi-major axis\ncan be used for detailed studies of atmospheric density variations, allowing\ncomputations of better atmospheric models, and eventually leading to a better\nphysical understanding of the reaction of the Earth's upper atmosphere in\nresponse to geophysical and solar activities. The highly precise a values\nalso enable an accurate determination of special resonance terms of the geo-\npotential, terms needed for satellite positions to be routinely computed at","-\n-\n0.020\nFig. 9. Frequency spectrum of inclination residuals, 11 , and node residuals,\n58\n62\n0.015\n1 Q. , for the frequency range 0.0-0.02 cycles per day.\nPeriod\n(Days)\nFREQUENCY (Cycles/Days)\n93\n0.010\n99\n175\n192\n0.005\n500\n0.0\n2.0\n1.0\n0.0\n-1.0\n-2.0\n1.0\n0.0\n-1.0","781\nthe submeter level. Accurate values for the solid Earth and ocean tide para-\nmeters that can be obtained from precise inclination values also are required\nfor ephemeris accuracy requirements at the submeter level. The mean elements\nare the tools to determine these parameters for accurate orbit predictions.\nAcknowledgements\nI am most grateful for the help and advice extended by Bruce Douglas\nand Clyde Goad of the Geodetic Research and Development Laboratory of the\nNational Geodetic Survey of NOAA.\nReferences\nBeuglass, L., and Douglas, M., Accuracy of a Predicted Satellite\nPosition, Naval Weapons Laboratory Report No. TR 2758, 1972.\nBurg, J. P. , Maximum Entropy Spectral Analysis, paper presented at\nthe 37th Annual International Meeting, Soc. of Explor. Geophys.,\nOklahoma City, Oklahoma, October 31, 1976.\nDiamante, J. M., and Der, V., Upper Atmosphere Density Satellite\nDrag Models, Wolf Research and Development Corp., Riverdale,\nMaryland, September, 1972.\nCOSPAR International Reference Atmosphere 1972, Akademie, Berlin,\n1972.\nDMA, Department of Defense National Geodetic Satellite Program,\nDefense Mapping Agency Technical Report 75-001, Washington, D.C.,\n1975.\nDouglas, B. C., Marsh, J. G., and Mullins, N. E., Mean Elements of\nGEOS-1 and GEOS-2, Celestial Mechanics 7, 1973, 195-204.\nDouglas, B. C., Klosko, S. M., Marsh, J. G., and Williamson, R. G.,\nTidal Parameters from the Variation of Inclination of GEOS-1\nand GEOS-2, Celestial Mechanics 10, 1974, 165-178.\nFelsentreger, T. L., Marsh, J. G., and Agreen, R. W., Analyses of\nthe Solid Earth and Ocean Tidal Perturbations on the Orbits of\nthe GEOS-1 and GEOS-2 Satellites, Goddard Space Flight Center\nReport No. X-921-75-194, 1975.\nGoad, C. , Private communcation, 1976.\nGraber, M. A., Polar Motion Spectra Based upon Doppler, I.P.M.S.,\nand B.I.H. Data, Goddard Space Flight Center Report, in\npress, 1975.","782\nKaula, W. M. , Theory of Satellite Geodesy, Blaisdell, Waltham,\nMassachusetts, 1966.\nLambeck, K., Cazenave, A., and Balmino, G., Solid Earth and Ocean\nTides Estimated from Satellite Orbit Analyses, Rev. of Geophys.\nand Space Phys. 12, No. 3, 1974, 421-434.\nO'Toole, J. W., The CELEST Computer Program for Computing Satellite\nOrbits, Naval Surface Weapons Center Report, in press, 1976.\nUlrych, T. J., , Smylie, D. E., Jensen, 0. G., and Clarke, G. K. C.,\nPredictive Filtering and Smoothing of Short Records by Using\nMaximum Entropy, Journal Geophys. Res. 78, 1973, 4959-4964.\nUlrych, T. J., and Bishop, T. N., Maximum Entropy Spectral Analysis\nand Autoregressive Decomposition, Rev. Geophys. and Space Phys. 13,\nNo. 1, 1975, 183-200.\nWagner, C. A., Douglas, B. C., and Williamson, R. G., The ROAD\nProgram, Goddard Space Flight Center Report No. X-921-74-144, 1974.\nWagner, C. A., and Klosko, S. M., Gravitational Harmonics from\nShallow Resonant Orbits, Goddard Space Flight Center Report\nNo. X-921-75-187, 1975.\nWagner, C. A., Lerch, F. J., Brownd, J. E., , and Richardson, J. A.,\nImprovement in the Geopotential Derived from Satellite and\nSurface Data, Goddard Space Flight Center Report No. X-921-76-20,\n1976.","783\nAPPLICATION OF DOPPLER SATELLITE TRACKING SYSTEM\nFOR POLAR MOTION STUDIES IN CANADA\nJ. A. Orosz\nJ. Popelar\nGravity and Geodynamics Division,\nEarth Physics Branch,\nDepartment of Energy, Mines and Resources\nOttawa, Canada\nAbstract\nThe Canadian PZT observatories near Ottawa, Ontario, and Calgary,\nAlberta, have been participating in the international polar motion studies\nusing precise astronomical techniques since 1956 and 1968 respectively.\nIn 1974 two Doppler satellite tracking stations were located near by the\nastronomical instruments to compare polar motion as determined by the astro-\nnomical and satellite techniques and analyze the error sources and station\nrelated effects. A real-time data acquisition, processing and communication\ncapability based on a distributed mini-computer system has been implemented\nand used for preliminary data analysis and storage. The mini-computer system\nfacilitates a high degree of automation of the tracking station operations\nand flexibility in data management. The Doppler data is transmitted daily\nby the computer to the Satellite Control Center and processed on a routine\nbasis by the DMATC Polar Monitoring Service. Results of simultaneous\nsatellite and astronomical observations at the Ottawa station show approxi-\nmately the same dispersion of the mean daily coordinates. The satellite\nresults do not indicate apparent seasonal variations which are characteristic\nfor the astronomical observations.\nIntroduction\nPrecise continuous astronomical observations of the earth rotation and\npolar motion in Canada commenced in 1952 when a PZT (Photographic Zenith\nTube) was installed at the Dominion Observatory in Ottawa. A relatively high\ninternal precision of PZT observations led to attempts to reduce or eliminate\nsources of external bias mainly due to independent sets of observed stars\nwhich define the reference frame. This resulted in the deployment of new\nPZT instruments on parallels of existing PZT observatories. The second\nCanadian PZT was installed in 1968 at a new site near Calgary on the parallel\nof the Herstmonceux PZT of the Royal Greenwich Observatory in England.\nThe geophysical significance of the PZT observations for global geodynamic\nstudies was recognized during the reorganization of the now defunct Dominion\nObservatory and the PZT operations became part of the newly established\nEarth Physics Branch of the Department of Energy, Mines and Resources in 1970.\nShort-term variations and abrupt changes in polar motion and earth rotation\nare of particular interest to geophysicists (Smylie, Mansinha, 1967). Since\nthe desirable homogeneity of data sets obtained by the optical astronomical\nobservations cannot be achieved due to the inherent limitations of the method\n(only night observations under favorable meteorological conditions are possible), ,\na review of the recent developments in polar motion studies resulted in a","784\nrecommendation to use the Doppler satellite tracking technique to complement\nthe PZT program. In 1974, two Doppler satellite tracking stations were\nobtained on loan from the U.S. Defense Mapping Agency and installed near the\nastronomical instruments with the intention to compare polar motion as deter-\nmined by the two independent techniques and analyzing sources of errors and\nsite related effects.\nThe character of both the PZT and the Doppler satellite operations is\nsuitable for a high degree of automation which is rather important for the\neconomy and efficiency of any long term polar motion program. An efficient\ndata management and communication system is particularly required for the\nDoppler satellite operation. The Polar Motion Group of the Earth Physics\nBranch has made a sustained effort to automate routine procedures while\nmaintaining a continuous observing program.\nAstronomical Observations\nThe two Canadian PZT observatories near Ottawa and Calgary have been\ncontributing data to the international time (BIH) and polar motion (IPMS)\nservices since 1956 and 1968 respectively. The nightly operations of both\nPZT are fully automated by means of an electro-mechanical system and the\nphotographic plates are measured and reduced daily. Internally the latitude\n( 0 ) and rotational time (UT) observations for individual stars are consistent\nto about 0.1 or 10 ms. The dispersion of the mean values of and UT for\nindividual plates around their highly smoothed curves varies between + 0.03-\n0.'05 or + 3-6 ms respectively (Popelar, et. al., 1975). The systematic bias\nof each station with respect to the mean system as maintained by the BIH\n(Guinot, et. al., 1967-1975) and IPMS (Yumi, 1962-1973) can be significantly\nhigher than the above mentioned figures which are based on raw data without\ncorrections for earth tides and diurnal nutation. The average night observa-\ntions at both PZT observatories with their reduced smoothed values of latitude\nand UT are summarized periodically in annual reports published in the Geodyna-\nmics Series Bulletins. The smoothed curve in Fig. 1 shows the PZT latitude\nvariation at Ottawa between January 1975 and July 1976, whereas the UT2-UTC\ncurve is given in Fig. 2 for the same period of time for which also Doppler\nsatellite observations at Ottawa are available. The UT2-UTC curve shows\nsignificant changes in the rate of earth rotation, for detection of which the\nPZT observations are presently most suitable. This information is required\nfor the present Doppler satellite data processing as an external variable.\nIn this way the classical astronomical techniques support the Doppler satellite\nsystem.\nDoppler Satellite Observations\nThe Doppler satellite tracking is a 24-hour all weather operation producing\nlarge amounts of raw data which require daily verification and transmission\nof selected satellite passes to the central processing facility. The staffing\nlimitations for the tracking operations (one technician per station) make any\nlong-term tracking program require a high degree of automation of data acquisi-\ntion, management and communication procedures.","785\nAfter obtaining a Geoceiver for the Calgary observatory and a Tranet\nstation for Ottawa in 1974 the tracking and data handling procedures were\ncarefully analyzed and a mini-computer based real-time data acquisition,\nprocessing and communication system was procured. Until now this Hewlett-Packard\ndistributed mini-computer system has been used mainly for data identification,\ntemporary storage and communication. The mini-computers in the system are\npermanently connected by means of dedicated low speed data communication lines.\nThe Ottawa mini-computer has been equipped for direct data input from the\nTranet station, the Geoceiver paper tapes have been used to input the Doppler\ndata into the computer system at Calgary. Requested satellite passes for both\nstations are transmitted to the Satellite Control Center by the central mini-\ncomputer which also maintains the necessary transmission log. All the passes\ntracked are temporarily stored on the central disc and periodically transmitted\nto a large computer installation for a permanent storage on magnetic tapes.\nBy means of a 2000 bps dial-up dataphone and the HP Remote Data Transmission\nSystem selective retrieval of the permanently stored data is a simple operation;\nthis system facilitates immediately very efficient data communication to any\ninstallation equipped with compatible facilities.\nRecently the distributed system has been expanded to include three mini-\ncomputers: the central computer at the main laboratory and two terminal\nprocessors at the tracking sites (Fig. 3). The up-graded software operating\nsystem enables full two-way central-terminal control. A Tranet station con-\ntroller has also been developed to provide complete computer control of routine\ntracking operations. The controller (Fig. 4) is interfaced with the mini-\ncomputer by means of a 16-bit microcircuit I/O board and according to the\ncomputer control word output controls all the necessary Tranet station functions\nand parameter selection including single frequency data acquisition. The\nTranet station output is converted by the controller to a data input word\nwhich besides the data also contains the station status. The computer control\nof the Geoceiver operations will be limited to a simple switching in the\nantennae circuitry and data input from the Geoceiver computer output connector.\nIn the last stage of the system development automatic weather stations\nwill be installed at both sites and interfaced with the terminal mini-computers\nto provide direct input of meteorological parameters (temperature, pressure\nand humidity) into the satellite data stream. The Climatronix Corp. modular\nmeteorological system components have already been purchased for this purpose.\nPreliminary Data Comparison\nDuring the system development Doppler satellite data is being obtained\non a continuous basis using manual or unattended modes of operation. The\nsatellite positions for the Ottawa station as obtained from the DARCUS solutions\nfor one satellite supplied by the U.S. Naval Surface Weapons Center are shown\nin Figs. 5 and 6 in the same form as the PZT results in Figs. 1 and 2. The\ndata points represent daily mean values for passes with the internal coordinate\nerrors not exceeding + 10 m. Unfortunately, due to local interference affecting\nmainly the low channel at the present antennae site in Ottawa, about 30% of the\npasses have been rejected. A closer analysis of some of the rejected passes\ntheir independent reduction by the GEODOP program (Kouba, Boal, 1976)\nand\nindicate that the rejection percentage can be reduced by adopting stricter","786\ncriteria for data filtering before the final solution. However, the Tranet\nstation will be moved shortly to its permanent location at Shirleys Bay near\nOttawa alongside the PZT where this sort of interference is supposed to be\ngreatly reduced. The dispersion of the individual latitude and longitude\nvalues with respect to the highly smoothed curves are about + 0.'05 or + 5 ms\nwhich is of approximately the same magnitude as the PZT results. Both curves\nshow no appreciable drift during the 450 days period and only the latitude\nshowed indications of periodic variations of very small amplitude (0\".005)\nwhen subjected to a least squares spectral analysis. Due to the invariant\ncharacter of the smoothed satellite coordinates the differences between the\nsmoothed satellite and astronomical results strongly resemble the variations\nof the smoothed PZT observations. The PZT latitude observations show very\nsmall drift, about 0.02/year, and an annual variation with an amplitude of\nabout 0.'04 is the most pronounced periodical term. On the other hand longer\nterm or irregular changes of the rate of rotation dominate the PZT time obser-\nvations. While there was a relatively stable difference between the UT2 and\nUTC time scales of about 2.7 ms/day during 1974 and 1975, the difference\nincreased by about 0.2 ms/day during the first half of 1976.\nConclusions\nThe Polar Motion Group of the Earth Physics Branch will continue PZT\nand Doppler satellite observations of variations of the station coordinates\nat Ottawa and Calgary to facilitate studies of polar motion and earth rotation\nand to provide permanent monitoring, reference and calibration points for\nmaintaining precise geodetic datum and for long term studies of crustal plate\nmovements. A high degree of automation of routine operating procedures, data\nprocessing and communication by means of mini-computer based system greatly\nincreases the efficiency of this long term program and substantially improves\nthe data management and exchange. Recognizing the importance of wide ranging\ninternational cooperation for polar motion studies, the group is prepared to\ndiscuss participation in experiments designed to study global geodynamics.\nReferences\nGuinot, B., 1967-1975, BIH Annual Report, Paris.\nKouba, J., Boal, J.D., 1976. The Canadian Doppler Satellite Network. Proc.\nInt. Geod. Symposium on Sat. Doppler Positioning, Las Cruces, N.M.\nPopelar, J., Sim, S.B., Wheeler, M.O., 1975. PZT Observations of Time and\nLatitude, Ottawa and Calgary, 1974. Geodynamics Ser. Bull. No. 66, Ottawa.\nSmylie, D.E., Mansinha, L., 1967. Effect of Earthquakes on the Chandler\nWobble and the Secular Polar Shift. JGR, Vol. 72, No. 18.\nVanicek, P., 1971. Further Development and Properties of the Spectral\nAnalysis by Least-Squares. Astrophysics and Space Science, 12.\nYumi, S., 1962-1973. Annual Report of the International Polar Motion Service,\nMizusawa.","OTTAWA PZT LATITUDE OBSERVATIONS\nJULIAN DATE\n3100.0\n1975-6 and the smoothed curve (latitude corrected for\nFIG. 1 PZT mean night observations of latitude at Ottawa in\n2900.0\nthe DPMS pole positions; STD + 0.'037). .\n2700.0\n2500.0\nPHI 1\n.200\n1.200","OTTAWA PZT TIME OBSERVATIONS\nJULIAN DATE\n3100.0\nand the smoothed curve for UT2-UTC + 2.7 ms/day (UTC step\nFIG. 2 PZT mean night observations of time at Ottawa in 1975-6\nadjustments removed and corrections for the DPMS pole\n2900.0\npositions introduced; STD + 3.1 ms).\n.\n2700.0\nUT2-UTC + 2.7MS/DAY\n2500.0\n.750\n.650","789\npolar\nmotion\nsatellite\nsystem\ntracking\nTELETYPE\nDMATC\n75 bps\n2000 bps\nIBM 2780\nDIAL-UP\nMODEM\nOTTAWA EPB\nREADER\nCARD\nPRINTER\n200 lpm\nLINE\nCONSOLE\nFIG. 3 Mini-computer distributed system for satellite data\n240 cps\nREADER\nCRT\nCARD\nRTE 2 -BSM\nCARTRIDGE\nCONSOLE\nHP 21 MX\nPRINTER\nCONSOLE\nacquisition, management and communication.\nPRINTER\n30 cps\n30 cps\n32 K\nDISC\nRTE-SCE/5\nRTE-SCE/5\nmodem\nmodem\nHP 2100\nREADER\nHP 2100\nREADER\n24 K\n24K\nPT\nPT\nGEOCEIVER\n400 150 MHz\n324 162 MHz\n400 MH Z\n150 MHz\nTRACKING\n324 MHz\nMHz\nRECEIVER\nSECTION\nFILTERS\n162\nPROCESSING\nCONTROL &\nDIGITIZER\nACU\nTBD\nRCU\nSTANDARD\nCOHERENT\nRb- FREQ.\nRECEIVER\nSECTION\nSTATION\nTRANET\nCLOCK\nCLOCK\nCLOCK\nWEATHER\nVLF\nCALGARY\nSTATION\nOTTAWA SB\nWEATHER\nSTATION","1901\nTRANET\nDIGITIZER\nACU\nRCU\nT.F.\nFIG. 4 Tranet controller functions.\nCONTROLLER\nCNTR ENABLE\nBREAK LOCK\nMEM. ERASE\nACU MODE\nRCU RATIO\nT.F. SELECT\nNC COUNT\nASCII/TTY\nQ STATUS\nHEADER\nDATA\nT.F.\nNC\nHP 2100\nBOARD\n16-bit\nI/O","791\nOTTAWA 028 LATITUDE OBSERVATIONS\nJULIAN DATE\n3100.0\nFIG. 5 Tranet mean daily latitude for Ottawa in 1975-6 and the\n2900.0\nsmoothed curve (STD + 0.'047) .\n2700.0\n2500.0\nPHI 1\n38.600\n39.600","OTTAWA 028 LONGITUDE OBSERVATIONS\nJULIAN DATE\n3100.0\nFIG. 6 Tranet mean daily longitude for Ottawa in 1975-6 and the\n2900.0\nsmoothed curve (STD + 5.3 ms) .\n2700.0\n2500.0\nLONG 2\n.360\n.260","793\nDOPPLER DATA TRANSMISSION AND HANDLING\nAT THE GEODETIC INSTITUTE OF UPPSALA\nMichael Shaughnessy\nGeod. Inst. Uppsala Univ.\nUppsala, Sweden\nYou have just become the owner of a Doppler receiver. This is a red\nletter day for you! However, do not immediately rush out and start measure-\nments, because you will be very sorry. Your problems are just about to begin.\nWhat problems? Well, the Doppler receivers are very powerful tools, but\nthey have one important disadvantage. They generate large amounts of data.\nIf you have not considered how to get the data from the receiver into your\ncomputer, you're in trouble. Stop, think, plan, how are you going to do\nthis, most easily, most efficiently, in the least time consuming way.\nI might take up three different ways of handling data. One: we've\nheard a lot this week of real time computer processing in the field. Second:\nwhat I call pseudo real time processing is sending the data by phone back\nfor processing in the office. Third: processing data at a later time at\nthe end of the survey when you come back to the office. All of these\nmethods have their advantages and disadvantages.\nIn the European Doppler Campaign last year we were working in real\ntime with a mini-computer. We had quite a few problems. Also when you\nconsider the cost of the mini-computer as against the cost of the receiver,\nI prefer to spend more money on hardware in the large computer and I\ndecided on the second of these three methods. Now what we have in the\nfield is a new paper tape reader. It's a very small portable unit.\nWe're planning to run at about 300 Baud. We have a modem from the\nSwedish Telecommunications Board. I should point out that in Sweden, all\ntelephones are on a plug. So all we do is we pull out the telephone from\nits normal jack, we plug in a modem, plug in a paper tape relay and we're in\nbusiness.\nDuring discussions of this with the Swedish Telecommunications Board we\nwere trying to arrive at the speed of transmission. All telephone lines are\nsupposed to accept 3K frequency levels but when you start asking them and\npressing them, they say no, no, no, its not possible. Twelve hundred, well\n300; they still won't commit themselves. So okay, we said 300. I can\nillustrate this. We wanted to send to Stockholm from Uppsala (about 50 miles)\ndata to another computer, and we said we'd like to send at 1200 Baud. Now\nwe have two telephone exchanges in Uppsala, a new one and an old one. We're\nin\nthe old one. Some of our cables are from around the turn of the century.\nIf you ring up, they said, we can't guarantee what line you're going to get.\nYou could however, use the new exchange but then we have to do a tie link\nfrom the old to the new and give you a complete set of new telephone numbers.\nWe thought, well we won't bother, so we standardized on the 300 Baud rate.\nWhen we did this campaign last year, the facilities we had were limited\nto the mini-computer. We had at the main computing center punch card facilities","794\nand one paper tape reader. However, we did not have control of the input data\nfor this reader, so that we didn't want to use it. Since then we have\nacquired a number of units. We have a mag tape unit, we have the General\nElectric Terminal 30, which is a 300 Baud printing terminal. We also have\na videa unit and we have two modems. When we're in the field we take one\nmodem and the paper tape reader.\nWe have also five channels, both send and receive. These five go right\naround our building and in every room we have outlets so we can interface into\nthe system. We don't have to have all that equipment collected together in\none room. There are a number of combinations which we can do with the\nequipment. What we plan to do is read from the paper tape reader. We directly\ntake the tapes off the punch from the receiver, put them on the paper tape\nreader, read them on mag cassettes, then we have no more handling of that\ndata. While we are doing this other people in the Institute working on other\nproblems can be using the printing terminal and a modem communicating with\nthe receiver. Somebody can be using a video from the other modem communicating\nwith the computer, so we are not tying up facilities for one person doing\ndoppler and no one else can do a thing. We just switch in the units, inter-\nconnect them just as we want to. Its just a simple switch system. When we've\ngot the data on the mag tape, then we interface with the tape unit and the\nprinting terminal and a modem and we can work either on line or we can work\non a batch mode computer. Also, some one else can still be working, using a\nvideo and a modem; we're not disturbing each other.\nAnother mode here is that if somebody is out in the field, he can be\nreading data through the modem onto the tape and we could also from the\ninstrument laboratory be reading from the paper tape reader using the video\nas a monitor and reading into the computer. These modems have an automatic\nmode. So we can set the machine in the evening, set the modem, set the tape\nunit, go and forget about it. Someone in the field just needs to ring up.\nAfter a couple of seconds the machine switches over, the modem is on, the\ntape unit is switched on and somebody can transfer his data on the mag\ncassete. Nobody needs to be there from the Institute.\nThat is the way I have attacked the problem in the Institute. Because\nI know we are going to have a lot of data, not from one station, but from a\nnumber of stations. If we don't sort out how to handle it now, we are going\nto have trouble later. Once you've made the measurements -- it always\nhappens -- oh we've made some measurements; let's see the results, let's see\nthe results, and you tend to make a sort of bad solution to get a result out\nin a hurry, and something goes wrong somewhere in the system. The data are\nbacking up and this poor guy is just sweating trying to keep up with it and\nthe stuff is still coming in the door.\nAlso this has been touched on now, about interchange of data from the\npeople using magnetic cassettes. This is why I said we had an RS232 inter-\nface because in Europe we have just a conglomeration of receivers. In my\nopinion, when you are working with a large project with ten or fifteen\ngroups, and you send the raw data, the pure raw data to one center and then\nthey reformat it to fit the standard reduction program at that place, there's\nonly one source of errors. However, if everybody starts majority voting\nthen what you're likely to end up with at half a dozen places is half a dozen\nsources of errors.","795\nDELAY DETERMINATION OF DOPPLER EQUIPMENTS\nJ. Usandivaras\nUniversity of Tucuman\nConicet, Argentine\nP. Pâquet\nObservatoire Royal de Belgique\nBruxelles\nSummary\nUsing the GUIER's relations to analyze Doppler data a method to improve\nthe estimation of the delay equipment is proposed.\nDifferent delays used on a separate analysis of the North-South and South-\nNorth passes, produce station coordinates variations directly connected with\nthe delay errors. The precision seems to be better than 30 usec.\nThis procedure has been applied on the data acquired by 5 stations during\nthe EDOC campaign of May 1975.\nIntroduction\nThe delay measurements of Doppler equipments are often performed by\nelectronic methods applied directly to receiving systems. Generally users\nhave to accept results obtained by this procedure.\nHowever, while reducing the EDOC data we acquired the idea that some\nproposed delays were not really the correct ones. This was suggested by\nsome large systematic and positive deviations of the along track components\nin the GUIER's filtering. Moreover, we knew that for some stations the\ndelay was not determined.\nWe are proposing here two criteria of computations from which the\nelectronically defined delay is confirmed or determined directly from the\nobserved data.\nRemark. The first approximation for the station coordinates used for\nthese estimates is always that obtained after convergence of the solution\nproposed in Usandivaras and al [1]. In this solution the conventional delay,\nwhen known, has been used.\nControl of the Delay Magnitude With the Along Track Component\nAs the delay is a constant time error and the along track axis is\nalways positively oriented towards the satellite motion, the delay error\nsystematically shifts the true satellite position along this axis.\nAn example is given in Table 1, where the column \"along track\" reflects\nsuch systematic deviation. A first approximation of the delay, better than\n100 usec, can be directly deduced from the mean along track displacement\ndivided by the satellite velocity.","796\nIn the data analysis, the use of a new delay value that shifts the\nsatellite along its orbit, can introduce a different number of passes for\nthe general single point positioning. This follows from the condition that\npasses giving a total station displacement greater than 10 meters are elimin-\nated. For example in a solution with 50 passes, if only one pass having an\nalong track error of 10 meters is included, the delay shift will be in error\nby about 30 usec.\nHowever when, for the determination of station coordinates, the equili-\nbrium between the North-South (NS) and South-North (SN) passes is realized\nthen the effect of the delay error is, within limits, negligible.\nIn Table 2, coordinates displacements are shown for different delays\nand for good distribution between NS and SN passes.\nThe three last columns give respectively the mean along track displace-\nments, mean range displacements and the deduced delays.\nSeparate Analysis of NS and SN Passes\nIf a delay error is still present in single point positioning performed\nwithout mixing the NS and SN passes, the systematic satellite along track\ndeviation is completely reflected in the station position. With separate\nanalysis for NS, SN passes and using a spherical system of reference (r, , 1)\nit can be easily seen that the coordinates most affected are in the order\n- the latitude\n0,\n- the range\nr,\n- the longitude\n1.\nThe best value for the delay is that for which the station coordinates\nare coherent disregarding the direction of the satellite motion. For EDOC\nstations, various delays were used and NS and SN passes computed separately.\nFor BRUSSELS the variations of the three spherical station coordinates are\nplotted in Fig. 1 and the same variations expressed in the (xyz) reference\nsystem are presented in Fig. 1A.\nFrom Fig. 1 and as expected, the latitude variations are the most\nexplicit to deduce one eventual delay error. For the other stations only\nlatitude and x, Z variations are given in Figs. 2, 2A to 5, 5A. In Table 3,\nthe corrections to the conventional delays, furnished by stations, are given\nas well as the total delays. The units are one microsecond.\nEffect of Delay Error on Satellite Frequency Determination\nFrom the classical Doppler formula\nN = ref - Fsat' sat (t2 - t1) + ref\n(T2\nT1)\n-\nwe have for the satellite frequency F\nsat","797\n(T2\nA constant delay does not influence the first term of the right hand member,\nthen\ndT2\nAt\n=\nsat\ndt\nwhich can be written\ndr2\ndr1\n1\nAF\nAt,\ndt\nsat\nC\ndr\ni\nbeing the range velocity of the satellite at time t2 and t1.\ndt\nThe coefficient\ndr2\ndr1\nAt\nrepresents the distance error induced by the delay error.\nIt can be easily seen that AF has always the sign of the time error:\nsat\n- if the delay is too large (At<0), AF sat is negative,\n- if the delay is too small (At>0), AF is positive.\nsat\nHowever the variation of AF sat is of the order of 0.01 Hertz for a\n500 usec variation in the delay estimation and the absolute value of the\nsatellite frequency is not known with such accuracy. So no improvement of\nthe delay can be obtained by this procedure and it is necessary to use the\nmethod described in the preceding paragraphs.\nFigure 7 shows the frequency shift for different delays.\nAcknowledgements\nJ. C. Usandivaras is indebted to the Director of the Royal Observatory\nof Belgium, Prof. Velghe, that allows him extensive use of its computer\ncenter, also to the Consejo Nacional de Investigaciones Cientificas y\nTecnicas of Argentine that supported a long stage in Belgium.\nReference\n[1] J. Usandivaras, P. Paquet, R. Verbeiren - An ORB Doppler program analysis\nand its application to European data - International Geodetic Symposium on\nsatellite Doppler positioning - Las Cruces, October 1976.","798\nTABLE 1 - Firenze, satellite 30190, days 75-122/75-136\nNST AN JO HE MI DL\nDR\nERL\nERR\nDOF SET\nEQM\n1.21\n3.14\n3\n75\n122\n12\n0.64\n47\n0.78\n-80.06655 0.009\n1\n3.38\n2.15\n1.73\n3\n75\n122\n14\n33\n1.33\n-80.06658 0.010 1\n3\n1.95\n75\n123\n-1.81\n0.60\n24\n0.55\n1\n-80.06658 0.005\n2\n3.32\n-2.27\n2.62\n3\n75\n124\n14\n47\n1.72\n-80.06659 0.010\n1\n4.11\n3\n75\n125\n1?\n-2.13\n0.84\na\n0.87\n-80.06660 0.009\n1\n1.01\n3\n75\n125\n13\n-2.42\n54\n0.77\n0.80\n-80.06656 0.008\n1\n2.97\n3\n75\n125\n-0.77\n24\n10\n0.44\n0.46\n-80.06660 0.005\n2\n3.60\n3\n75\n126\n2.10\n0.80\n1\n57\n0.74\n-80.06059 0.007\n2\n-1.45\n3\n75\n126\n1.27\n2.72\n11\n19\n1.78\n-80.06654 0.011\n1\n3\n75\nE.46\n126\n23\n-2.16\n2.78\n22\n1.80\n-80.06606 0.010\n2\n0.53\n1.73\n3\n75\n127\n0.58\n1\n0.73\ni\n-60.06658 0.011\n2\n2.66\n0.21\n3\n75\n127\n0.73\n12\n18\n0.92\n-80.06659 0.009\n1\n5.63\n-3.37\n3\n75\n127\n14\n1.02\n0.34\n-80.06560 0.007\n4\n1\n1.47\n3\n75\n127\n-0.63\n24\n20\n0.46\n0.55\n-80.06658 0.007\n2\n2.51\n3\n75\n128\n2\n-0.62\n1.45\n7\n1.12\n-80.06661 0.010\n2\n0.0%\n-4.07\n3\n75\n128\n11\n29\n1.03\n0.89\n-80.06661 0.007\n1\n3 71 128 13 10 -0.81\n3.24\n0.48\n0.61\n-80.06662 0.007\n1\n2.66\n-1.78\n3\n75\n128\n23\n31\n1.80\n1.53\n-80.06661 0.013\n2\n1.84\n0.61\n3\n75\n129\n1\n18\n0.48\n0.57\n-80.06660 0.008\n2\n0.04\n0.12\n3\n75\n129\n12\n27\n0.54\n0.66\n-80.06661 0.008\n1\n0.45\n3\n75\n129\n0.88\n1.64\n14\n14\n1.32\n-80.06661 0.008\n1\n0.83\n4.14\n3\n75\n130\n()\n29\n0.35\n0.46\n-80.06661 0.007\n?\n1.24\n-2.34\n3\n75\n130\n1.54\n0.88\n2\n17\n-80.06659 0.005\n2\n-11.14\n-1.40\n1.08\n3\n75\n130\n11\n39\n1.09\n-80.06662 0.010\n1\n1.22\n-0.58\n0.85\n3\n75\n136\n13\n20\n0.97\n-80.06662 0.011\n1\n1.19\n-1.54\n3\n75\n130\n23\n0.99\n61\n0.97\n-80.06668 0.010\n2\n0.60\n-1.58\n0.62\n3\n75\n131\n1\n28\n0.66\n-80.06663 0.707\n2\n5.81\n0.51\n3\n75\n3.56\n131\n10\n50\n2.07\n-80.06671 0.011\n1\n0.12\n-0.98\n0.72\n3\n75\n131\n12\n37\n0.66\n-80.06667 0.008\n1\n2.62\n-5.16\n2.18\n3\n75\n131\n14\n23\n1.27\n-80.06668 0.006\n1\n0.28\n-2.39\n0.74\n0.92\n3\n75\n132\n-80.06667 0.010\n11\n40\n1\n3.01\n-2.13\n1.21\n3\n75\n132\n13\n1.09\n35\n-80.06669 0.010\n1\n3 75 132 23 50 0.06\n-0.89\n0.67\n0.71\n-80.06667 0.009\n2\n0.41\n0.27\n1.29\n3.75\n133\n1.19\n1\n37\n-80.06665 0.011\n2\n2.40\n-1.51\n1.47\n3\n75\n133\n11\n1.06\n-80.06665 0.007\ni)\n1\n2.57\n-1.73\n0.37\n3\n75\n133\n0.42\n-80.06666 0.005\n12\n47\n1\n3.11\n-6.42\n2.15\n-80.06671 0.012\n3\n75\n133\n23\n2\n1.74\n2\n-0.04\n0.19\n0.79\n1.00\n-80.06666 0.014\n3\n75\n134\nG\n49\n2\n1.13\n4.85\n0.42\n0.54\n-80.06664 0.006\n3\n75\n134\n1\n11\n59\n3 75 134 13 45 -0.78\n-1.77\n0.72\n0.57\n-80.06665 0.004\n1\n3.44\n-2.14\n2.25\n2.24\n-80.06668 0.012\n3\n75\n135\n1\n11\n1(\n2.03\n-3.63\n0.81\n0.94\n-80.06067 0.010\n1\n3\n75\n135\n12\n57\n1.80\n-2.82\n1.07\n1.01\n-80.06670 0.009 2\n3\n75\n135\n23\n17\n4.90\n-0.60\n1.20\n1.36\n-80.06667 0.017\n2\n3\n75\n136\nn\n58\n-2.23\n3.34\n0.63\n0.78\n-80.06669 0.010\n1\n3\n75\n136\n12\n&\n3 75 136 1 ? 54 1.86\n-1.69\n3.04\n1.96\n-80.06673 0.012\n1\nnote: columns: DL = ALONG TRACK\nDR = RANGE\nDOFSET = satellite offsnt","799\nTABLE 2 - BARTON STACEY\nCOMP\nMEAN\nMEAN\nCORR\nDeT.\nLAMB\nPHI\nDR\nMO\nD.T.\nAL TR\nRANGE\n-600\n0.18\n-0.03\n-0.09\n0.3549\n-205\n395\n- -1.481\n-0.54\n-420\n0.08\n-0.07\n-0.0?\n0.3469\n- 47\n373\n-0.341\n-0.53\n-350\n0.03\n-0.08\n0.01\n0.3455\n12\n362\n0.086\n--0.52\n-310\n0.00\n-0.03\n0.03\n0.3451\n46\n356\n0.330\n-0.52\n-280\n-0.02\n-0.09\n0.04\n0.3451\n71\n351\n0.513\n-0.49\n-140\n-0.11\n-0.12\n0.10\n0.3477\n188\n328\n1.365\n-0.51\n0\n-0.20\n-0014\n0.15\n0.3546\n308\n308\n2.219\n-0.51\nMEAN VALUE\n353\nTABLE 3\nSTATION\nCONVENTIONAL\nCOMPUTED\nTOTAL\nDELAYS\nCORRECTIONS\nBARTON STACEY\n-192\n--280\n-472\nBRUSSELS\n-489\n30\n-459\nFIRENZE\n-180\n-180\n0\nGRASSE\n()\n0\nO\n75\n-475\nWETTZELL\n-550","800\n20\n1.0\n-1.0\n-2.0\n-200\nO.\n+200\nFigure 1 - Brussels","801","802\n2.0\n1.0\nO.\n-1.0\nP\n2.0\n-200\n600\n400\nFigure 2 Stacey","803\n2.0\n1,0\n-1.0\nx\nZ\n-20\n-600\n-400\n-200\no\nFigure 2A - Barton Stacey","804\n20\n1.0\n-1.0\nP\n-2.0\n200","805\n2.0\n1.0\nO.\n-1.0\n-2.0\n-200\nFigure 3A - Firenze","","807\n1.0\nO.\n-10\n-20\n200\n-200\nFigure 4A - Grasse","808\n2.0\n1.0\nO.\n-1.0\n-2.0\n-200\n200\nFigure 5 - Wettzell","809\n2.0\n1.0\nO.\n-1.0\nX\nZ\n-2.0\n-200\n200\n0\nFigure 5A Wettzel]","810\nKm/s\n6.0\n4.0\n2.0\nO.\n-2.0\n-4.0\n-60\n2\n4\n6\n8\n14\n10\n12\n16\n18\n20\nmin\nFigure 6 - Range velocity - maximal elevation 41:2","811\n-0.17\n140\n280\n420\nFigure\ntimes\n7","812","813\nERRORS OF DOPPLER POSITIONS OBTAINED FROM RESULTS OF\nTRANSCONTINENTAL TRAVERSE SURVEYS\nB. K. Meade\nNOAA - National Ocean Survey\nNational Geodetic Survey (Retired)\nRockville, Maryland 20852\nAbstract - Point to point inversed distances in space, using Doppler\ndata and preliminary results from the high precision transcontinental\ntraverse survey network of the U. S., have been compared in order to\nobtain error estimates of Doppler results. The average chord distance\ndifference, Doppler minus TT, was 0.50 m. for 15 lines in a north-south\ndirection and 0.65 m. for 25 lines in an east-west direction. These\nresults are in close agreement with standard errors in latitude and\nlongitude as determined previously from repeated Doppler observations\nat several stations. The average distance between Doppler stations\nused in these comparisons was 300 km.\nAs a byproduct of these computations in space, the azimuths computed\nfrom Doppler data were converted to geodetic azimuths referred to the\nClarke 1865 Spheroid. These converted azimuths, along with distances\nfrom the TT, were used to compute position closures of the 6 loops of\nthe traverse net. The results are compared with closures obtained\nfrom the TT azimuths.\nIntroduction\nIn order to evaluate the accuracy of distances determined from Doppler\npositions, point to point inverses in space were computed using 49 Doppler\nstations spaced at intervals of 200 to 600 km. along the transcontinental\ntraverse network. These results were then compared with chord distances\ncomputed from positions obtained from preliminary adjustments of the trans-\ncontinental traverse. Along the traverse in a north-south direction, the\nchord distance differences give an estimate of latitude errors of the\nDoppler positions. For lines in an east-west direction, longitude errors\nof Doppler positions are indicated by the distance differences. The trans-\ncontinental traverse net and Doppler stations used in this evaluation are\nshown in figure 1.\nDoppler Data\nThe Doppler positions used in this evaluation are referred to the NWL 10F\nSystem. That is, the NWL 9D System coordinates have been corrected for\na small scale discrepancy and a small longitude rotation. (Anderle 1974).\nCorrections to obtain the NWL 10F System coordinates are as follows.","814\nNWL 10F System\nNWL 9D System\nLatitude\nLatitude\n=\nLongitude + 0.26\n(east long. positive)\nLongitude\n=\nGeodetic Ht.\nGeodetic Ht. - 5.27 m.\n=\nThe ellipsoid parameters of the NWL System, a = 6,378,145 meters and\nf = 1/298.25, were used to compute X, Y, Z coordinates of each Doppler\nstation. These coordinates and the Doppler positions were then used to\ncompute inversed azimuths and distances in space between ad jacent\nstations along the transcontinental traverse net.\nSeveral additional Doppler stations have been established at points\nalong the TT, however, the positions available were determined from\ncomputer programs of other agencies. All Doppler data used in this\nevaluation, with the exception of stations 10000, 30098 and 51033,\nwere obtained from computer programs of the National Geodetic Survey.\nThe three stations mentioned above were included in order to maintain\nuniform distances between Doppler points.\nTranscontinental Traverse Data\nPositions of stations along the traverse which are given in this report\nwere determined from free adjustments of various sections of the traverse.\nThat is, in each section only one position was held fixed and azimuths,\ndirections and Geodimeter distances were used as observation equations.\nThe various section adjustments are as follows.\nEastern Loop - (1) Florida to Mississippi, (2) Mississippi to Nebraska,\n(3) Nebraska to Maryland, (4) Maryland to Florida, and (5) Indiana to\nMississippi.\nWestern Loop - (1) Nebraska south and west to California, (2) California\nto Washington, (3) Washington east and south to Nebraska, (4) Nebraska to\nWyoming to Montana, (5)* Wyoming to Utah to California, and (6)* New Mexico\nto Utah. (* Adjusted positions for points along these two sections were\nnot available when this investigation was started. The positions used\nwere preliminary unadjusted values).\nPosition closures of the 6 loops as shown in figure 1, determined from\nresults of the various free adjustments, are given below.\nLoop Length (km.)\nLoop\nLatitude\nLongitude\n- 0.252\n- 0.'024\n0.61 m.\nI\n3,732\n7.77 m.\n4,049\n0.028\n0.86 m.\n+ 0.043\nII\n1.09 m.\n+ 0.087\n2.68 m.\n- 0.143\n3.24 m.\nIII\n3,395\n4,053\n0.277\n8.54 m.\n- 0.082\n2.05 m.\nIV\n- 0.026\n0.80 m.\n- 0.116\nV\n3,773\n2.91 m.\n3,643\nof 0.344\n10.62 m.\nVI\n+ 0.123\n2.79 n.","815\nSimultaneous ad justments have been performed for the two eastern loops\nand the outer ring of the western loop of the traverse, however, these\nresults were not used in this evaluation. It was decided that positions\nfrom the free ad justments, which would not be constrained to satisfy the\nposition closures, would serve as a better yardstick to evaluate the\nDoppler results.\nIn order to eliminate small errors in distance along the traverse, due\nto any uncertainty in azimuth, lines in a north-south and east-west\ndirection were used for the evaluation of Doppler latitude and longitude\nerrors. In accordance with the standards and specifications under which\nthe TT distances were measured, the estimated accuracy of inversed dis-\ntances used for comparison with Doppler is better than one ppm.\nElevations of stations along the TT were determined from reciprocal\nvertical angles with bench mark elevation control at intervals of 100 km.\nor less. Geoid heights were obtained from a 1975 simultaneous adjustment\nof approximately 2800 astro-geodetic stations. Astronomic positions in\nthe TT net were spaced at intervals of about 30 km. The estimated errors\nof the TT geodetic heights, obtained from these geoid heights and elevations,\nshould not exceed 1.5 meters.\nComparison of Results\nPositions - Geographic positions and geodetic heights for the 49 stations\nshown in figure I are given in Table 1 for the Eastern Loop and in Table 2\nfor the Western Loop. The Doppler station numbers are identified by station\nnames in the tables. Coordinates given in the 4 columns of the tables are\nidentified as follows.\nDF - Doppler 10F System.\nTT - Transcontinental traverse (free ad justments).\nTR DF - Doppler 10F coordinates transformed to the Clarke 1866\nSpheroid. The shift parameters used, AX = of 19.60 m.,\nAY = - 155.02 m., AZ = 175.12 m., are based on the\nmean result of 35 stations of the TT, (Vincenty 1975).\nDF TT - Geographic positions determined by traverse computation\nusing Doppler space azimuths converted to the Clarke\n1866 Spheroid and inversed distances from the TT positions.\nStations in the tables are listed by sections in the order computed around\nthe loops. Junction stations are duplicated in each section, however, the\npositions (TT and DF TT) may differ depending on the direction in which\nthey were computed. Latitude and longitude closures of the various loops\ncan be obtained from positions of the junction stations.\nGeodetic Heights - A direct comparison, transformed Doppler (TR I DF) versus\nTT, can be obtained from the tables. At most of the stations in the east-\nern loop, the TT heights are greater than the TR DF results. The maximum\ndifference is 2.5 meters at station 51008 (HARVELL). In the western loop\nthere are 19 positive and 9 negative differences (TR DF minus TT) with a\nmaximum of - 2.5 m. at station 53078 (FOSS 2).","816\nRecent recomputations of Doppler data at several station, based on minor\nrevisions made to the NGS computer program, give results on the order of\n0.7 meters greater than previously computed values. Strange and Hothem,\nNational Geodetic Survey, are making extensive evaluations to determine\nthe refinements required for the NGS computer program to produce the best\npossible results from Doppler observations.\nChord Distances - Point to point inversed distances for Doppler (DF) and\ntraverse (TT) are given in Table 3 for the Eastern Loop and in Table 4\nfor the Western Loop. Distances in a north-south direction are indicated\nby (N) and those in an east-west direction by (E). Distance differences\nwhich are not identified by (N) or (E) are for lines more than 25 degrees\nfrom the meridian or parallel.\nThe chord distance differences, in the order given in tables 3 and 4, are\nlisted in Table 5. The average of differences in a north-south direction,\n0.50 m., and those in an east-west direction, 0.65 m., are in close agree-\nment with Doppler latitude and longitude standard errors, respectively.\nThe Doppler standard errors, based on repeated observations at several\nstations, have been determined previously by Strange and Hothem, National\nGeodetic Survey (NGS) and by the Defense Mapping Agency Aerospace Command\n(DMAAC).\nIf we assume that the chord distance differences approximate the standard\nerrors of latitude and longitude (1 sigma), then the maximum differences\nin (1) and (2), Table 5. are in close agreement with the outside error\n( 3 sigma)\nDifferences under (3), Table 5, reflect small uncertanties in azimuth\nbetween stations at an angle to the meridian and parallel.\nSpace Azimuths - Point to point inversed azimuths in space are given in\nTable 3, Eastern Loop, and Table 4, Western Loop for the Doppler (DF)\nand traverse (TT) positions. In order to obtain a direct comparison of\nazimuths, Doppler versus TT, it was necessary to apply a correction to\nthe Doppler azimuths. This correction is based on differences in position,\nDF minus TT, equivalent to corrections for Laplace and deflection. After\nthis correction is applied we have a direct comparison of the space azimuths.\nGeodetic azimuths can be obtained from the space azimuths by applying the\ngeodesic and skew corrections. However, these corrections are essentially\nthe same for the corrected Doppler space azimuths and the TT space azimuths.\nTherefore, if we apply the space azimuth differences to the inversed TT\ngeodetic azimuths we obtain geodetic azimuths of the Doppler results\nreferred to the Clarke 1866 Spheroid. Traverses were then computed around\neach of the 6 loops using the converted Doppler azimuths and the inversed\nTT distances. Closures obtained were as follows.\nLoop\nLatitude\nLongitude\nI\n0.074\n2.28 m.\n0.025\n0.63 m.\n+\n-\nII\n+ 0.002\n0.06 m.\n0.073\n1.85 m.\nIII\n- 0.016\n0.49\n0.028\n0.63\n+\nm.\nm.\nIV\n- 0.107\n3.30\n0.142\n3.56 m.\nm.\n-\nV\n0.000\n0.00\n0.042\n+\n1.05 m.\nm.\nVI\n- 0.009 0.28 m. 0.035 0.79 m.","817\nIt is interesting to note the latitude and longitude closures obtained\nfrom the converted Doppler azimuths as compared with closures from the\nTT azimuths given on page 2. These results confirm the high accuracy\nof TT distances throughout the net.\nThe converted Doppler azimuths, geodetic azimuths computed from the\ntransformed Doppler positions, and geodetic distances from the TT\npositions are given in Table's 6 and 7. See comments, Table 6, regard-\ning azimuths from transformed Doppler positions versus the converted\nDoppler azimuths.\nConclusions\nThe procedure of converting Doppler space azimuths and distances to\nanother spheroid, without using the conventional shift parameters,\nmight be useful in revising a geodetic datum. As shown in this report,\nthe space azimuths from Doppler data need to be corrected before compar-\ning with space azimuths based on the datum positions. The corrections\nto be applied are equivalent to the Laplace and deflection corrections.\nIn a triangulation network, with Doppler stations spaced at intervals\nof about 300 km., space azimuth and chord distance differences would\nbe applied to the geodetic datum inversed azimuths and distances. The\nconverted Doppler results obtained could then be used as observation\nequations in a readjustment of the net. This would eliminate the\nconventional procedure of determining shift parameters for transforming\nDoppler positions to another spheroid.\nThe results from this evaluation show conclusively that Doppler positions\nwill add considerable strength to the orientation and scale of a triangu-\nlation network. With Doppler stations space at about 300 km., the relative\naccuracy of azimuths and distances between stations should be on the order\nof one part in 200, 000 or better.\nA simultaneous adjustment of the total transcontinental traverse net, to\nbe accomplished within 6 to 8 months, will provide additional information\nfor further evaluations of Doppler data.\nReferences\nAnderle, R. J. (Naval Weapons Laboratory, Dahlgren, Virginia), personal\ncommunication, dated March 6, 1974.\nVincenty, T. 1973: Three-dimensional adjustment of geodetic networks,\nunpublished at this date, October 1976.\nVincenty, T., 1975: Experiments with ad justments of geodetic networks\nand related subjects, unpublished at this date, October 1976.","818\nInverse Solution in Space (Vincenty 1973)\nS2 = AX2 + AY2 + AZ2\nwhere, AX = X2 - X1 ; AY = Y2 - Y1 ; AZ = Z2 - Z1\n- AX sin A - AY cos A\ntan\nA = sin 0 (AX cos A - AY sin X) - AZ cos\ncos (AX cos l - AY sin X) + AZ sin\nsin V =\nS\nin which all arguments are for the standpoint.\nA = geodetic azimuth of the normal section referred to the\nforepoint in space.\nV = vertical angle referred to geodetic horizon.\n= Latitude (positive north)\nl = Longitude (positive west)\nAzimuth (A) is referred to south as the initial.\nComments on deflection corrections applied to space azimuths.\nOver the long lines used in this evaluation, 200 to 600 km., , the geodetic\nheight differences are not significant when computing the deflection\ncorrections. In these corrections, the vertical angle V, from the\nformula above, was computed for a few lines. For all lines in this\nreport, V is always negative. In the basic formula for deflection\ncorrections, S/2R was used for tan V. For the number of significant\nfigures required in the result, this approximation will give the same\ndeflection correction as that determined from the computed vertical\nangle. R was used as a constant equal to 6,375,000 meters.","819","820\nTable l\nGeographic Positions and Geodetic Heights - Eastern Loop of TT\nSection 1\nLatitude, Longitude & Geodetic Height (m.)\nStation No. & Name\nDF\nTT\nTR DF\nDF TT\n51144-\n26.609\n26.686\nMEADES RANCH\n39\n13\n26.6622\n26.6850\n98\n32.268\n30.505\n32\n30.5002\n30.5060\n560.29\n599.4\n599.38\n599.4\n51033- MEFFORD 2\n41\n42\n12.609\n12.711\n12.7262\n12.7317\n40.341\n95\n38\n38.836\n38.8380\n38.8657\n384.07\n425.5\n424.76\n425.5\n51175- KENT 2\n41\n48\n20.457\n20.582\n20.5408\n20.5476\n26\n92\n57.708\n56.504\n56.5728\n56.5309\n251.44\n294.9\n293.41\n294.9\n51174- GINRICH RM 4\n40\n49\n20.356\n20.425\n20.3794\n20.3948\n89\n17\n20.231\n19.439\n19.4768\n19.4553\n204.19\n249.0\n247.04\n249.0\n51166 - FRANKTON\n40\n14\n06.998\n07.033\n05.9814\n06.9918\n85\n49\n33.278\n32.852\n32.9284\n32.8935\n214.90\n259.0\n258.34\n259.0\n51176-\nATCHISON\n40\n05\n10.576\n10.559\n10.5491\n10.5562\n81\n44\n20.532\n20.556\n20.6534\n20.5965\n316.22\n361.8\n359.81\n361.8\n52001 - BCTS NO. 3\n39\n01\n*\n39.777\n39.659\n39.7176\n39.7280\n75\n49\n32.686\n33.326\n33.3614\n33.3291\n- 5.29\n39.9\n37.70\n39.9\n51122- SPRING HILL RM 3\n37\n02\n23.153\n22.955\n22.9786\n23.0208\n77\n01\n16.554\n17.207\n17.1900\n17.1557\n- 15.10\n28.9\n28.05\n28.9\n51008- HARVELL\n34\n02\n10.816\n10.336\n10.4145\n10.4150\n78\n09\n20.076\n20.550\n20.5686\n20.5496\n- 39.59\n6.8\n4.25\n6.8\n51069- DOONE RM 3\n45\n31.674\n31.057\n32\n31.1537\n31.1321\n80\n22.966\n33\n23.233\n23.2004\n23.2239\n- 43.95\n2.2\n0.53\n2.2\n51068\n45.311\nEVERGREEN\n30\n41\n45.492\n45.5875\n45.5599\n81\n44\n00.626\n00.763\n00.7347\n00.7610\n- 24.69\n21.3\n20.55\n21.3\n* This DF position is the mean result of observations made on different\ndates and identified as follows.\n52001\n60001\nLatitude\n39.775\n39.779\nLongitude\n32.585\n32.686\nHeight\n- 4.82\n- 5.75","821\nTable 1, continued\nGeographic Positions and Geodetic Heights - Eastern Loop of TT\nLatitude, Longitude & Geodetic Height (m.)\nSection 2\nStation No. & Name\nDF\nTT\nTR DF\nDF TT\n26.686\n26.609\n25.6622\n26.6850\n51144- MEADES RANCH\n39\n32.268\n98\n30.505\n30.5050\n30.5002\n32\n560.29\n599.4\n599.38\n599.4\n47\n01.442\n01.2704\n01.2751\n52030 SCHRODER\n35\n01.279\n58\n48.718\n47.046\n47.0881\n47.0912\n97\n322.15\n363.2\n361.66\n353.2\n51057 RICHIE\n44.997\n44.602\n44.5908\n44.5985\n32\n57\n24.636\n98\n05\n23.009\n23.0489\n23.0533\n318.58\n358.0\n358.46\n358.0\n18.9062\n51153- KASTNER\n30\n17\n19.592\n18.937\n18.9355\n01.827\n00.342\n00.3576\n97\n15\n00.3794\n130.23\n171.9\n171.39\n171.9\n24.080\n24.0580\n24.0828\n51025- SABINE\n30\n54\n24.714\n35\n93\n03.975\n02.857\n02.8717\n02.9053\n44.63\n88.4\n87.44\n88.4\n54.592\n54.5348\n54.5625\n51121- CARRON\n30\n37\n55.231\n56.374\n56.3724\n55.4207\n92\n09\n57.328\n- 21.26\n22.7\n22.24\n22.7\n37.768\n51167- LITTLE AZ MK\n37.178\n31\n12\n37.1159\n37.1476\n89\n43\n29.782\n29.052\n29.0597\n29.0992\n68.99\n113.5\n113.09\n113.5\n35\n07.114\n06.501\n05.3870\n06.4324\n51125 POLK\n30\n85\n60.0180\n57\n60.358\n59.958\n59.9312\n2.68\n47.5\n47.53\n47.5\n51126 HIGH\n36.997\n36.389\n36.2557\n36.3016\n30\n31\n83\n47\n28.162\n28.058\n28.0600\n28.1211\n54.81\n9.50\n55.8\n55.8\n45.716\n51068 - EVERGREEN\n30\n41\n46.311\n45.5875\n45.6321\n81\n44\n00.626\n00.744\n00.7347\n00.8092\n- 24.69\n21.3\n20.55\n21.3\nSection 3\n51166 FRANKTON\n40\n14\n06.998\n07.033\n06.9814\n05.9918\n85\n49\n33.278\n32.862\n32.9284\n32.8935\n214.90\n259.0\n258.34\n259.0\n51168- CASH RM A\n06.900\n06.823\n06.7469\n06.7763\n37\n33\n86\n04\n50.007\n49.678\n49.6421\n49.6077\n221.69\n265.6\n265.22\n265.6\n15.4276\n51169- KNOB\n34\n47\n15.719\n15.503\n15.3820\n88\n29.860\n14\n30.351\n29.7775\n29.7309\n205.72\n250.4\n249.25\n250.4\n37.768\n37.206\n37.1495\n51167 - LITTLE AZ MK\n31\n12\n37.1159\n89\n43\n29.782\n29.095\n29.0697\n29.0261\n68.99\n113.5\n113.09\n113.5","822\nTable 2\nGeographic Positions and Geodetic Heights - Western Loop of TT\nSection 1\nLatitude, Longitude & Geodetic Height (m.)\nDF\nStation No. & Name\nTT\nTR DF\nDF TT\n26.609\n26.686\n26.6622\n26.\"6860\n51144- MEADES RANCH\n98\n32.268\n30.506\n30.5002\n32\n30.5050\n560.29\n599.4\n599.38\n599.4\n52030- SCHRODER\n01.442\n35\n47\n01.280\n01.2704\n01.2753\n48.718\n47.037\n47.0881\n47.0905\n97\n58\n322.15\n363.2\n361.66\n363.2\n51057- RICHIE\n44.603\n44.5908\n32\n57\n44.997\n44.5988\n98\n24.635\n05\n22.997\n23.0489\n23.0525\n318.58\n358.0\n358,46\n358.0\n51124- CALLAN 2\n06.716\n06.6601\n31\n02\n07.231\n06.6675\n100\n04\n52.001\n50.261\n50.2504\n50.2566\n677.46\n715.7\n716.55\n716.7\n51039- MID 2\n30\n14.8081\n52\n15.370\n14.854\n14.8178\n101\n61.455\n55\n59.506\n59.5279\n59.5024\n861.70\n900.5\n899.49\n900.5\n51123- MCDONALD RM 1\n30\n40\n16.420\n15.884\n15.8692\n15.8754\n104\n01\n23.344\n21.238\n21.2192\n21.2373\n2032.31\n2066.7\n2068,47\n2066.7\n51103- DONA ANA EB\n04\n19.495\n32\n19.119\n19.1354\n19.1319\n106\n28\n56.000\n53.626\n53.6070\n53.6038\n1234.08\n1268.7\n1267.71\n1268.7\n51052- BURRO RM A\n43\n24.947\n24.761\n24.7587\n32\n24.7570\n111\n30\n54.750\n51.889\n51.8666\n51.8752\n441.90\n472.5\n470.32\n472.6\n51161- MOLE\n34\n07\n23.373\n23.425\n23.3986\n23.3773\n114\n40\n34.535\n31.364\n31.4144\n31.3770\n243.75\n267.8\n268.49\n267.8\n53053- OXALIS 2\n35\n54\n50.743\n51.250\n51.1826\n51.1688\n120\n33\n15.210\n11.271\n11.3447\n11.3060\n- 6.71\n10.2\n10.92\n10.2\n51089- MAYHOOD\n38\n08\n31.754\n32.415\n32.3253\n32.3070\n121\n43\n26.211\n22.056\n22.1790\n22.1338\n4.95\n21.7\n21.36\n21.7\n30098- ORLAND\n44\n44.086\n44.864\n44.7782\n44.7437\n39\n06.697\n122\n09\n02.330\n02.5351\n02.4824\n27.19\n43.1\n43.56\n43.1\n52074 - MIDLAND RM 3\n42\n07\n21.388\n22.280\n22.1914\n22.1652\n121\n49\n37.980\n33.409\n33.6968\n33.6342\n1213.75\n1231.0\n1231.51\n1231.0\n52056- BIG FALLS\n44\n23\n31.251\n32.230\n32.1132\n32.1186\n121\n17\n47.527\n42.796\n43.1326\n43.0508\n856.38\n875.6\n875.82\n875.6\n51127- SAT TRI STA 003\n47\n11\n06.552\n07.448\n07.3821\n07.3352\n119\n20\n16.547\n11.805\n12.1283\n12.0633\n333.34\n355.7\n356.33\n355.7","823\nTable 2, continued\nGeographic Positions and Geodetic Heights - Western Loop of TT\nLatitude, Longitude & Geodetic Height (m.)\nSection 2\nDF\nTT\nTR DF\nDF TT\nStation No. & Name\n26.609\n26.686\n26.6860\n26.6622\n39\n13\n51144- MEADES RANCH\n32.268\n30.506\n30.5060\n30.5002\n98\n32\n560.29\n599.4\n599.38\n599.4\n00.916\n00.9148\n00.9527\n43\n00.738\n53\n52079 CAMERA\n43.6902\n45.284\n43.571\n43.6935\n95\n55\n518.66\n560.9\n559.40\n560.9\n46\n05\n05.143\n05.347\n05.3512\n05.3902\n53078 FOSS 2\n96\n01.965\n02.0432\n02.0355\n03.771\n32\n296.26\n298.8\n298.8\n255.55\n38.7786\n38.8530\n48\n04\n38.521\n38.827\n52077 CHARLES\n12.406\n10.143\n10.1875\n10.2378\n99\n53\n506.8\n467.82\n506.8\n507.12\n55.368\n55.2660\n55.3425\n48\n11\n54.922\n52076- COW\n30.954\n28.177\n28.2222\n28.2753\n103\n57\n726.5\n690.49\n726.5\n727.38\n07.396\n07.8654\n07.9434\n47\n47\n07.971\n51104- CHANCE\n55.480\n52.184\n52.2088\n52.2791\n108\n37\n979.34\n1011.5\n1012.74\n1011.5\n45\n08.949\n08.9203\n09.0057\n55\n08.315\n52075- NEVADA RM 2\n53.4365\n57.104\n113\n02\n53.305\n53.3839\n1293.58\n1321.3\n1322.89\n1321.3\n33.8290\n33.7450\n47\n40\n33.027\n33.739\n52093- BUMBLEBEE\n35.2144\n35.1755\n116\n18\n39.311\n35.095\n1442.0\n1416.94\n1442.0\n1443.34\n07.3821\n07.4685\n47\n06.552\n07.320\n51127 - SAT TRI STA 003\n11\n16.547\n12.023\n12.1283\n12.1698\n119\n20\nSection 3\n356.33\n355.7\n333.34\n355.7\n26.6860\n26.609\n26.686\n26.6622\n39\n13\n51144 MEADES RANCH\n30.5060\n32.268\n30.505\n30.5002\n98\n32\n599.4\n560.29\n599.4\n599.38\n26.9364\n26.9808\n41\n38\n26.726\n27.043\n51041 MEYER\n56.171\n56.2189\n56.2542\n101\n58.395\n35\n1184.09\n1183.4\n1146.71\n1183.4\n60.268\n60.2068\n60.2539\n41\n07\n59.949\n10000 TRANET 747\n02.670\n02.7343\n02.7643\n104\n52\n05.251\n1888.8\n1890.08\n1888.8\n1855.10\n56.0825\n56.202\n56.0228\n41\n36\n55.678\n51044- HORSE\n03.1041\n107\n47\n05.852\n02.982\n03.0019\n2203.46\n2236.4\n2236.13\n2236.4\n01.9614\n44\n48\n01.457\n02.089\n01.9028\n51043- LAKE\n40.4661\n43.430\n40.265\n40.3542\n108\n20\n1188.08\n1220.1\n1220.97\n1220.1\n07.9269\n47\n47\n07.396\n08.058\n07.8554\n51104 CHANCE\n52.3074\n108\n55.480\n52.041\n52.2088\n37\n979.34\n1011.5\n1012.74\n1011.5","824\nTable 2, continued\nGeographic Positions and Geodetic Heights - Western Loop of TT\nSection 4\nLatitude, Longitude & Geodetic Height (m.)\nStation No. & Name\nDF\nTT\nTR DF\nDF TT\n36\n55.678\n56.202\n56.0028\n56.0025\n51044- HORSE\n41\n107\n47\n05.852\n02.982\n03.0019\n03.1041\n2203.45\n2236.4\n2236.13\n2236.4\n51055- KEARNS\n40\n36.150\n38\n36.832\n36.5739\n36.6363\n111\n58\n17.171\n13.954\n13.9296\n14.0348\n1364.63\n1392.9\n1393.19\n1392.9\nSection 5\n51103- DONA ANA EB\n04\n32\n19.495\n19.119\n19.1354\n19.1319\n106\n28\n55.000\n53.626\n53.6070\n53.6088\n1234.08\n1268.7\n1267.71\n1268.7\n51048- SAT TRI STA 110\n34\n56\n43.490\n43.373\n43.3965\n43.3854\n106\n36.435\n27\n33.996\n33.9638\n33.9668\n1796.58\n1829.8\n1829.98\n1829.8\n51054- MONTY USGS\n19.408\n37\n23\n19.554\n19.5589\n19.5237\n06\n109\n46.358\n43.489\n43.5424\n43.5196\n1593.89\n1625.6\n1624.77\n1625.6\n51056 - KEARNS\n40\n38\n36.160\n36.555\n36.5739\n36.5292\n111\n58\n17.171\n13.872\n13.9296\n13.8931\n1354.63\n1392.9\n1393.19\n1392.9\n51057- DRY\n40\n41.717\n23\n42.170\n42.2137\n42.1688\n28.807\n115\n12\n25.217\n25.2565\n25.2407\n1823.29\n1846.6\n1848.36\n1846.6\n51058- DIATOM\n49\n39\n37.578\n38.203\n38.1621\n38.1277\n118\n07.400\n59\n03.469\n03.5210\n03.4715\n1269.87\n1288.7\n1290.37\n1288.7\n30098- ORLAND\n44\n44.086\n39\n44.890\n44.7782\n44.7439\n122\n09\n06.697\n02.445\n02.5351\n02.4403\n27.19\n43.1\n43.55\n43.1","825\nSpace Azimuths and Chord Distances (meters) - Eastern Loop of TT\nDF\nDF\nTable 3\ncorr'n*\nAzimuth\nTT\nDiff.\nDistance\nTT\nDiff.\n220°\n49'\n15.29\n+1.14\n17.43\n- 0.52\n358,990.25\n51144\n51033\nof 0.75\n17.95\n89.50\n266\n28.00\n51033\n51175\n+1.00\n29.00\n265,958.69\n+ 1.32\n1.65 E\n29\n27.68\n60.34\n36.38\n0.09\n286,248.59\n+ 0.68 E\n51175\n51174\n291\n+0.79\n22\n35.59\n36.47\n47.91\n51174\n51166\n281\n46.45\n46.98\n+0.52\n+ 0.25\n300,542.78\n0.62 E\n23\n46.73\n43.40\n51165\n51175\n04.54\n04.91\n0.69\n348,507.68\n271\n24\n+0.27\n0.59 E\n05.60\n08.27\n51175\n52001\n283\n58\n43.79\n-0.02\n43.77\n- 1.07\n438,171.12\n+ 0.44 E\n44.84\n70.68\n52001 51122\n4\n30\n30.89\n-0.39\n30.50\n1.26\n221,312.08\n+ 0.93 N\n31.76\n11.15\n51122\n51008\n17\n14.34\n-0.38\n13.96\n348,694.10\n29\n+ 0.79\n1.45\nN\n13.17\n95.55\n51008\n51069\n58\n15\n26.84\n27.10\n-0.26\n0.41\n264,471.41\n1.39\n27.25\n72.80\n49.66\n51069\n51068\n26\n18\n49.81\n-0.15\n+ 0.14\n254,439.11\n0.25\n49.52\n39.35\n51144\n41.27\n42.34\n+ 0.61\n385,018.78\n52030\n24\n0.66 N\n352\n+1.07\n41.73\n19.44\n52030\n51067\n1\n52\n57.15\n+0.95\n58.10\n0.02\n313,105.23\n+ 0.05 N\n58.12\n05.18\n51067\n51153\n344\n44\n14.51\n+0.86\n15.47\n0.13\n306,957.62\n+ 0.68 N\n15.60\n56.94\n49.48\n51153\n51025\n+0.78\n50.26\n0.07\n356,573.10\n257\n59\n+ 0.58 E\n50.33\n72.52\n14.43\n51025\n51121\n282\n08\n13.85\n+0.57\n+ 1.49\n140,729.44\n+ 0.39\nE\n12.94\n29.05\n51167\n51121\n254\n00\n17.58\n+0.50\n18.08\n+ 0.03\n241,950.52\n0.51 E\n18.05\n51.03\n51167\n51125\n283\n38\n26.85\n+0.38\n27.23\n+ 0.93\n272,141.04\n+ 1.60 E\n26.30\n39.44\n51125\n51126\n270\n45\n21.76\n+0.21\n21.97\nof 0.40\n304,729.09\n0.67 E\n21.57\n29.76\n51125\n51068\n264\n+0.05\n+ 0.36 E\n02\n38.85\n38.91\n198,185.66\n0.11\n85.30\n39.02\n51156\n51168\n4\n18.65\n298,690.03\n19\n18.39\n+0.26\n1.73\n+ 0.54 N\n89.49\n20.38\n51168\n51159\n56.78\n33\n00\n+0.19\n56.97\n0.98\n353,098.62\n+ 0.54\n98.08\n57.95\n51169\n51167\n- 0.44 N\n19\n58.78\n+ 0.84\n420,161.23\n+0.27\n59.05\n39\n61.67\n58.21\nStations underlined are the first lines of each section.\n6.\nSum of equivalent Laplace and deflection corrections. See\ncomments\npage\n*","826\nSpace Azimuths and Chord Distances (meters) - Western Loop of TT\nDF\nTable 4\nDF\nAzimuth\ncorr'n*\nDiff.\nDistance\nTT\nDiff.\n41.27\n+1.07\n+0.73\n42.34\n52030\n352\n24\n385,018.78\n- 0.66 **\n41.61\n19.44\n52030 51067\nl\n52\n57.15\n+0.95\n58.10\n+ 0.03\n313,105.23\n+ 0.05 **\n58.07\n05.17\n51057 51124\n41\n53\n+0.86\n29.59\n30.45\n1.52\n284,694.56\n0.06\n31.97\n94.62\n51124\n84\n51039\n35\n53.00\n+0.89\n53.89\n+ 0.47\n177,969.99\n+ 0.84 E\n53.42\n69.15\n51039\n84\n51123\n13\n07.68\n+0.99\n08.67\nof 0.85\n201,282.49\n- 1.13 E\n07.82\n83.62\n51123\n51103\n124\n13\n02.99\n+1.09\n04.08\nof 0.58\n280,839.98\n+ 0.55\n03.50\n39.43\n51103 51052 100 01 06.97 +1.26\n08.23\n0.24\n478,900.81\n- 0.30 E\n08.47\n01.11\n51052 51161 118 41 53.33 +1.58\n54.91\n0.95\n332,413.82\n+ 1.29\n55.86\n12.53\n51161 53053 121 49 52.57 +1.90\n54.47\n0.45\n616,164.35\n+ 0.01\n54.92\n64.34\n53063\n51089\n143\n10\n17.15\n+2.41\n19.57\n1.63\n171,069.94\n+ 0.21\n21.20\n69.73\n51089\n30098\n168\n41.52\n21\n+2.62\n44.14\n2.08\n181,821.82\nof 0.53 N\n46.22\n21.29\n30098\n52074\n185\n48\n26.48\n+2.85\n29.34\n1.30\n265,396.41\n0.26 N\n30.64\n96.67\n52074 52065 189 31 03.41 +3.13 06.54\n0.52\n255,805.05\n1.03 N\n07.06\n06.08\n52065 51127 205 26 00.09 +3.38\n03.47\n+ 0.01\n345,754.92\n+ 1.59\n03.46\n53.33\n51144\n52079\n201\n06.01\n59\n+1.16\n07.17\n1.07\n561,330.57\n0.57 N\n08.24\n31.14\n52079\n53078\n169\n15\n21.74\n+1.21\n22.95\n+ 0.88\n251,051.76\n0.10 N\n22.07\n51.86\n53078\n52077\n132\n00\n45.03\n46.35\n+1.33\n0.43\n336,149.03\n1.63\n46.79\n50.65\n52077\n52076\n94\n43.90\n+1.69\n45.59\n1.10\n303,313.28\n+ 0.10 E\n45.69\n13.18\n52076\n51104\n84\n14\n14.62\n+2.08\n16.70\n0.05\n351,772.43\n- 0.15 E\n16.76\n72.58\n51104\n52075\n75\n31\n58.45\n+2.44\n60.89\n+ 1.60\n347,320.33\n+ 0.63 E\n59.29\n19.70\n52075\n52093\n110\n01\n40.74\n+2.81\n43.55\n+ 0.85\n260.662.63\n+ 0.45 E\n42.70\n62.18\n52093 51127\n77\n40\n56.25\n+3.12\n59.37\n+ 1.64\n234,797.00\nof 0.10 E\n57.73\n96.90\n** Duplicated, see Eastern Loop.","827\nSpace Azimuths and Chord Distances (meters) - Western Loop of TT\nTable 4, continued\nDF\nDF\ncorr'n\nDiff.\nDistance\nDiff.\nAzimuth\nTT\nTT\n135°\n+1.14\n- 1.51\n12.06\n13.20\n51144\n51041\n57\n373,192.35\n- 0.89\n14.71\n93.25\n26\n10.46\n08.99\n51041\n10000\n79\n+1.47\n+ 1.11\n279,161.06\n+ 0.22 E\n60.84\n09.35\n10000\n51044\n103\n18.85\n20\n+1.71\n20.57\n249,871.17\n- 1.65 E\n- 2.75\n23.32\n72.82\n51044\n356,803.07\n51043\n172\n51\n23.12\n+1.97\n25.09\n- 1.03\n+ 0.03 N\n26.12\n03.04\n51043\n176\n51104\n17\n39.74\n+2.28\n42.02\n0.85\n332,554.92\n- 0.04 N\n42.87\n54.96\n51044\n51055\n74\n18\n47.19\n+1.91\n49.10\n- 1.41\n357,751.01\n+ 0.04 E\n50.51\n50.97\n51103\n51048\n180\n21\n47.23\n48.54\n+1.31\n+ 0.20\n318,741.77\n+ 0.21 N\n48.34\n41.56\n61.31\n51048\n361,218.43\n51054\n139\n24\n59.87\n+1.44\n- 1.12\nof 0.96\n62.43\n17.47\n51054\n51056\n145\n28\n21.66\n+1.81\n23.47\n+ 0.11\n437,952.09\n+ 0.39\n23.36\n51.70\n51055\n51057\n85\n18\n32.45\n34.60\n+2.15\n+ 0.57\n275,694.66\n- 0.49 E\n34.03\n95.15\n51057\n51058\n80\n08\n38.39\n40.72\n- 1.48\n+2.33\n328,172.79\nof 0.85 E\n42.20\n71.94\n51058\n30098\n89\n06\n08.70\n- 1.67\n+2.53\n11.23\n271,385.19\n+ 1.09 E\n12.90\n84.10\nSum of equivalent Laplace and deflection corrections. See comments page 6.\n*","828\nTable 5\nChord Distance Differences in Meters\nDoppler 10F minus TT\nEastern Loop of TT\n(1)\n(2)\n(3)\n+ 0.93\n- 1.65\n+ 0.75\n- 1.45\n+ 0.68\n- 1.39\n- 0.66\n- 0.62\n- 0.25\n+ 0.05\n- 0.59\n+ 0.54\n+ 0.68\n+ 0.44\n+ 0.54\n+ 0.58\n- 0.44\n+ 0.39\n- 0.51\n+ 1.60\n- 0.67\n+ 0.36\nWestern Loop of TT\n+ 0.53\n+ 0.84\n- 0.06\n- 0.25\n- 1.13\n+ 0.55\n- 1.03\n- 0.30\n+ 1.29\n- 0.57\nof 0.10\n+ 0.01\n- 0.10\n- 0.15\n+ 0.21\n+ 0.03\nof 0.63\n+ 1.59\n- 0.04\nof 0.45\n- 1.63\n+ 0.21\n+ 0.10\n- 0.89\n+ 0.22\n+ 0.96\n- 1.65\n+ 0.39\n+ 0.04\n- 0.49\n+ 0.85\n+ 1.09\n0.50\n0.65\n0.75\naverage\nTotal sum\nsum (+)\n+ 6.29\n+ 2.97\n+ 8.37\nof 16.26\nsum (-)\n- 4.55\n- 7.76\n- 4.22\n- 16.53\n(1) North-south lines. Azimuths are within 25 degrees of the meridian.\n(2)\nEast-west lines. Azimuths are within 25 degrees of the parallel.\n(3) Azimuths of lines more than 25 degrees from the meridian or parallel.","829\nTable 6\nGeodetic Azimuths and Distances (meters) - Eastern Loop of TT\n(1)\n(2)\n(3)\n(4)\n(5)\n220°\n49'\n0.52\n17.23\n17.75\n17.23\n369,011.334\n51144\n51033\n-\n266\n27.67\n28.99\n28.99\n265,964.522\n51033\n51175\n29\n+\n1.32\n35.55\n36.46\n51174\n35.42\n286,259.695\n291\n0.09\n51175\n22\n51166\n281\n45.78\n47.03\n51174\n23\n0.25\n47.01\n300,559.189\n+\n51165\n51175\n24\n05.62\n0.59\n271\n04.93\n04.88\n348,534.560\n51176\n45.00\n52001\n283\n58\n1.07\n43.93\n43.87\n438,242.790\n-\n52001\n4\n- 1.26\n30.49\n51122\n30\n31.75\n30.47\n221,321.124\n13.04\n13.83\n13.84\n348,738.262\n51122\n51008\n17\n29\n+\n0.79\n51008\n51069\n58\n16\n26.70\n27.12\n0.41\n26.71\n264,491.571\n-\n51069\n51068\n26\n18\n49.42\n0.14\n49.56\n49.58\n254,455.870\n+\n51144\n41.80\n0.61\n42.41\n42.40\n385,049.044\n52030\n352\n24\n+\n58.11\n52030\n51067\n1\n52\n0.02\n58.09\n58.07\n313,119.078\n51057\n344\n44\n15.69\n51153\n0.13\n15.55\n15.54\n305,973.928\n-\n356,611.622\n51153\n51025\n257\n59\n50.23\n0.07\n50.16\n50.14\n-\n14.45\n140,730.656\n51025\n51121\n282\n08\n12.95\n+ 1.49\n14.45\n51167\n51121\n254\n00\n17.99\n+ 0.03\n18.02\n18.02\n241,962.923\n51157\n51125\n283\n38\n26.37\n0.93\n+\n27.30\n272,156.618\n27.30\n51125\n51125\n270\n45\n0.40\n21.57\n+\n21.97\n22.00\n304,756.229\n51125\n51068\n254\n02\n39.01\n0.11\n38,90\n38.89\n198,192.064\n51166\n51168\n4\n20.35\n18.63\n19\n1.73\n18.59\n298,704.616\n-\n51168\n51169\n56.79\n353,132.601\n33\n00\n57.75\n0.98\n56.77\n-\n51169\n51167\n19\n58.00\nof 0.84\n58.84\n58.88\n420,226.125\n39\n(1) & (5) - Inversed azimuths and distances from TT positions.\n(2) - Space azimuth difference, corrected Doppler minus TT.\nFrom Table 3, Eastern Loop and Table 4, Western Loop.\n(3) - Doppler geodetic azimuth converted to Clarke Spheroid.\n(4) - Inversed azimuths from Doppler positions transformed\nto Clarke Spheroid.\nComments - Azimuths (3) and distances (5) were used to compute the\npositions identified as DF TT in Tables 1 and 2. If an\niteration is performed, that is, revised Laplace correc-\ntions computed using the DF TT positions, azimuths (3)\nwill equal (4).","830\nTable ?\nGeodetic Azimuths and Distances (meters) - Western Loop of TI\n(1)\n(2)\n(3)\n(4)\n(5)\n24\n41.67\n0.\"73\n42.40\n42.40\n51144\n52030\n352\n385,049.041\n+\n52030\n51067\n58.05\n1\n0.03\n58.09\n58.07\n52\n+\n313,119.076\n51067\n51124\n41\n31.85\n30.34\n53\n1.52\n30.32\n284,694.034\n51124\n51039\n84\n35\n53.43\n0.47\n53.90\n53.89\n+\n177,952.281\n51039\n51123\n84\n08.68\n13\n07.83\n0.85\n08.68\n+\n201,241.803\n51123\n51103\n124\n03.56\n04.14\n13\n0.58\n04.15\nof\n280,787.543\n51103\n51052\n100\n01\n08.61\n0.24\n08.37\n08.38\n478,947.455\n51052\n51161\n118\n41\n56.03\n0.95\n55.08\n55.09\n332,430.800\n-\n51161\n53053\n121\n49\n55.57\n0.45\n55.12\n55.09\n616,390.692\n-\n53053\n51089\n143\n10\n21.25\n1.53\n19.62\n19.58\n171,074.445\n51089\n30098\n168\n45.24\n21\n2.08\n44.16\n44.08\n181,826.556\n-\n30098\n52074\n185\n48\n30.54\n1.30\n29.34\n29.18\n265,386.684\n-\n52074\n52065\n189 31 07.05 0.52 06.53 06.32\n255,780.718\n52066\n51127\n205\n26\n03.34\n+\n0.01\n03.35\n03.12\n345,761.950\n51144\n52079 201 59 07.90 1.07 06.83 05.84\n561,461.893\n52079\n53078\n169\n15\n22.10\n0.88\n+\n22.98\n22.89\n251,051.038\n53078\n52077\n132\n00\n45.92\n0.43\n45.49\n45.43\n335,168.249\n-\n52077\n52075\n94\n03\n46.70\n1.10\n45.60\n45.57\n303,312.311\n52075\n51104\n84\n14\n16.73\n0.05\n16.67\n16.64\n351,769.050\n-\n51104\n52075\n75\n31\n1.60\n60.85\n60.83\n59.25\n+\n347,298.929\n52075\n52093 110 01 42.71 + 0.85 43.55 43.50\n250,623.858\n52093\n51127\n77\n40\n1.54\n57.70\n59.34\n+\n59.29\n234,774.569\n51144\n51041\n135\n14.87\n57\n1.51\n13.35\n13.37\n373,193.912\n-\n51041\n10000\n26\n79\n09.35\n1.11\n10.45\n+\n10.43\n279,115.033\n10000\n51044\n103\n20\n23.31\n20.56\n2.75\n20.51\n249,807.831\n-\n51044\n51043\n172\n26.15\n51\n1.03\n25.12\n25.11\n356,751.437\n-\n51043\n51104\n176\n42.88\n17\n0.85\n42.03\n41.93\n332,534.413\n51044\n51056\n74\n18\n50.44\n1.41\n49.03\n49.00\n367,696.324\n51103\n51048\n180\n48.33\n21\n0.20\n48.53\n48.55\n+\n318,696.780\n51048\n51054\n02.55\n139\n25\n1.12\n01.44\n01.45\n361,167.846\n-\n51054\n51055\n145\n28\n23.59\n0.11\n+\n23.70\n23.67\n437,934.149\n51055\n51057\n85\n18\n34.03\n0.57\n34.60\n34.56\n+\n275,645.274\n51057\n51058\n80\n08\n42.17\n1.48\n40.69\n40.60\n328,127.020\n-\n51058\n30098 89 05 12.89 1.67 11.22 11.27\n271,373.356\nSee Table 5 for identification of column's (1) thru (5).","831\nDETERMINATION OF NORTH AMERICAN DATUM 1983\nCOORDINATES OF MAP CORNERS\nT. Vincenty\nNational Geodetic Survey\nNational Ocean Survey, NOAA\nRockville, Maryland\nThis publication describes the\nAbstract.\nuse of Doppler data in predicting approxi-\nmate changes of coordinates of map corners\nfrom the North American Datum 1927 (NAD 27)\nto the North American Datum 1983 (NAD 83)\nsystem. A brief description of the\ncomputer program and pertinent mathematical\nformulas are included.\nGeneral Considerations\nThe redefinition of the North American Datum (NAD) , scheduled\nfor 1983, envisions the use of the world reference ellipsoid and\na simultaneous adjustment in a geocentric system of all avail-\nable observations, including geocentric positions derived from\nDoppler data. It now becomes necessary to predict the impact of\nthis readjustment on cartographic materials published to date or\nto be published. Specifically, cartographers need to know by\nhow much and in which direction the coordinates of map corners.\nare expected to change. The accuracy of the prediction should\nbe compatible with a plotting accuracy of 0.2 millimeter (5\nmeters at 1:24,000 scale).\nDoppler geocentric X,Y, Z coordinates are computed in a system\nknown as NWL 9D. Before they can be used in an adjustment of a\ngeodetic network, they must be corrected for a small scale error\nand rotated in the xy plane to reduce them to the proper longi-\ntude origin. At the present time two such best fitting\ncorrection constants have been adopted for transforming NWL 9D\ncoordinates to a system known as WGS 72 (NWL 10F).\nThe principle of the prediction is simple. Doppler station\npositions are known to be accurate to about 1 meter (1 sigma) in\neach component and when adjusted simultaneously with terrestrial\nobservations are not expected to change by much more than a meter.\nTherefore, for the present purpose they can be considered\nerrorless and can be used as control coordinates to which map\ncorners will be fitted.\nThe validity of the prediction presupposes the knowledge of\ncertain parameters on which the readjustment will be based.\nThese are now considered.","832\n1. Ellipsoid parameters. The ellipsoid to be used for the\nNAD 83 datum will have very nearly the same defining parameters\nas those of the WGS 72 (NWL 10F) ellipsoid. A change of 10\nmeters in equatorial radius or of one unit in the second decimal\nof the reciprocal of flattening will not change horizontal\npositions by more than 5 meters.\n2. Scale of Doppler data. The correction value now adopted\nfor application to Doppler (NWL 9D) scale is -0.8263 ppm. This\nis equivalent to lengthening the equatorial radius by 5.27 meters\nin transforming rectangular geocentric to geodetic coordinates.\n3. Longitude origin of Doppler data. This correction is\nbeing re-evaluated by the National Geodetic Survey (NGS) and is\nexpected to change in the first decimal. If the prediction is\nto be accurate to +5 meters, this parameter must be known to\n+0.18.\nIt should be noted that the new datum will have no datum\norigin associated with any station (such as MEADES RANCH in\nNAD 27). No stations will be held fixed in the adjustment;\nabsolute positioning will be accomplished by Doppler data.\nComputer Program for Determination of Shifts\nA computer program has been developed for the purpose of\ndetermining shifts of coordinates of map corners and related\ndata. The shifts are expressed in seconds and in millimeters at\na specified scale. Graticule interval, map scale, and all\nparameters discussed above are a part of the input.\nThe program accepts X, Y, and Z coordinates of Doppler\ncontrol stations in the NAD 27 and the NWL 9D systems. The\nlatter set of coordinates is corrected for scale and rotation\nabout the z-axis. This yields for each control station\nAx, Ay, AZ values (Doppler minus NAD 27). If Doppler data were\nerrorless and if NAD 27 contained no distortions, these values\nwould be the same at all stations. Changes in latitude, longi-\ntude, and geodetic height (height above the ellipsoid), however,\nwould still exist because of a change in ellipsoid parameters\nand orientation. The departures of Ax, Ay, Az from the means or\nfrom values at any arbitrary station reflect distortions of\nNAD 27 in all three components, assuming that Doppler\ncoordinates contain no errors.\nThe model for predicting shifts of map corners is\nunsophisticated but quite satisfactory for the intended purpose.\nGiven latitude and longitude of a map corner and assuming\ngeodetic height as zero, the corresponding x,y,z values are\ncomputed in the NAD 27 system. The Ax, Ay, Az shifts for the\ncorner are computed from shifts at all control (Doppler) stations\nwhich are weighted inversely as the square of the straight line","833\ndistance from the map corner to the control station. In this\nway the closest control station has the largest weight, while a\nvery distant station contributes practically nothing to this\ndetermination.\nThe weighted means of Ax, Ay, Az of each map corner are then\nconverted to changes in map coordinates.\nThe program also computes related data which may be of\ninterest in analyses performed for other purposes. These\ninclude maximum, minimum, and mean Ax, Ay, Az shifts; changes in\nlatitude, longitude, and geodetic height at control stations;\ndistortions of NAD 27 in three components based on departures\nfrom the mean shifts; and NAD 27 errors in straight line\ndistances, azimuths, and vertical angles over lines between\nwidely separated points.\nMathematical formulas used in the program are given in\nappendix 1. Contours of changes in latitude, longitude, and\ngeodetic height from NAD 27 to the best present estimate of\nNAD 83 are shown in figures 1, 2, and 3.\nConclusion\nComparisons of X, y, and Z coordinates at control stations\nwithin the conterminous States give the mean shift values\n(Doppler NWL 10F minus NAD 27)\nAx = -22 m\nAy = 157 m\nAz = 176 m\nand the spreads in Ax, Av, and Az of 24 m, 13 m, and 16 m\nrespectively.\nIn Alaska the mean shifts are:\nAx = -13 m\nAy = 143 m\nAz = 175 m\nwith spreads of 47 m, 46 m, and 22. m respectively. At a scale\nof 1:100,00 a plotting error of 0.2 mm corresponds to 20 meters\nthe ground. Therefore, for medium scale maps the mean\non\nAx, Ay, Az shifts may be adopted and the changes in latitude and\nlongitude (in meters) computed by the following approximations:\nAQ = sino(-cos l Ax + sin l Ay) + cos dz\n+ 2 (a Af + fAa) sin Q cos\nAr = (sin r Ax + cos l Ay)\nUsing of = -0.0000373 and Aa = -71.4 m, 2 (a Af + fAa)\n-476.\n=\nAt 1:500,000 scale the shifts are within plotting accuracy and\nneed not be applied.","834\nAPPENDIX 1. CONSTANTS AND FORMULAS\nLongitude positive west.\n1. Ellipsoid parameters.\nNAD 27\nNWL 9D\nNWL 10F (WGS 72)\nEquatorial radius\n6,378,206.4 m\n6,378,145 m\n6,378,135 m\nFlattening\n1/294.978698\n1/298.25\n1/298.26\n2. Conversion of o, l, h to X, y, Z.\ne2 = 2f - £2\n(2.1)\nN = a(1-e2sin20) -1/2-\n(2.2)\nX = (N + h) cos cos l\n(2.3)\ny = - (N + h) cos sin l\n(2.4)\n[N(1-e2)+h] sin 0\n(2.5)\n3. Conversion of X, y, Z to o, 1, h. Formula by B. R. Bowring. *\np = (x2 + y2 1/2\n(3.1)\ntan u = (z/p) (a/b)\n(3.2)\ntan Q = z + e 2 b sin³u\n(3.3)\np - e2a - cos³u\ntan u = (1-f) tan 0\n(3.4)\nh = + [(p-a cos u) 2 + (z-b sin u)211/2\n(3.5)\ntan l = -y/x\n(3.6)\nThe sign of h is the same as the sign of (p-a cos u) .\n*Bowring, B. R. (Directorate of Overseas Surveys, Tolworth,\nSurrey, England), 1975 (personal communication); and Bowring,\nB. R. , 1976: Transformation from spatial to geographical\ncoordinates. Survey Review (Tolworth, England), 181, 1-5.","835\n4. Conversion of rectangular NWL 9D to NWL 10F coordinates. .\nScale correction: -0.8263 ppm\nRotation in xy plane:\nby = -X or\n(4.1)\n8x = y or\nwhere or = -0.00000 12605 (= -0.26\"). .\n5. Inverse solution in space.\nS is straight line distance, A is astronomic azimuth (from north),\nV is vertical angle positive upwards from astronomic horizon.\nAx, Ay, Az are X2 - X1 etc. ' and '' are astronomic values at P1.\nS = (Ax2 + Ay2 + Az2) 1/2\n(5.1)\nAx sin X'+ Ay cos X'\n(5.2\ntan A =\n- sin ' (Ax cos l' - Ay sin X') +Az cos ' ' '\nS sin V = cos ' (Ax cos '' - Ay sin X') + Az sin &'\n(5.3)\n6. Errors / in X, y, and Z expressed as errors in latitude,\nlongitude, and geodetic height. Results in linear units.\nR is mean radius of the Earth.\np = (x2 + y2) 1/2\n(6.1)\n(6.2)\nso = (-z X &x - Z y 8y + p282)/ (p R)\n(6.3)\nor = (y 8x - X dy)/p\n(6.4)\noh = (x 8x + y by + Z Sz)/R","","837\n07\nappearance","838","839\nDOPPLR-A POINT POSITIONING PROGRAM\nUSING INTEGRATED\nDOPPLER SATELLITE OBSERVATIONS\nSECTION I. INTRODUCTION\n1. DATA REDUCTION. a. This report is concerned with the point positioning mode\nof reduction of Doppler satellite tracking data. It describes the mathematical\ndevelopment of the pertinent equations and describes the operation of a computer\nprogram, DOPPLR, for accomplishing the data reduction.\nb. Point positioning uses the Doppler shift of stable signals broadcast from satellites\nto determine the precise geodetic coordinates of the receiving antenna. Thus, these\ncoordinates are the principal unknowns of the problem, and all known error sources\nare accounted for in the mathematical model in order to obtain the greatest possible\naccuracy and precision. Two features distinguish point positioning from other data\nreduction methods. First. the satellite ephemeris is obtained from some outside source\nand is held fixed in all computations: second, the solution is made in a multipass mode,\ninvolving the simultaneous adjustment of data from many passes of one or more\nsatellites over a single receiving station.\n2. DOPPLR PROGRAM. a. As a diagnostic aid, the DOPPLR program will perform\nnavigation mode solutions, solving for the receiving station coordinates separately for\neach satellite pass. The program may also be used in an error analysis mode. In this\nmode, simulated data are generated and perturbed by specified random and bias errors.\nThe perturbed data are then adjusted to show the effects of the specified error sources.\nb. The program operates on integrated range rate data produced by Geoceiver, ITT\n5500, and Backpack observing equipment. Each data point consists of an observed\nDoppler count, the epoch of the beginning of the count, and the time interval over\nwhich the count was accumulated. The program applies necessary corrections for\nrefraction and other effects. A separate preprocessor may be used to put data recorded\nby various receivers into the proper format for operation of the program.\nSECTION II. MATHEMATICAL DEVELOPMENT\n3. BASIC CONCEPTS. a. Most Doppler receivers work in the same basic way: the\nreceived frequency, fr, is mixed with a locally generated reference frequency, fo, to\nproduce a beat frequency, fb . The cycles of this beat frequency are counted from\nAny mention herein of a commercial product does not constitute endorsement by the U.S. Government.\nRandall W. Smith; Charles R. Schwarz; William D. Googe\nBy:\nDefense Mapping Agency Topographic Center","840\ntime T1 to time T2 The Doppler count (often called integrated Doppler count) is\nthus:\nT2\nI\nfbdt\nN =\nT1\nThe interval, AT = T2 - T1, over which the Doppler count is accumulated, depends\non the type of receiver being used and the mechanization used to produce the time\nmarks Ti and T2 The intervals used by existing receivers range from less than 1\nsecond to approximately 2 minutes. The average beat frequency over the interval is\nN/AT. When the interval is sufficiently short, this quantity may be regarded as an\napproximation of the instantaneous beat frequency and may be ultimately related to\nrange rate.\nb. In the DOPPLR program, the observation equation is always written in terms of\nthe Doppler counts, which can be ultimately related to range difference. The exact\nform of the observation equation depends on the receiver and the source of the time\nsignals. Two sources of time marks are recognized by the program.\n(1) The satellite clock is the source of the time signals when Navy Navigation\nSatellites (NNS [or Navsats] are tracked. These satellites transmit stable carriers at\napproximately 400 and 150 megahertz (MHz). Digital data are phase modulated on the\ncarrier at the rate of 6,103 bits per 2 minutes of satellite clock time. The satellite clock\nis generally kept within 50 microseconds (us) of Universal Time Coordinated (UTC) by\ndaily monitoring. The format of the digital data repeats every 2 minutes, and the\nbeginning of the format (satellite time mark) may be recognized by a unique bit\npattern. Thus, 2-minute intervals may be realized simply by recognizing successive\nsatellite time marks. Shorter intervals may be realized by counting the bits within the\n2-minute format. When the appropriate number of bits have been counted by the\nreceiver, a time mark is sent to the Doppler counting circuits. In the receivers\nconsidered here, the accumulation of the current Doppler count ends and a new one\nbegins at the first positive-going zero crossing of the beat signal following the reception\nof the time mark. Thus, no partial cycles of the beat signal are lost between successive\ncounts, and the counts are called continuously counted integrated Doppler.\n(2) The Doppler beacons in the GEOS (Geodetic Earth-Orbiting Satellite) series\nof satellites transmit pure tones at approximately 324 and 162 MHz. In this case, the\ntime marks are generated by the local clock. As before, the Doppler counts begin and\nend at the first positive-going zero crossing of the beat signal following the reception of\nthe locally generated time mark.","841\nC. For both the NNS and the GEOS satellites, the measurement of the Doppler\ncount is made on the higher frequency, while the lower frequency is used only for the\ncomputation of ionospheric refraction. Both frequencies of a pair are derived from the\nsame basic oscillator and are coherent at transmission. The actual transmitted\nfrequencies are offset from the nominal values for both satellite types. The offset for\nthe NNS is -80 parts per million (ppm), or -32 kilohertz (kHz) at 400 MHz; for the\nGEOS satellites, it is -50 ppm, or - 16.2 kHz at 324 MHz.\nd. For the receivers considered here, the locally generated reference frequencies are\nthe nominal frequencies of 400 MHz for the navigation satellites and 324 MHz for\nthe\nGEOS satellites. The Doppler shift for an observer fixed on the Earth never exceeds\n+20 ppm of the transmitted frequency. Thus, the received frequency (transmitted\nfrequency plus Doppler shift) is always lower than the reference frequency, and the\nbeat frequency is always in the sense fb = fo - fr.\n4. BASIC FORMULAS\na. Navigation Satellite Reception\n(1) Counting Intervals. For the receivers considered here, the first time mark is\ngenerated upon recognition of the first format beginning (satellite time mark)\nfollowing signal acquisition and receiver lock. Successive time marks are generated as\nfollows.\n(a) Backpack-A time mark is generated every 6,103 bits, or 2 minutes of\nsatellite time.\n(b) ITT 5500-Ea 2-minute interval is divided into 26 subintervals. The first\n25 subintervals are each 234 bits, or 4.601016 seconds, of satellite time in length. The\n26th subinterval lasts for 253 bits, or 4.974603 seconds of satellite time.\n(c) Geocciver-Each 2-minute interval is divided into 4 subintervals as follows:\nSubinterval\nNumber of Bits\nTime Duration\n1\n1638\n32.207111 sec.\n2\n1404\n27.606094 sec.\n3\n1638\n32.207111 sec.\n4\n1423\n27.979683 sec.\nThus, in all cases, the time and duration (at the satellite) of each Doppler count is fixed\nand known simply from the position of the Doppler count in the format output by the\nreceiver. Additionally, the Geoceiver outputs the reading of its local clock at the","842\nbeginning and the end of each Doppler count. From these data, the epoch error of the\nlocal clock with respect to the satellite clock may be computed. This feature also\nallows the computation of a small quantity known as the \"partial cycle count\ncorrection.\" This small correction. which cannot be computed for data received by\nother receivers, eventually accounts for the higher precision and accuracy of the\nGeoceiver.\n(2) The Doppler Equation. (a) Let t be the time of transmission from the\nsatellite of a time mark (or a bit which will generate a time mark in the receiver). Then\nthe counting of the beat signal begins at At + €, where At is the propagation\ndelay of the signal and E is a further delay composed of the time required to sense the\ntime mark in the receiver and the wait for the next zero crossing of the beat frequency.\nThe Doppler equation is written as\nt2\nti+A+1+E1\nIgnoring refraction effects (which are treated separately), At1 and At2 are given by\nr1/c and r2/c, where r1 and r2 are the ranges to the satellite at times t1 and t2,\nrespectively, and C is the vacuum speed of light. The ranges are in turn given by r1=\n(R1-x) - and r2 = V(R2-x)2 where R1 and R2 are the (assumed known)\nposition vectors of the satellite (in an Earth-fixed basis) at t1 and t2, respectively,\nand x is the receiving antenna's position vector (assumed constant, but unknown).\n(b) Substituting for fb,\nt2++++++++2\n(1)\nti+At1++1\nSince fo is constant (or at least can be considered to be SO over the span of a satellite\npass), the first integral is simply fo (t2 - t1 + At2 - At1 + E2 - (1) The second\nintegral is more complicated. If the delay € is ignored, it may be evaluated by arguing\nthat the number of cycles received between t1 + At1 and t2 + At2 must be the same\nas the number of cycles transmitted between t1 and t2, or ft(t2 t1), where ft is\nthe transmitted frequency. This leads to\nN = t1t2-At1)-ft2-t1\n= (fo-ft)t2-t1)+fo(t2-t1)","843\nor\nN =\nwith\nAF =fo-fi and\nThis form of the Doppler equation is often used in navigation applications. A more\ncareful evaluation of the second integral in equation (1), considering the delay (E), is\ngiven in paragraph 7. Using the result given there,\nN =\nRegrouping terms, this equation is rewritten as\nN = (2)\nwhere F = fo - ft is the frequency offset (close to 32 kHz), AT & tz - t1 is the\ntime interval at the satellite, and A = c/f is the wavelength of the transmitted signal.\n(c) The term fo(At2-At1) - contains the contribution of the Doppler shift to\nthe count. For convenience, the term is rewritten as\nAF(At2-At1)+f(At2-t1),\nor\nThe first term, AF(r2 - r1)/c, is labeled C1. In the program it is computed from\napproximate values of AF, r2, and r1 . The last term now shows the Doppler shift as\noccurring on the transmitted rather than on the reference frequency. In addition, the\nequation is now in a form that can be applied to GEOS satellite observations.\n(d) The sum is labeled the PC (for partial cycle)\ncorrection. The PC term can be identified as the average beat frequency times the\ndifference in delays at the beginning and end of the counting interval.\n= (AF+17)(e2 =\nAlthough the individual delays are unknown and cannot be determined directly from\nthe data, the difference E2 - E1 can be determined by comparing the counting\ninterval as measured by the local clock and by the satellite clock. For Geoceiver data,\nthis difference is computed from approximate values of r2 and r1, using\nE1 =","844\nwhere AT is the actual counting interval measured by the Geoceiver clock. The\naverage beat frequency for the interval AT's is estimated by\ncount\n=\nFor data from other receivers not having a local clock, the PC term is ignored.\n(e) The final form of the Doppler equation is thus:\nN = PC + i1)E\n(3)\n.\nb. GEOS Satellite Reception\n(1) Counting Intervals. (a) For GEOS satellites, time marks are controlled\nentirely by the local clocks. Counting of the beat frequency begins at the first even\n2-minute time mark (according to the local clock) following signal acquisition and\nreceiver lock.\n(b) The ITT 5500 simulates the bit stream from the satellite by the local\ngeneration of 6,103 bits per 2 minutes of local clock time. The subintervals within the\n2-minute format are the same as for the navigation satellites.\n(c) The Geocciver generates a time mark every 30 seconds, on the minute and\nthe half-minute, according to the local clock. Again, the Geoceiver also outputs the\nreading of the local clock at the beginning and end of each Doppler count. These times\ndiffer from even 1/2-minute times by the wait for the next positive-going zero crossing\nof the beat frequency.\n(2) The Doppler Equation. Equation (2) also applies to GEOS satellite reception,\nexcept that the receiver delays do not enter into consideration. Since the interval at the\nsatellite is not known, the Doppler equation must be written in terms of the interval\nmeasured on the ground clock. This is accomplished by rearranging equation (2) as\nN =\n(4)\n(3) General Form. The DOPPLR program uses the following single form to\ninclude equations (3) and (4):\nN =\nWhen navigation satellites are tracked, AT is AT and C1 is computed from","845\napproximate values. When GEOS satellites are tracked, AT is AT and C1 = 0. The\nof\nterm PC is zero in all cases except for Geoceiver tracking of navigation satellites. The\nlast term is the time bias unknown and is explained in paragraph 7. When used as the\nbasis for the adjustment of the station location in the point positioning mode, the\nquantities 1, AT, R1 R2, R1, and R2 are always assumed perfectly known. The\nfrequency offset AF is an unknown whose value varies from pass to pass. The station\nposition X, as contained in the factor (r2 - r1), is usually treated as completely\nunknown. However, provision is made to constrain any combination of latitude,\nlongitude, and height to agree with input values; the degree of the constraint is\ndetermined by a priori input estimates of accuracy. The time bias unknown € may be\nallowed to vary from pass to pass, satellite to satellite, receiver to receiver, or it may be\ndropped from the equation and ignored altogether.\n5. CORRECTIONS TO OBSERVED DATA. The Doppler count N of the preceding\nsection is the ideal count, which would be obtained in the absence of physical effects\non the signal. The actual measured count, dm, is corrected to the ideal count N by\nN = dm - corrections,\nwhere the corrections are due to tropospheric and ionospheric refraction and to the\nrelativity effect.\na. Tropospheric Refraction. (1) The correction for the tropospheric refraction\n(TROP) to the Doppler count is computed using the tropospheric refraction correction\nfor each slant range. If the calculated range delay for slant range r1 is TR1 and for r2\nis TR2, then\nN TROP = AFAT+1(T2 + TR2 r1 TR1). .\nConsequently,\nTROP -A(TR2-TR1)\nTRi is calculated by integrating the atmospheric refractivity along a line from the\nstation to the satellite. The integral is computed for both the dry and wet components\nof the refractivity and the results added to give the total tropospheric delay in meters.\nThe integral computed for each refractive component is\nRT + upper\n/\nN(8)8\ndo\nTRi =\n,\n(5)\nV82 RT2cos2 e\nRT + lower","846\nwhere\n8 = distance from the center of the Earth to a point on the straight line propa-\ngation path.\nupper = upper limit of integration (height above station).\nlower = lower limit of integration (height above station).\ne = cosine of elevation angle.\ncos\n= refractivity at height 8.\nN(S)\n= distance from Earth's center to station.\nRT\nThe two-quartic refractivity model developed by Hopfield1 is used for the refractivity\nprofile\n= 10-** = --\n,\nwhere N is the surface refractivity.\n(2) For Backpack and ITT 5500 data, the surface wet bulb (Tw) and dry bulb\n(Td) temperatures and pressure (p) are measured for each pass. The surface refractivity\nis calculated from these values using\nN1 =77:02\n=\nVap = Sat 0.00066(1.0 + 0.00115 p (Td - Tw).\nSat = 10-5Tw4\n-11.9792 X 10-4Tw3 + 10.7253 x 10-3Tw2\n+\n(3) When Geoceiver observations are processed, the surface refractivity is calcu-\nlated from surface temperature (Td), pressure (p), and relative humidity (H) values.\nThe integral, equation (5), is evaluated by using the series expansion given by\nYionoulis.\nHOPFIELD, H.S. \"A Two-Quartic Tropospheric Refractivity Profile for Correcting Satellite Data.\" Presented to\n1\nthe International Symposium on Electromagnetic Distance Measurement and Atmospheric Refraction, Boulder,\nColorado. June 1969.\nYIONOULIS, S.M. \"Algorithm to Compute Tropospheric Refraction Effects on Range Measurements.\" Applied\n2\nPhysics Laboratory Technical Memorandum TG-1125. Silver Spring, Md.: Johns Hopkins University. July 1970.","847\nb. Ionospheric Refraction. In addition to the basic frequency from which the\nDoppler count is measured, both navigation and GEOS satellites transmit on a second,\ncoherently related frequency. A comparison of the reception of the two frequencies\nyields a measurement of the first-order effects of ionospheric refraction. Both the\nGeoceiver and the ITT 5500 produce a refraction count derived from the two\nfrequency observations. The ionospheric correction (ION) is obtained by scaling the\nmeasured refraction count. The scaling factors for the Geoceiver (Stansell, et al ³ and\nthe ITT 5500, are\nFrequency Pair\nGeoceiver\nITT 5500\n400/150 MHz\n6/55\n24/55\n324/162 MHz\n1/9\n8/9\nIn the case of the Backpack, the ionospheric correction is applied to the measured\nDoppler count by analog means in the receiver, SO that no further correction for\nionospheric refraction need be made.\nC. Relativity. Because of special relativity, the frequency of the signal transmitted\nfrom the satellite appears to an observer fixed on the Earth to be lowered by a factor\n(1 - , where 1' is the velocity of the satellite in an Earth-fixed frame. This\namounts to approximately 0.1 Hz at the 400 MHz frequency, or 3 counts over a\n30-second counting interval. This effect is indistinguishable from a real drift of the\nsatellite oscillator. Since the program always solves for the frequency offset (difference\nbetween transmitted and local reference frequency) on a pass-by-pass basis, it is not\nnecessary to make a separate correction for the relativity effect. Thus, the frequency\noffset obtained in the solution is actually a composite of the actual frequency offset\nand the relativity effect.\nd. Corrected Doppler Equation. The final form of the observation equation, with\nall known terms on the left and all unknown terms on the right, is\nd = dm - TROP - ION - C1 - PC = AFAT - (6)\n6. LOCAL CLOCK SYNCHRONIZATION. a. The quartz crystal oscillators used in\nDoppler receivers exhibit excellent short term stability. but typically drift slightly\naway from their intended frequency over periods of days or weeks. The receiver clock\nis normally started at the beginning of an operational period and allowed to run\ncontinuously for the whole operation, SO that the epoch carried by the local clock\ntypically drifts slowly away from the inital synchronization to UTC.\n3\nSTANSELL, T.A., et al. \"Geoceiver: An Integrated Doppler Geodetic Receiver,\" Applied Physics Laboratory\nTechnical Memorandum TG-710. Silver Spring, Md.: Johns Hopkins University July 1965.","848\nb. When navigation satellites are tracked, the local clock epoch error may be\ndetermined by comparing the recorded time of the beginning of a Doppler count with\nthe known time (in UTC) of the transmission of the corresponding bit in the navigation\nsatellite message. If A tc is the correction for the local clock epoch error, tr the time\nrecorded by the local clock, and t the corresponding satellite (approximately UTC)\ntime, then the UTC of the beginning of the Doppler count is\n=\nSO that\nWith the Geocciver, a reading of the local clock tr is obtained with each Doppler\ncount. The reading tr is recorded to a precision of 4 us, the transmission time t is\nknown to within 50 us in UTC (the accuracy of the satellite clock in UTC), and the\npropagation delay r/c may be predicted to a few us. In the program, the quantity\nAt - E is computed for Geoceiver observations of navigation satellites, and an\naverage is taken over all points in the pass. Thus, the computed correction for the local\nclock epoch error is\nAtc-e.\nAssuming the partial cycle wait for the zero crossing of beat frequency to be random,\nthe average value E of E may be identified as the average receiver delay. The quantity\nCE is computed by the program.\nC. In normal field operations, the tracking of navigation satellites is the only means\nof determining the local clock epoch error and calibrating the drift of the local clock.\nThus, navigation satellites must be tracked for timing purposes even when GEOS\nsatellites are tracked for positioning or orbit determination purposes. When GEOS\ntracking data are processed by the DOPPLR program, the local clock epoch error and\ndrift rate at a specified epoch are input and used to correct the recorded time of each\ndata point to UTC.\n7. RECEIVER DELAY. a. The delay E is composed of the wait for the zero crossing\nof the beat signal and the actual receiver delay, which is the time required for a given\nbit in the satellite message to be recognized by the receiver logic and a signal sent to\nthe Doppler counting circuitry. Let t be the time of transmission of a bit in the\nsatellite message which corresponds to a time mark in the receiver. Then, the counting\nof the beat frequency begins at ++r/c+e, where r is the range at t.\nb. In the receivers considered here, the delay E averages approximately 1,000 us.\nBy contrast, the delay in the receiver of the received carrier is negligible; that is, the","849\ndelay between the time the signal is received at the antenna and the time it is mixed\nwith the local reference frequency to produce the beat frequency is negligible\n(typically less than 10 us. This means that the wave front reaching the mixer at t+At\n+ € is that which was transmitted from the satellite at Atte - At', where At' is\nthe propagation delay of the signal arriving at + Atte. Again ignoring refraction,\nAt' is 1/1 times the range at t + Atte - At', which is approximately r++(Atte- -\nAt') . Solving C this relationship and neglecting second-order terms in yields At' = At\n+ L/E, and the time of transmission is t At + E - At' = + (1 -i)e Thus, the\nnumber of cycles received at the transmitter between t1 + At1 + E1 and t2 + - At2 +\nE2 must be equal to the number transmitted between t1 + (1 r1/c)E, and t2 + (1\ni2/c)E2. or\nt2+At2+E2\nI\nf,dt =\nt,+++++1\nSince the exact delays are unknown and cannot be determined from the data, the last\ntwo terms are rewritten in terms of the mean delay e, the difference in delays (E2 -\nE1), and the mean range rate T as\n=\ntherefore,\nt2 + - At2 + E2\nI\nE1) i)E]\nt1\nC. The term E is identified as the mean receiver delay, and may, on option, be\ncarried as an unknown by the program. However, it is indistinguishable from a constant\nalong-track or time error in the satellite ephemeris. and may not be carried as an\nunknown in a problem where the satellite ephemeris is also carried as unknown.\nFurthermore, it is also indistinguishable from an along-trac error in the receiver\nposition. Therefore, it cannot be solved for in a navigation solution which uses only a\nsingle pass, or even in a multipass solution using only passes in a given direction. The\nlatter situation can arise, for instance, when a receiver tracks only daytime passes of a\nnavigation satellite for a period of several days. The restriction to only daytime passes\nwill cause the receiver to see only the ascending (northgoing) or only the descending\n(southgoing) branch of the orbit.","850\nd. When a reasonably well-balanced set of northgoing and southgoing passes is used,\nthe mean delay E is well determined. On option, the program will solve for a separate\nvalue of E for each pass, for each satellite, or for each receiver. If the receiver delay is\nfairly stable, it is most reasonable to solve for a single value of this parameter for each\nreceiver rather than for each pass. A separate solution would be made for each satellite\nif there were a possibility of time biases in the given satellite ephemerides. The program\nalso allows a value for the receiver delay to be input, in which case the parameter\nsolved for is a correction to the input value.\n8. LINEARIZED OBSERVATION AND NORMAL EQUATIONS. a. The linearized\nobservation equations are obtained by expanding equation (6) in a first-order Taylor\nseries around approximate values of the unknowns AF (frequency offset), X\n(receiving antenna coordinates), and E (mean receiver delay). Thus,\n(7)\nIn the program, the approximate value of AF at each iteration will be either 32 kHz\n(for navigation satellites) or 16.2 kHz (for GEOS satellites), although other values may\nbe input by the user. Initial approximate values of the station coordinates are input by\nthe user and improved at each iteration. The approximate value of the delay E is\nalways zero on the first iteration.\nb. In equation (7), do is equation (6) evaluated with approximate values of the\nunknowns; SAF,8X and de are corrections to the approximate values. The partial\nderivatives are\nad\nAT\n=\ndAF\ndr2\n=\nwhere\nX),\nU2\n(R2\nU1\nX),\n=\n=\n-\nad","851\nFor the jth observation, let\nlj = dc dc ,\nad\nF\nad\nbj\nde\nad\n,\nax\nThen the normal equation (for the data from a single pass) can be written as\nA AT2 BT A12 A2 B2 B B C THE de 8X = E2 F\nSAF\nE\n,\nwhere\n=\nA12 = sajwibi\nA2 =\nC\nE-mail\nE2 = Ebywili\nF2 =\nThe summation is taken over all the observations during the pass. The weights, Wj, are\nequal to either unity or to the reciprocal of the square of the input observational\nstandard derivation. In addition, the quantity\nis useful for statistical computations. In the program, subroutine NORST generates all","852\nthese quantities for each pass. Subroutine NORSE is similar but omits the calculation\nof bj and the matrices A2 , A12, B2, , and E2\n.\nC. The three subroutines, STASTA, STASOT, and STASOL, combine the matrices\nfrom all the passes. They perform very similar series of matrix manipulations designed\nfor a system of normal equations which, when partitioned, take the form\nG1\nH1\nY1\nP1\nG2\nH2\nY2\nP2\n.\n.\n.\n=\n.\n.\n.\n.\n.\n.\nGN HN\nP\nN\nHT HT\nHTT\nQ\nR\n(8)\nIn each case Yk refers to the pass unknowns.\nIn STASTA:\nSAF for the kth pass,\n= 8X plus a de for each satellite (receiver),\nZ\nA for the kth pass,\nGk\n=\nan array made up of A12 and B for the kth pass,\nHk\n=\nE for the kth pass,\nPk\n=\nthe summation (over all passes of A2, B2, BT and C, appropriately\nQ\n=\narranged by satellite [receiver]),\n= the summation (over all passes of E2 and F, appropriately arranged\nR\nby satellite [receiver])\nIn STASOT:\nYk= = SAF and de for the kth pass,\nZ=8X,\nGk = A A2 for the kth\npass,","853\nHk Pk A for kth pass, pass,\nB\nthe kth\nfor the\n= where the summation is over all passes,\nQ\n= EF where the summation is over all passes.\nR\nIn STASOL:\nYk = SAF for the kth pass,\nZ=8X.\nGk = A for the kth pass,\n= B for the kth pass,\nHk\nE for the kth pass,\nPk\n=\nsummation over all passes,\nQ\n=\nEF summation over all passes.\nR\n=\nAlso let\nED summation over all passes.\n=\nWith a system of equations in the form of equation (8), Yk can be eliminated to give\n(Q EHTG = R CHIGA ,\nSO that the solution for Z is\nZ= (Q (R\nAlso, the sum of the squares of the residuals is given by\nV --- PIGH - - - CHIGH Pk\nfrom which their root mean square (rms) can be calculated. This, together with the\ninverse of the normal equations\n(Q - -\ncorresponding to Z, forms the basis for calculating the error statistics for Z.\n.","854\nY1k is calculated from\nand the inverse of the normal equations corresponding to Yk is\nG\nThis, with the rms, gives the basis for calculating the errors of Yk.\n9. WEIGHT MATRIX FOR OBSERVATION EQUATIONS. a. Normally, each obser-\nvation is weighted inversely proportional to the variance of the range difference\nobservation. This variance is defined in an input array and is assumed equal for all\nobservations. It is also assumed that the range difference observations are independent,\nhaving a random error with zero mean and constant (but unknown) standard deviation.\nIt is possible within the program to treat range as the independent uncorrelated\nvariable rather than range difference. This is accomplished by redefining the weight\nmatrix.\nb. Assume the range observation equation can be written as\nwhere ro is the zero set (initial range) and P are other parameters. Further assume\nthat ranges (ri) are all independent with equal uncertainties, o.\nThen\nand\n-1\n0\nr2 -r1 -\nr1\n0\n0\nr3 - r2\nr2\n.\n.\n=\n.\n.\n.\n.\n.\n-1\nrm\nrm-1\nrm\nrm","855\nThe\nof\ncovariance\nmatrix\n[r2\n]\nis then\nr3\nr2\nrm\nrm-1\n-\n-1\n1\n0\n0\n02\n0\n0\n0\n-1\n0\n0\n0\n0\n-1\n1\n0\n0\n1\n-1\n0\n.\n.\n0\n0\n0\n--1\n1\n0\n0\n0\n0\n-1\n0\n0\n0\n1\n-1\n2 -1\n0\n0\n2\n0\n0\n= 02\n=\n.\n.\n.\n0\n0\n2\n-1\n0\n0\n2\nThe appropriate weight matrix is then and this can be calculated using\nfor pi\n.\ni>j\nThe introduction of this weight equation allows the integrated Doppler observations to\nbe treated as if they were equivalent to range observations.\n10. ERROR ANALYSIS CAPABILITY. An error analysis capability has been\nincluded in DOPPLR. This capability permits the investigation of the effects of\nunestimated errors on estimated parameters in the Doppler solutions. The effects of\nbiases and random errors are calculated as perturbations to either observed or perfect\nDoppler counts and solutions performed using the perturbed data.\n11. CALPRT ROUTINE. The routine (CALPRT) calculates perturbations to the\nobserved Doppler counts. Acceptable error source parameters are defined as follows.\na. Observation-An error in the corrected integrated Doppler count. This includes\ndigitizing, receiver phase shifts, and refraction truncation errors.\nb. Timing-An error in the time recovery within the receiver due to varying\nsignal-to-noise ratio. This is calculated for each time mark.","856\nC. Offset Frequency-An error in the assumed frequency difference between the\nfundamental satellite transmission frequency and the local oscillator frequency.\nd. Satellite Frequency-An error due to an incorrect satellite transmission\nfrequency.\ne. Troposphere-An error resulting from the limitation of the tropospheric model.\nThis is calculated as a percentage error of the modeled tropospheric correction.\nf. Ionosphere - An error due to neglecting higher-order terms in using the\ntwo-frequency technique. This error is modeled as a percentage of the measured\ntwo-frequency ionospheric correction.\ng. Ephemeris-An error due to the uncertainty in the position of the satellite at the\ntime of observation. The error is subdivided into radial, along-track, and crosstrack\ncomponents.\nThe perturbation, Adm , for each error parameter, Pi , is calculated using\nAd, m = add api APi i ,\nad\nwhere\ndc\n= basic integrated Doppler observation equation and\nAPi = the magnitude of the error parameter.\nThe calculated perturbation may be combined with the Doppler counts as a bias, as a\nrandom perturbation per Doppler count, or as a bias per pass but random between\npasses. The options available for each parameter are shown in table 1.\nTable 1. Parameter Options\nPARAMETER\nBIAS\no/POINT\no/PASS\nObservation\nX\nX\nTiming\nX\nX\nX\nOffset Frequency\nX\nX\nSatellite Frequency\nX\nX\nTroposphere (%)\nX\nX\nIonosphere (%)\nX\nX\nEphemeris\nRadial\nX\nX\nX\nCrosstrack\nX\nX\nX\nAlong Track\nX\nX\nX","857\nSECTION III. PROGRAM OPERATION\n12. GENERAL RUN STRUCTURE. The data deck necessary for a Doppler solution\nis built from the initializing constants deck, the pass observation deck, and the system\ncontrol cards as shown schematically in figure 1. It is possible to do more than one\nDoppler solution at a time by stacking decks similar to the single solution deck as\nshown in figure 2, and multiple solutions using different options with the same set of\ndata can be accomplished as shown in figure 3.\nConstants\nSpheroid\nStation\n=\nInitializing Constants\nOptions\nDeck CONST\nTitle\nDopplers\n=\nEphemeris\nPass Observation\nDeck POBS\nPass\nBlank Card\n@FIN\nPOBS\n9999999999999999999999999\nOBS\n=\nObservation Data\nCONST\nDeck OBS\nSYSTEM\nPOBS\nPOBS\n@XQT DOPPLA\n@COPIN,A PROGTP DOPPLR\n@FIND,A PROGTP.DOPPLA\n@REWIND PROGTP\n=\n@ASG.TM PROGTP,T (Tape Name)\nSYSTEM\n@RUN\nFigure 1. Single Doppler solution data deck structure.","858\n@FIN\n9999999999999999999999999\nOBS\nCONST\nOBS\nCONST\nOBS\nCONST\nSYSTEM\nFigure 2. Structure for multiple Doppler solutions\nusing the same options.\n@FIN\n9999999999999999999999999\nOptions\nThis deck cannot include a\nCONST\nSTATION card and must have\nthe OPTION card as the last\ncard.\nOptions\nOptions\nOBS\nCONST\nSYSTEM\nFigure 3. Structure for multiple Doppler solutions\nusing different options.","859\n13. INITIALIZING CONSTANTS DECK. a. The initializing constants which can be\nspecified for a solution include any of the following: station coordinates, spheroid\nparameters, datum shifts, velocity of light, station receiver delay, satellite frequency\noffset, satellite transmitting wavelength, title, and various program control options. The\ninput of any of these values is identified by the appropriate word left-justified on the\ninput card. Table 2 lists the acceptable card formats to be included in the deck of\nconstants. These inputs form the initializing constants deck and may appear within this\ndeck in any order. If more than one card appears with the same identification\nleft-justified on the card, the last definition overrides previous definitions.\nb. Input of the perturbations to be included in an error analysis run can also be\nincluded in the initializing constants deck. This input requires two or more cards in\nsequence; these cards, however, may be in any order with respect to the other input in\nthe initializing constants deck. The perturbations are read as a NAMELIST and,\ntherefore, obey all FORTRAN V rules pertaining to NAMELISTS. In addition, one\nheader card must be included in the NAMELIST and all numerical input must be\nexpressed as double precision. Table 3 gives acceptable parameters in the NAMELIST.\nValues for any or all of these parameters may be specified in any NAMELIST\ndefinition. The random perturbations are normally applied per observation; however, if\nthe value for the random error parameter is negative, the perturbation is applied as a\nbias per pass but random between passes. The card formats for entering perturbation\ndata are shown in table 4.\nC. In computing a solution with real data, it is only necessary to input the OPTION\nand STATION cards, provided the station is input on the NWL 8D datum. If the\nstation is input on another datum specified by column 80 on the STATION card, a\nSPHEROID card defining the datum shifts to the geocentric NWL 8D datum is also\nrequired. If not input, the following constants are preset to the indicated values:\nTitle = solution for xxxxxx, where XXXXXX is the station name,\nVelocity of Light = 299 792 500.0 meters per second (m/sec),\nSatellite a = 0.74954121 m (400-150 MHz Mode),\nOffset Frequency = 32,000 Hz,\nSpheroid Name = 3H NWL,\nA0 = 378 145.0 m,\nFlattening = 0.003352892,\nDry Component of Surface Refractivity = 292.9,\nWet Component of Surface Refractivity = 75.6.","860\nTable 2. Deck of Constants Card Formats\nCARD\nCARD NAME\nPARAMETER\nCOLUMN\nFORMAT\n5H TITLE\n1-5\nA6\nTITLE\n70-Character Title\n10-80\n11A6,A4\nCARD\n7H STATION\n1-7\nA6\nSTATION\nCARD\nStation Name\n10-15\nA6\n= 0 for 0, A, h input (degrees, degrees, meters)\n17\nI1\n= 1 for x, y, 2 input (meters, meters, meters)\nStation Code (as defined on the pass ID)\n18\nA1\nStation or x\n20-34\nD15.3\nA or y\n35-49\nD15.3\nh or 2 (where h is the total height of the antenna\nabove the ellipsoid)\n50-64\nD15.3\nGeoid Separation (meters)-used only in the computation of\nthe tropospheric correction\n65-79\nD15.3\nDatum Code-matches the first character of the datum named\non the SPHEROID card\n80\nA1\nSPHEROID 8H SPHEROID\n1-8\nA6\nDatum Name-first character of this name matches datum code\nCARD\non the STATION card\n10-15\nA6\nSemimajor Axis (meters)\n20-34\nD15.3\nEllipsoid Flattening\n35-49\nD15.3\nDatum Shift (Geocentric coordinates of origin of system\ndefined on this card)\nx component (meters)\n50-59\nD10.3\ny component (meters)\n60-69\nD10.3\nZ component (meters)\n70--79\nD10.3\nCONSTANT 9H CONSTANTS\n1--9\nA6\nVelocity of Light (meters/sec)\nCARD\n20-34\nD15.5\nReceiver Delay (us)\n35-49\nD15.5\nFrequency Offset (Hz)\n50-64\nD15.5\nSatellite Wavelength (meters)\n65-79\nD15.5","861\nTable 2. Deck of Constants Card Formats-Continued\nCARD\nCARD NAME\nPARAMETER\nCOLUMN\nFORMAT\nA6\n6H OPTION\n1-7\nOPTION\nCARD\nOPTION\nPunch Code\nNO.\nyes\nno\nNumber of Iterations\n1\n10\nI1\nPrint residuals on last iteration only\n2\n1\n0\n11\nI1\nPrint Residuals\n3\n0\n1\n12\nI1\n4\nPlot Residuals\n1\n0\n13\nI1\n5\nObservation Sigma (meters)\nPreset to 0.75m if not input\n14-17\nI4\n6\nStation Latitude Sigma (meters)\n18-21\nI4\nStation Longitude Sigma (meters)\n7\n22-25\nI4\n8\nStation Height Sigma (meters)\n26-29\nI4\nPlot station positions obtained from single\n9\npass solutions\n1\n0\n30\nI1\n10\nApply tropospheric correction\n0\n1\n31\nI1\nDo single-pass navigation solutions\n11\n0\n1\n32\nI1\n12\nData Source\n33\nI1\n= 0 use real data\n= 2 use data from previous run with\noriginal station input as on\nSTATION card\n= 3 use data from previous run with\nstation position from last solution\n= 9 Stop\nLocal Time and Satellite Track Plots\n13\n46\nI1\n> 1 Print distribution of passes in local time\n= 1 also plot subsatellite points\n= 0 do neither of above\n14\nPerform solution without time bias\nadjustment\n0\n1\n47\nI1\nDelete samples with elevation angles less than\n15\nthis value (degrees)\n48-49\n12","862\nTable 2. Deck of Constants Card Formats-Continued\nCARD\nCARD NAME\nPARAMETER\nCOLUMN FORMAT\nOPTION\nPunch Code\nNO.\nyes no\n16\nLocal Time Deletion of Passes\n= 0 no deletion on local time\n50-51\n12\n= xx and\n= yy keep those with xx