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GEOPHYSICALESEARCHETTERS,OL.19,NO.14,PAGES487-1490,uly24, 1992PRECISEDETERMINATION OF EARTH'S CENTER OF MASS USINGMEASUREMENTS FROM THE GLOBAL POSITIONING SYSTEM

Yvonne igue,Stephen. Lichten, eoffreylewitt,Michael . Heflin, ndRajendra. MallaJetPropulsionaboratory,alifornianstitutefTechnology

Abstract.GlobalPositioningystemGPS)data romaworldwide eodetic xperimentwere collected uringa 3week eriod arly n 1991. We estimatedeocentrictationcoordinatessing heGPSdata, husdefining dynamicallydeterminedeferencerameoriginwhichshould oincide iththeEarthcenterof mass,or geocenter.The 3-weekGPS av-erageeocenterstimatesgreeo 7-13cmwithgeocenters-timates eterminedromsatellite aser anging, well-estab-lishedechnique. he RMS of daily GPSgeocenterstimateswere cm for x and y, and 30 cm for z.Introduction

Thesatellites f theGlobalPositioning ystem GPS)canbeusedo preciselymeasure lobalgeodynamicaluantitiessuch s changes n Earth's otationvector and rotation ate,crustalmotion, and location of the Earth's center of mass.Arecent pportunityo test hese apabilities as provided ythe1991 G._PS_ERS InternationalEarth RotationService)andG._eodynamicsxperimentGIG), which ookplaceJan22- Feb13 1991. Althoughonly 15 GPSsatellites ereop-erational, he GPS constellation will include 24 satelliteswhen omplete nd substantialmprovementn theaccuracyof geodetic easurementss expectedn the next ew years.TheEarthorientation ndbaselineesultsecently ublished(Herring t al., 199 , Heftinet al, 1992,Lichten t al., 1992,Lindqwistert al., 1992) show hatevensuch imitedGPSdata rovidedentimeter-levelccuracyor measurementsfEarth rientationariationsndground tation aselines.The ocation f the Earth's enter f mass, r geocenter,sa fundamentaleasurementhichhasgeophysicalndprac-ticalsignificance.The definitionof a terrestrial eferenceframeequirespecificationf theorigin, cale, ndorienta-tion f a coordinateystem.Since hemass istributionftheEarths constantlyhanging,t is mportanto measurethe ime ariationsf thegeocenterelativeo points n heEarth'srust.Sincegeodetic easurementsreoftenmadewith ifferentechniquesnd nstrumentsn slightly ifferentterrestrialeferencerames, recisemeasurementf theori-gin,scale, ndorientation f these rames elative o onean-others neededn order o combine ifferent eodeticata.Oeocenterstimatesresentednhere re asedna compar-ison ith heSV5 eferencerameMurraytal.,1990] ri-gin. TheSV5 frame s constructedromboths..atellite_aser

Copyright992by theAmerican eophysicalnion.Paper umber92GL015750094-8534/92/92L-01575503.00

rangingSLR) andvery ongbaselinenterferometryVLBI)data.TheSV5 scale ndorigin re romSLR, and heoriginis choseno be thegeocenter.SinceGPS satellitesmove n high-Earth rbits, hey arerelativelynsensitiveo errorsn thegravity ield,particularlyfor elativelyhort ata res f a fewdays r ess Bertiger tal., 1986]. With each round ite racking -6 GPSsatellitessimultaneously,hegeocenteranbe estimated uickly in afew daysor less). Use of GPS with shortarcs o quicklydeterminehegeoeenter ould n principle nable imevaria-tionsovera few daysor less o be measuredor the irst ime,without omplicationsf re-estimationf thegravity ield. Inthispaper,we presenthe firstdecimeter-quality PS solu-tions or the geocenter hich we obtained rom 21 days ofdata.We discuss otonlyaccuracy y comparing ith otherindependentata,butalsoshort-termdaily) precision f theestimatesnd hepotentialor further mprovement.Over 100 globallydistributedracking itesparticipatednthe GIG'9 experiment.Only data rom the 21 RogueGPSreceiver ites Fibre 1 andTable1) were used n our analy-sis. The Rogue receiver s described y Srinivasan et al.[1989]. Thesites over 79 o -35 atitude, utonly4 ofthese 1 siteswere ocatedn thesouthern emisphere.Datafrom Jan 31 and Feb 13 were not included n this analysissince n inputerror n antenna eightwas discovered.DatafromsatellitePRN6 wasnot usedbecauset was spinning.

Estimation trategyThe data collectedduring he GIG'91 experimenthavebeenprocessedsing he GIPSY (GPS nferredPositioningSYstem) oftwareLichten ndBorder,1987;Sovers ndBorder,1990]. A standardstimationechniques used nthisanalysis, onsisting f single-day re solutions.Threesites are fixed as fiducial sites in the SV5 reference frame,while all other station locations are estimated. A fiducial net-

work can establish a well-defined terrestrial reference framewith2 or 3 receiversixed o theirknown oordinatesMaIlaand Wu, 1989]. The fixed vectors etween iducialsitesdefine rientationndscale n accordanceith SV5 [Murrayet al., 1990]. The fiducia s dopted or this studyareTroms, orway;Pinyon,California USA); andWettzell,Germany. atelliterbits, on-fiducialtationocations,nd3 componentsf thegeocenterffsetrom henominalriginare estimated. The satellite orbits are estimated about adynamicallyefined riginwhichdeterminesheEarth'scenterof mass,or geocenter.The 3 estimatedgeocenterparametersepresenttranslationalffset etweenheoriginof the eferencerame nd hedynamicalrigindefined y the

1487

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1488 Vigue tal.' PreciseeterminationfGeocentersing PS90i I I ' I i ..... I .....ALL/FA, __yoL JOLDLG'- '-u St)ou _ SCR / MA _ St _

0- --30-d0 -

-90 I i I I .... I-180 -120 -60 0 60 120 180lo.gitude deg)

Fig. 1' GIG'91 GS RogueReceivercationsGPS orbits.Thusgeocentric tation ocations redeterminedforall non-fiducialites. arth rientationarameters,solarradiation oefficientsersatellite, PScarrier hase iases,randomwalk zenith roposphereelays or eachsite, andtransmitter/receiver clocks were also estimated. Details on theestimationtrategyregiven yLichten1990a, 990b].An alternativeno-fiducial techniquedemonstrated yHeftineta . [1992] nvolvesstimatingll stationoordinatesandsatellite ositions ith veryweakconstraints~1 km).This defines rigidnetworkwhichhasan ill-conditionedri-entation ut s neverthelessonstrainedy thedata o hegeo-center hrough he dynamics f the GPS satellites.To definegeocentric oordinates,he network anbe translated,otated,andscalednto hereferencerameof choicee.g.,SV5). The3 estimatedranslationalarametersre hegeocenterffsetfrom heorigin f this rame B ewitt t al., 1992].

Results and Discussion

Figure2 showsdaily x andy geocenteromponentsti-mates as offsets from the nominal values. The nominal valuesused for each component f the geocenter ome rom theglobalSV5 station ocation olutions.The x andy compo-nentsof thegeocenterxhibitvariations hichappearo benegatively orrelated.An erroranalysis redictshiscovari-ant behavior, nd t is thought o be due to the asymmetricglobal distribution f sites. The weightedmeanvalues(3-week weightedGPS averages) re 8.3 cm and 13.4 cm,

TABLE 1:G G'91 GPS RogueReceiverSitesGo-Algonquin,anada '" NALL-Nylend, orw'ay.............CANB-Canberla,ustralia PINY-Pinyon, alifornia(USA)FAIR-Fairbanks, laska USA) PGC1Victoria,CanadaGOLD-Goldstone,aliforniaUSA) SANT-Santiago,hileHART-Hartebeesthoek,outhAfrica SCRI-LaJolla,CaliforniaUSA)HONE-Honefoss,orway TROM-Tromso, orwayJPLM-Pasadena,aliforniaUSA) WETB-Wettzell, ermanyKOKB-Kokee, awaii USA) USUD-Usuda,apanKOSG-Kootwijk, etherlands YAR1-Yarragadee,ustraliaMATE-Matera, taly YELL-Ye lowklfife, anadaMADR-Madrid, Spain

4030

10a 4o

-20-30-4020 25 30 35 40Day of Year 1991)

Fig. 2: GPSGeocenter stimatesx,y comp.

i ' '1 ' I ' I...............................2...1..d.a...y.s:tationsombined

..... ..........

.........:............................................................[ ......:........... ..... .......[., geoc X mean-8.3 m,ms 4.0 rn/i/ .........g;:%"'......?'"/ii';/i'ii'-::"i'5':':F"//i"FL__ I I , , I I J

45

for x andy components,espectively;hese aluesepresentthedifference etweenheGPSsolutionor thegeocenterndthe nominalvalues,which are basedon yearsof SLR dataandarebelievedo be accurateo better han5 cm [Eanes tat., 1990]. Thedaily msscatter bout hemean or thex andy components f the geocenter re 4.0 cm and 4.4 cm, re-spectively. This daily rms scatter s a measureof internalprecision f the technique resented ere,andcanbe consid-eredan indication f the potentialo measure ariationsn thegeocenter verone day.

The estimatesor the geocenter componentrom 3 weeksof GIG'91 data are shown n Figure 3. This componentshows argervariations han he x andy components,utwedo not believe hat these esults howactualdaily center fmass variations. The 3-week weighted mean offset fromnominal or the z components 7.7 cm, while the daily rmsscatter s 30 cm. It is likely that the estimationof thiscomponents muchmoresensitive o the unevendistributionof fiducial and non-fiducial stations between the northern andsouthern hemispheres, and to the uneven 1991 GPSconstellation.Although he z component ormal errors reare ndeedarger han hose or the x andy components,hedaily z geocenterormalerrors re aboutone-halfas arge sthe observed rms scatter. Additional systematic error

100 ........... I '" I I ...... i"' --21 days:Stations ombinedX,Y PolarMotion Estimated

-60 ......................I I 130era'10020 25 30 35 40 45Dayof Year 1991)

Fiff. 3: GPS Geocenter Estimate- z component

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Vigue tal.: Preciseeterminationf GeocentersingGPS 489contributionsor thez componentascomparedo x andy)may edue o heweak overagen the outhernemisphereduring he experiment. or instance, artebeesthoek,southern emisphere ite whosedatawere geometricallyimportant,asoperatingess han 2 hours erdayduringthis xperiment.imulationshow hat hesigmasor x, y,and geocenterstimatesrenearly hesamewhenusingfull 24-sate lite onstellationnd full groundcoverage e-tweenhenorthern ndsouthernemispheresMaIlaet al.,1992]. hez componentlso ppearso exhibit disconti-nuity earFebruary, which s notwellunderstood.anyalternativenalysis echniques ere tested n an attempt odeterminewhat systematic errors may have caused hediscrepancyn thez geocenterstimatesetweenhe irstandsecond alf of the experiment.Omittinga questionableta-tionor satellitedid notchange hispattern.

Variationsn the estimation trategywere studied n an ef-fort o observe hangesn the geocenter stimates. ifferentfiducial networks yielded little variation in the results,althoughhe different etworks e trieddid notresult n awide ariation f the iducialnetwork eometry. sensitivityanalysishowedhata 3 cm iducial rror n all components(x,y,z) ould iveanerror f approximately-15cm n thegeocenter,lthoughhis rrorwould eexpectedrimarilysanoverall iaswith smaller ay-to-dayariations. he"3 cmfiducialrror" efers o independent-cmerrorsn each f x,y, z componentsor eachof 3 fiducials,with no errorcancellationassumed.However, results of Blewitt et al.[1982]nidicatehat iducialrrorsremoreikely obeat helevel of 1-2 cm. Both the fiducial and non-fiducial sites werenotwell-distributedn z duringGIG'91, thusmagnifyingerrorsn the z-component. ith a full constellationf 24GPS nd qual orth-southemisphereoverage,he atiooffiducialo geocenterrror s closero :1, accordingallaandWu [1989].Polarmotion Earthorientation)arametersereheldfixed n anothercase,with only slight degradationn thegeocenterstimates. e alsoestimatedarth otationUT1-lyrc) stochasticallyevery 2 hours) roducingittlechange.Longer rbitarc engths erealsostudied.n these ases,eclipsingatellites'rbitswereestimatedssingle-dayrcs ominimizerbitmodelingrror.Eclipsingatellitesresatel-lites whose orbit orientation is such that the satellites enter ashadowedegionwhere hesun's adiation ffects n thespacecraftrereducedpenumbra)r completelylocked(umbra)y theEarth.n general, clipsingatellite rbiter-rors ave een ound obesignificantlyargerhan hoseor

TABLE : Comparisonf GeocenterstimatesetweenFiducial ndSevenParameter ransformationechniquesGPS estimates of the

geocenterffsetusing iducialsGx=-8.3 cm +/- 2.7 cmGy= 13.4cm +/- 2.4 cmC,z -7.7cm +/- 13.7cm

GPS estimates of thegeocenterffset yestimationof a 7 ParameterransformationTx = -7.5 cm +/- 2.6 cmTy = 13.0cm +/- 2.5 cmTz = -14.8 cm +/- 13.8 cm

non-eclipsingatellitesSchutz t aI., 1990].The 2-dayarccaseyieldedmixed results.One fiducial networkslightlyreduced he variationsand another iduciaI networkslightlyincreasedhem. For 3-dayarcs, heresults egradedurther.Table2 shows summary f the geocenter stimates b-tainedusing he technique resentedn this paperas com-paredwith thosen Blewittet aI. [1992]wherea 7-parametertransformation3 translations,rotations,nda scaleactor)is estimated.Tx, Ty, and Tz shown n Table 2 are the 3translationalffsets f thegeocenterrom hereferencerameorigin; he values rom each echnique greevery well in astatistical sense. The differences are much less than the corre-sponding -c formaluncertaintiesf the estimates.BothtechniquesseGIG'91 databut useslightlydifferentstrate-gies n obtaininghegeocenterffsets. t is importanto notethatBlewittet al. [1992]uses 2 sitescollocated ith theInternational errestrialReferenceFrame (ITRF) [IERS,1991]. SinceSV5 is intendedo be alignedwith TRF, it isnotsurprisinghat heresults re n close greement.

GravityField Sensitivity nalysisThe useof GPS o determinehe geocenterrom the dy-namicalnformationn theorbitsmaybe a powerful echniquesince he large numberof GPS satellitesenables ull geo-graphicaloveragef theglobewitha relatively mallnumberof ground tations10-20) in a dayor less.This enablesapiddetermination f the geocenter ith GPS data. In addition,

therelativelyhighaltitude f GPSsatellitesmore han wicethe distance rom the centerof the Earth as LAGEOS) makesthe GPS solutionsmuch esssensitive o drag and gravitymismodeling.o quantify his,we examined he effectofgravityerrors n theGPSgeocenterstimates.Our analysis omputeshe error which is introduced yestimating he geocenterwith GPS data while leaving thegravity ieldunadjusted.heeffectof notestimatingertainparameters an be quantified hrougha sensitivity,orconsider nalysis. n this type of error analysis, he filtercomputeshe sensitivityhe estimated arameterso thoseparametersot beingestimated.Let vectorYc contain heconsideredunestimated)arameters,nd "'; are he om-putedilter estimatesndcovariancenot ncluding ffectsfrom heconsideredarameters).hen hesensitivity atrix,S is defined as

s = o(x- x) O)Oycwhere S is calculated rom the measurement artials seeBierman1977]).The otal rror ovariance,ncludingheformal errorscomputedn the filter as well as the errorcontributionromunestimatedconsidered)arameters,s

Pcon=+ SPcT (2)where c s thea priori ovarianceor theconsiderarame-ters.Usually, c sa diagonal atrix, uta more ealisticep-resentationometimes tilizesa full matrix in order o accountfor correlations etweenconsidered arameters. For ouranalysis,he onsiderarametersre implyhegravityoef-

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1490 Vigue tal.' Preciseeterminh[ionf Geocentersing PSficients. A very simple ndsomewhat bbreviatednalysisby Bertiger t al. [1986] ndicatedhat heeffectof gravity r-rors on GPS orbits determined from less than 24 hours ofdatawas an orderof magnitude maller hanothererrors uchas data noise, fiducial errors,etc. One would infer from thisthat other GPS-inferredquantities,such as the geocenter,would also be relativelyunaffected y gravity ield errors.Howeverwe re-analyzedhisusing he full GEM-T2 covari-ance Marshet al., 1990] or Pcwith theglobal racking et-work for GIG'91, in order to better understand he effect ofleaving he gravity ield fixed while estimating new origin(geocenter). he new calculationshow hat heerrors ntro-duced n the GPS geocenter stimatesrom holding he grav-ity field fixed areonly 0.05 mm, 0.7 mm, and0.5 mm in thex, y, andz components.hese rrorsare less han1% ofother observed rrorsand are clearly insignificantn theoverallGPS geocenter rrorbudget.

Summaryand ConclusionsThe mean GPS geocenter stimate rom a 3-week 1991experiment agrees to 7-13 cm in each componentwhencompared with an SLR (SVS) reference measurement.Individualsingle-dayGPSsolutions xhibited msvariationsof 4 cm in x andy and30 cm in z. Geocenterstimates adewith a standard iducial strategy nd with a fiducial-free7-

parameter ransformation roducesimilar answers,withformal errorsof 2-3 cm in x and y, and 15 cm in z. TheincompleteGPS conste lation nd very limited southernhemisphereround ataarebelievedo be factorsimiting heprecision ndaccuracy f dailyestimatesrom he199 dataset. With satellite launches in the near future, the GPSconstellation ill grow by about50%. Additionalsouthernhemisphere ata should mprove he z component f thegeocenter articularly.GPS geocenter ccuracy n a dailybasiswith a full constellation nd uniformglobalnetwork sexpectedo be better han5 cm; ncorporationf data romlow earthorbiters uchas TOPEX is expectedo strengthenthesolutionvenmore Mallaet al., 1992].Further PSandSLR intercomparisonsouldpotentially ncover ystematicerrorshatmayexist n either echnique.

Acknowledgements.he work describedn thispaperwascarried utby theJetPropulsionaboratory,aliforniaInstitute f Technology, ndercontractwith the NationalAeronauticsndSpaceAdministration. e thank hemanyparticipantshohelpedmakeGIG'91a success,ndYoazBar-Sever and Ron Muellerschoen, who contributed tospecial oftware sedn thiswork.

ReferencesBertiger,W., S. Wu, J. Border,S. Lichten,B. Williams,and J. Wu, High PrecisionGPS Orbit DeterminationUsingMarch1985 Demonstrationata, AIAA 24thAerospacecienceseeting, aper IAA-86-0089,986.Bierman,G., Factorization ethodsor Discrete equentialEstimation, 128, Academic ress,New York, 1977.Blewitt, G., M. Heflin, F. Webb, U. Lindqwister nd R.Malla,GlobalCoordinatesithCentimeterccuracyn the

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1992.Herring, T., D. Dong, and R. King, Sub-milliarcsecondDeterminationf PolePosition singGlobalPositioningSystemData, Geophys.Res. Lett., 18, pp. 1893- 896,1991.IERS, Annual Report for 1990, IERS Central Bureau,Observatoire de Paris, 1991.Lichten,S., S. Marcus,and J. Dickey, Sub-Daily Resolutionof Earth RotationVariationswith Global PositioningSystem Measurements,Geophys. Res. Lett., 19, 537-540, 1992.Lichten, S., Towards GPS Orbit Accuracy of Tens ofCentimeters, eophys. es.Lett., 17, 215-218,1990a.Lichten,S., Estimationand Filtering for High-PrecisionGPSPositioning Applications,Manus. Geod., 15, 159-176,

1990b.Lichten, S., and J. Border, Strategies or High PrecisionGlobal Positioning System Orbit Determinatin, J.Geophys.Res., 92, 12751-12762,1987.Lindqwister, U., A. Freedman, and G. B ewitt, DailyEstimates of the Earth's Pole Position with the GlobalPositioningSystem,Geophys.Res. Lett., 19, 845-848,1992.Malla, R., and S. Wu, GPS Inferred Geocentric ReferenceFrame for Satellite Positioning and Navigation, Bull.Geod., 63, 263-279, 1989.Malla, R., S. Wu, and S. Lichten, Geodetic ReferenceFramefor Geodynamics, J. Geophys. Res., Solid Earth:ModellingCrustalDeformation pecialSection, n Press,1992.Marsh, J., F. Lerch, B. Putney, T. Felsentreger,B.Sanchez, S. Klosko, G. Patel, J. Robbins, R.Williamson,T. Engelis, W. Eddy, N. Chandler,D.Chinn,S. Kapoor,K. Rachlin, . Braatz, ndE. Pavlis,The GEM-T2 GravitationalModel,J. Geophys. es., 5(B13), 22043-22071,1990.Murray,M., R. King,andP. Morgan, V5:A TerrestrialReferencerame or Monitoring rustal eformation iththe GlobalPositioning ystem, Abstract),EOS Trans,AGU, 71, p. 1274, 1990.Schutz, ., C. Ho, P. Abusali, ndB. Tapley,CASAUN0GPS Orbit and BaselineExperiments,Geophys.Res.Lett., 17, 643-646, 1990.Sovers,O., andJ. Border,Observation odel andParameterPartials for the JPL GeodeticGPS Modelling Software

"GPSOMC",JPL Pub. 87-21, Rev. 2, Jet PropulsionLaboratory, asadena, A, 1990.Srinivasan,., T. Meehan,and L. Young,CodeandCodelessonospheric easurementsithNASA'sRogueGPSReceiver,roceedingsnst.ofNavigationPS-89Conference,989, 451-454Inst.of Navigation).GeoffBlewitt,MichaelHeflin,Steve ichten, ajjuMalla,andYvonne igue,JetPropulsionaboratory, ail Stop.238-600, 800OakGroveDrive,Pasadena,A 91109.

(Received arch10, 1992;accepted ay 8, 1992.)