global coordinates with centimeter accuracy in the ... - CiteSeerX

GEOPHYSICAL RESEARCH LETTERS, VOL.19,NO.9,PAGES 853-856, MAY4, 1992 GLOBALCOORDINATES wrDt CENTIMETER ACCURACY IN THE INTERNATIONAL TERRESTRIAL REFERENCE FRAME USINGGPS Geoffrey Blewitt, Michael B.Herin,Frank H. Webb, Ulf J.Lindqwister, andRajendra P.Malla

JetPropulsion Laboratory, California Institute ofTechnology Abstract.Using21 daysof GlobalPositioning System

Of the 21 sites in this GPS solution, we have obtained

(GPS) datafrom21 globally distributed receivers operating local surveysfrom the GPS antennato an ITRF monument during early1991,we solvefor a 7-parameter transformation for !3 "collocated" sites. (Thesesurveysare completely betweena GPS free-network solution and coordinatesof 12 independentof the GPS solution used in this study). stations listedin the InternationalTerrestrialReferenceFrame ITRF'90coordinates andstandard deviations at epoch1988.0 (ITRF).Standard errorsof GPScoordinates arederivedby aregivenbyIERS[1991]. !TRF'90represents a combination applying anorthogonal projection operator tothefree-network of solutionsby variousgroupsusingvery long baseline covariance.The weighted RMS difference between 33 interferometry(VLBI) or SatelliteLaser Ranging(SLR). transformedGPS and ITRF coordinates is 12 mm in the Sincethecoordinates for YELLOWKNIFE havelargeerror northern hemisphere.Bestresultsareobtainedby mapping bars in ITRF'90, this site is excluded from the ITRFcoordinates to theepochof thisexperiment assuming no intercomparison. Theremaining 36 coordinates havestandard verticalsitemotions.Fixing selectedsitesin theGPS solution deviations no largerthan2.1 cm. Local surveysolutionsare toITRF'90doesnot improvethe agreement. We concludethe useof fiducialconstraints is unnecessary for globalnetworks.

listed in Table 1 for the GPS monuments in our solution.

SiteVelocityModels Introduction

To accountfor tectonic motion between ITRF'90 reference

In orderto useGPSfor monitoring large-scale geophysical signals suchasglobalsea-levelchangeandpost-glacial crustal rebound, GPS must be capableof providingglobalstation coordinates with centimeter-levelaccuracy. The "fiducial concept," in which a subsetof coordinatesare constrainedto values previously determined by other space-based

techniques, has been a successfulGPS techniqueover regional scales. Use of thefiducialconceptimpliesthatsuch solutions are no longer independentof other techniques; fiducia! coordinate errors can bias the GPS coordinates and

evenstrain-rates [Larsonet al., 1991]. Moreover,on a global scale it becomes difficultto interpretGPSsolutions whichare strongly constrained a priori. In thispaper,we showthat(1) high-precision GPS coordinates can be derivedwithoutuseof fiducial constraints,and (2) fiducial constraintsdo not

improve theaccuracy of ourglobalnetwork solution. Heftinet al. [ 1992]appliedthefree-network approach in ananalysis of 21 daysof datafrom 21 globallydistributed receivers in the GIG'91 campaignbeginning January22, 1991.Expanding on this,we assess coordinate accuracy by performing a similaritytransformation of thisnetwork intothe

epoch!988.0 and epoch1991.1 we apply two models. ModelA usesempiricalsitevelocitiesfromsolutionGLB718 for VLBI sites [C. Ma, D.S. Caprette, and J.W. Ryan, private communication,1991], and solutionSSC-(IERS)90C01for SLR sites[Boucherand Altamimi,1991]. Model B is the same,exceptthatthe 4 collocatedsiteswhichhave

verticalvelocities > 1 mm/yrin GLB718 (e.g.,MADRID at TABLE 1. Local SurveySolutions(GPS- !TRF'90) SITE

DELTA COORDINATE(ram) ANTENNA*

NAME

X

ALGONQUIN FAIRBANKS GOLDSTONE

PASADENA

94763 -74141 2879994

InternationalTerrestrial Reference Frame, ITRF'90. The

7941 -12461 -134193 -14128 125588 36288 39384 -18605

utilityoffiducialconstraints for thisglobalnetwork is tested.

YELLOWKNIFE

-327848

Data Usedin This Study

For this study,we use a free-network GPS solution, conveniently represented by Cartesian sitecoordinates, very loosely constrained to theITRF. We referthereadertoHeftin

SIDNEY

etal. [1992]for detailsof the datareduction.In thisstudy,

USUDA

Z ,, HEIGHT

61017 49280 5222210

1987

KAUAI KOOTWIJK MADRID MATERA PINYON TROMSO WETTZELL YARRAGADEE

CANBERRA JOHANNESBURG HONEFOSS NY ALLESUND

¾

(not (not (not (not

BC

SCRIPPS

166 0

-22•052

163

-23617 -37503 159660 -13229 117655 -33115 71978 -12471

-4407 23024 164320 18027 279910 -9219 -58362 -5835

163 156 0 352 1914 2543 1668 143

314599

82882

yet available) yet available) in ITRF'90) in ITRF' 90) Until

(not (not (not

184

-18063

From SANTIAGO

6666 -31231 8549901

181

0 9754 4017 1810

Jan

28:3360

Jan

29:1349

yet available) in ITRF'90) in ITRF'90)

183 1915 0

theEarth's poleposition andsatellite orbitswereestimated *GPSantenna heightis to thetopof theRoguechokering. independently every24hours toreduce systematic errors.

An additional phasecenterheightof-20.7 mmwasassumed forthedual-frequency combined phaseandpseudorange observables. Theseantenna heightsmaynotbe validfor datesotherthanJanuary22- February13, 1991.

Copyright 1992by theAmerican Geophysical Union.

Paper number92GL00775 .

0094-8534 / 92/92GL-00775 $03.00 853

854

Blewitt et al.: GlobalCoordinates in ITRF usingGPS TABLE 2. ITRF'90 Coordinates of GPS Monumentsat Epoch 1991.1 SITE

NAME

ALGO FAIR GOLD PASA

COORDINATE

ERROR(ram)* *

VELOCITY (mm/yr) X

Y

g

.

X

Y

-4346071223 -1453595751 -4641385442

4561977794 5756961960 3676976512

-18.7 -24.1 -17.4

-3.6 -0.1 11.1

1.1 -10.3 -9.9

7 8 8

8 9 10

B*-2353614082

-4641385457

A

-4655215589

3676976523 3565497327

-18.5 -35.2

5.3 23.9

-5.2 3.4

8 13

10 18

3565497331 2387809490 5015078290 4114913118

-35.9 -13.1 -15.3 17.9

4.4 29.7 10.5 44.2

-10.2

13 9 18 15 15

18 9 19 10 10

14

4114913058

22.6 69.8 16.0 18.9 18.8

1393056751 -4761207198

4133280313 3511396053

-16.2 -25.7

11

11

11

11

15

13

-4761207226

3511396075 5958192044

A

918129630 -2281621298 -2353614080 -2493304032

A

-4655215595

-5543838061 3899225380 4849202647

-2054587585 396731754 -360329222

B* 4849202592 MATE PINY

(ram) Z

B*-2493304035 KAUA KOOT MADR

AT EPOCH 1991.1

MODEL

A

-360329223

4641950906 -2369510349

B*-2369510362 TROM WETT

2102940468 4075579405 -2389025280

YARR

721569359 931807155 5043316823

9

9 9 9 14 10 17 17

23.7

13.6 12.1 -3.4

-29.3 -19.0

16.1

2.1

11

15

13

10.4

5.4

14

12

21

4801570931

-14.4

-3078530992

-51.5

12.5 8.0

9 12

9 12

13

18.1

9.5 53.0

17

9

*Model B hasbotha differentvelocityandepochvalueat 1988.0.In thecaseof Goldstone, thevelocitysolutionfor stationMOJAVE12(7222)wasappliedfromGLB718. **Errors aspublishedin IERS [1991]aremostlyunderestimated sincetheyreferto 1988.0

41 mm/yr) were mappedto 1991.1assumingno vertical motion. Since ITRF'90 implicitly containsGLB718, we

whereW is an assumed weightmatrixdesigned toreflectthe relativestrengthof thevariousinputcoordinate data.

were able to account for the correlation between !988.0 site

coordinates andvelocitycomponents in mappingcoordinates to 1991.1. Table2 listsITRF'90 coordinates mappedto GPS monuments at epoch!991.1 for bothvelocitymodels. SimilarityTransformation Model

The similaritytransformation usedby IERSis:

s y z

=

y Z

+

ty

+

O:

% (1)

s

tz

-0•

O•

s

wherex, y, and z are GPS-derivedcoordinates; X, Y, andZ

areITRF'90coordinates; tx, ty, andtzrepresent anoffsetin origin;$ represents a differencein scale;Ox,Oy,andOz representdifferencesin orientation.Someparameters have physicalinterpretations: (1) the offsetin originrepresents a discrepancyin the estimatedlocationof the Earthcenterof massandshouldbestatistically consistent withzero;(2) since

both systemsadoptthe samespeedof light, gravitational coefficientGMo, and definition of coordinatetime, the scale

differenceshouldbe consistentwith zero; (3) orientation

differenceshaveno physicalsignificance, sincethey are arbitrarilyconstrained by loosea priorivariances. For purposes of estimatingthe transformation parameters, equation(1) canberearrangedandrewrittenin matrixform:

6x =

+v

(2)

where/Sxis thevectorof coordinate differences (GPS-ITRF), [I is thevectorof 7 nanformation parameters, A is thematrix of partial derivatives, and a vector of errors v has been

included. Theweightedleast-squares estimate of • is

Constructing theWeightMatrix

Wedonotmaketheusual choice ofweights W=E'l where 2Eis the initial GPS covafiance,because2;is only savedfrom beingnon-singularby loosea priori constraints.Thisarises from (1) perfect correlationbetweenthe satelliteascending nodesandthe originof longitudes,and (2) perfectcorrelation between station coordinatesand pole (X,Y) coordinates. Nevertheless, we still use2; to computestandard errorsin the translation andscaleparameters to assess theirsignificance. In derivingcoordinatecovariances, geodeticinvestigators haveappliedvariousad hocmethods,including,for example, constraininga number of coordinatesand/or directionsto establish a reference framefor thetechnique in question. We choseto allow ourGPS networkto remainfree-floating until performing the similarity transformation, however the covariance

matrix was modified

so that covariances are

relative to an internally-definedframe, as opposedto thea prioriframe. Correlated errorsarisingfromreference-frame uncertainty

areremovedfrom F with the applicationof an orthogonal projection operator B, which projects GPS coordinate variations ontoa spaceorthogonal to a reference framethatis implicitlydefinedthroughtheinitial GPS coordinates:

rñ= BFB where

B=I- A(ATA}'IA T

(4)

(5)

and where all station coordinatesin the initial GPS solution

areusedto compute matrixelements of A, irrespective of whether theyarein theITRF.Thiscovariance transformation

is equivalent to imposing thecondition thatATxhaszero variance, whichintuitively corresponds tofixingthedirection, originand scaleof the coordinateaxesin an averagesense to

• = {ATWA)'IATW•x

(3)

the initial GPS coordinate solutionx [Koch,1987]. We

B!ewitt etal.:Global Coordinates inITRFusing GPS ernphasise thatonlycovariances (notthecoordinates) are

855

Results

transformed; wearesimplyconstructing a weightmatrix.

Fñishasa 7-rankdeficiency because B is indempotent. Equation (7) showsthe estimatedtranslationand scale between GPSandrrRF (ModelB), computed usingequation deviations for theseparameters derived Fñusing the3x3 covariance submatrices between the (3), with standard GPSeovariance forZ. coordinates of individual stations. In thisstudy, onlythe fromtheinitialloosely-contrained variances areused(forbothGPSandITRF)because only diagonal termsfor ITRF wereavailable.In ignoring offtx=(-7.5+_2.6)cm Nevertheless, a weightmatrixcanbeformedfromblocks of

diagonal terms,the relativeprecisionof verticalversus horizontal components is notaccounted for in theweight

%=(13.0 :k2.5)cm tz=(-14.8 +_13.8) cm =(-3.6_1.3)x10-9 =(6.0:i:530) x 10-9

matrix.We still retainthe informationthat somestationsare

better determined thanothers.Therefore, theweightmatrixis

W--[diag(lrl.fl)]'x

(7)

30)x 10-

(6)

--(-299.s_+ 20) x 10where fl istheITRF90covariance, B isdefined byequation Theframeorientation hasno physicalsignificance. The (5),andF is ourGPScovariance derivedusingveryweak originis generally believed tobeaccurate at constraints. Applyingequation(3), thisweighting method ITRFgeocentric the 2-cm level, therefore the geocentric offset deviates produces estimates andeovarianees whichareinsensitive to fromzero.At thispoint,wecannot explainthis loosea prioriconstraints.We scaledthe covariance F such significantly result. The estimated offset closely agrees with Vigue et al. thatthemeanformalerrorin baseline lengthwas2.8 x 10-9L

[1992],who,usingthe samedata,insteadheld 3 stations (where L is length)corresponding to the empiricalstandard fixedin theSV5frameandexplicitlyestimated a geocenter deviation in lengthdifferences observedbetweenthef•t- and parameter. The scaledifferencedoes not appearto be second-half of theexperimentfor lengths> 4000km. significant sinceITRF errorsareexpected to be at the10-9 Tables2 and 3 list the standard deviations for ITRF90 and

GPS,definedby the diagonalelementsof fl and F•.. The

level. Results fromModelA differfromModelB by