GEOPHYSICAL
RF3EARCH
LETTERS,
VOL.19,NO.9, PAGES
845-848,
MAY 4, 1992
DAILY ESTIMATES OF THE EARTH'SPOLE POSITION
WITH THE GLOBAL POSITIONING SYSTEM
Ulf J.Lindqwister,
AdamP.Freedman,
andGeoffrey
Blewitt
JetPropulsion
Laboratory,
California
Institute
ofTechnology
Abstract.Daily estimatesof the Earth'spolepositionhave
beenobtained
with measurements
from a worldwidenetwork
of Global Positioning System (GPS) receivers,obtained
The GPS data were reduced
with
the GIPSY
orbit
determinationand baselineestimation software using two
basicstrategies:
(1) a standard
parameterestimationstrategy
duringthe three week GIG'91 experimentin January- with three "fiducial" stations constrained to a priori
February,
1991. For this short-termstudy,the GPS based coordinates
[LichtenandBorder,!987], and(2) a variationof
polarmotionseriesagreeswith the otherspacebased the abovestrategywith no fixed sites,i.e., the free network
geodetic
techniques
(VeryLongBaseline
Interferometry
and strategy[Heflin, et al., 1992]. The standardstrategyfor the
SatelliteLaserRanging) to -0.4 mas rms, after the removal
of meanbiasesof order 1-3 mas. The small error in day-to-
daily solutionsmay be summarized as follows' station
locations,satellite epoch states, and carrier phase bias
dayvariability
is notsensitive
to thefiducialstrategy
used, parameterswere estimatedas constants.Station and satellite
nor are fiducial sites even necessaryfor monitoring high
clockswere estimatedas white processnoise.A 2.2 meter
frequency
poleposition
variability.
Thesmallbiases
indicate zenithtropospheric
delaywasremovedandtheresidualdelay
thatthe applied referenceframes of the three geodetic
techniques
arenearlyaligned,thattheGPSfiducialerrorsare
wasestimated
usinga random-walkstochastic
model.When
fiducialconstraints
wereimposed,the stationlocationswere
small,and that systematicerrorsin GPS are also small (of
constrained to coordinates from the SV5 reference
frame
order
5 ppb).A well determined
reference
frameis necessary [Murray,et al., !991]. The SV5 referenceframein principle
formonitoring
the long-termstabilityof polarmotionandfor has the sameorigin and orientationas the International
separating
it from otherlong-termsignalssuchas tectonic Terrestrial ReferenceFrame (ITRF) used by IERS. In
motionandinternalsystematicerrors.
addition, the offset of the Earth's center of mass from the
originof the SV5 frame(thegeocenteroffset)was assumed
Introduction
to be zero.
The locationof the rotation axis with respectto a crustThe variations in direction of the Earth's rotation vector
fixedaxis(e.g.,the iERSreferencepole [McCarthy,1989])
with respectto a terrestrial referenceframe have been
measured
for over a centurywith opticalastrometry[Munk
can be describedby two coordinates,polar motion x (PMX)
and y (PMY), where the x-axis lies along the Greenwich
meridian,orthogonal
to thereferencepole z-axis,andthe yaxisis 90 degreesto the west,as indicatedin Figure 1. The
andMacDonald,1975]. More recently high precisionpolar
motionestimation has been the province of two space
geodetic
techniques:Very Long BaselineInterferometry two pole parameterswere estimateddaily as constant
(VLBI) and Satellite Laser Ranging (SLR). Reported adjustments
to nominalvalues obtainedfrom the IERS
accuracies
from thesetechniquesare typicallyat the level of
0.3-0.7mas, and thesetechniquesgenerateeither 24-hour
estimates
every few days (VLBI) or three-day averaged
estimates
every three days (SLR) [IERS, 1990; 199!]. A
GlobalPositioningSystem (GPS) experiment (GIG'91)
performedin early 1991, under the auspices of the
InternationalEarth Rotation Service (IERS), using GPS
receivers
distributedworldwide,providedan opportunityto
[BulletinsB37 and B38, 1991]. The daily Bulletin-B values
90OE
testGPSasa complementary
technique
for measuring
Earth
orientation
[Freedman,1990]. The goalsof this letterare to
determine
the internalprecisionand accuracyof the GPS
measurements
of polarmotion,suchthatreliableconclusions
maybedrawnconcerning
anysignalsobtainedwith theGPS
technique.
Analysis
TheGIG'91experimentwascardedoutbetweenJanuary
22andFebruary13, 1991by numerous
international
agencies
and utilized over 120 GPS receivers of several different
manufacturers
andantennatypes.'
A subset
of 21 RogueGPS
receivers was chosen to minimize
the effects of antenna
phasecenter offsets and systematicerrors internal to
receivers
[Thomas,1988].The Roguereceivers
wereglobally
distributed
as indicatedin Figure1, whereonly the setof
fixed(fiducial)stationshavebeenlabelledexplicitly.For a
complete
list of stationnamesand coordinates,
seeHerin, et
al.[1992].
90øW
Fig. 1. Shownare 18 of the 21 Roguesites,distributed
worldwide during the G!G'91 experiment (3 additional
Roguesin SouthernCaliforniawere also includedin the
analysis).The fiducial sitesat Goldstone(CA), Wettzell
(Germany),Tromso(Norway), Kootwijk (Holland), and
Kokee(HI) havebeenlabelledexplicitly.
Copyright
1992bytheAmerican
Geophysical
Union.
Papernumber92GL00576
0094-8534/92/92GL-00576503.00
845
846
Lindqwister
et al.:Measuring
PolarMotionwithGPS
were interpolatedand smoothedfrom solutionsevaluatedat
five-dayintervals.
All parameters were simultaneouslyestimated in a
factorized
Kalman
filter.
The
satellite
states were
re-
estimatedevery day to minimize systematicforce model
errors.Most parameterswereessentiallyunconstrained,
with
a priori formal errorsordersof magnitudelarger than the
final computederrors.Meaningfulconstraints
wereonlyused
Table1. GPSpolepositionestimates
using3 fixedstations
(SV5). Listedare estimatedcorrectionsto the BulletinB
values for PMX and PMY. In parenthesisare the full
estimatesincludingBulletin B values.
Date
PMX [mas]
PMY [mas]
01-22-91
01-23-91
spanswere computed,hencepole positionswere obtained 01-24-9!
dailyas estimatedoffsetsfrom theBulletin-Bvalues.
0!-25-91
Results
01-26-91
Fiducial Network Studies
0!-27-91
-2.7+ 0.3 (-53.3)
-1.9+ 0.3 (-55.7)
-0.8 + 0.3 (-57.7)
0.8+ 0.3 (-59.3)
!.8 + 0.3 ( -61.6)
!.8 :t:0.3 (-65.1)
1.7ñ 0.4 (89.!)
1.8ñ 0.3 (90.2)
2.4 ñ 0.4 ( 9 !.9)
2.7ñ 0.4 (93.5)
2.4 ñ 0.4 (94.6)
3.6 + 0.3 (97.3)
0!-28-91
entirethree week interval, defininga rigid polyhedronfor 01-29-91
which daily variations of the pole position could be 01-30-91
estimated.Solutionswere obtainedfrom 22 separate24-hour
periodsbetweenJanuary22 - February13 (solutionsfor 02-01-91
January31 werenot available).Shownin Figure2 andlisted 02-02-91
in Table ! arethedaily GPSpolepositionestimates
for PMX
02-03-91
and PMY versus time as corrections to the nominal BulletinB values.The opensymbolsindicatesolutionsemploying 02-04-91
three fiducial sites:Goldstone(CA), Tromso (Norway) and 02-05-91
Wettzell (Germany).The GPS polar motionseriesexhibits
bothan apparentbiasand systematic
variabilitywith respect 02-06-9!
to the IERS solution. The mean bias of (GPS-Bulletin B) is
02-07-91
2.1 + 0.3
0.8 + 0.3
0.1 + 0.2
-1.1 + 0.2
-2.0 + 0.2
-1.9 + 0.2
-2.5 + 0.2
-2.7 + 0.2
-!.6 +_0.2
-1.4 + 0.2
3.6 +_0.3 (98.8)
3.4 +_0.4 (100.1)
3.7 _+0.3 (102.0)
3.5 + 0.3 (104.9)
2.2 +_0.3 (105.1)
2.6 + 0.3 (106.8)
2.4 + 0.3 (!07.9)
2.7 +_0.3 (109.7)
2.3 + 0.3 (110.9)
2.0 +_0.3 (112.2)
for the fiducial stations,whose coordinateswere constrained
to 0.1 mm. Solutions from distinct, consecutive24 hour data
Station
locations
-0.5 mas in PMX
were estimated
as constants over the
and 2.5 mas in PMY.
In addition to the
02-08-91
(-68.3)
(-73.1)
(-77.6)
(-86.6)
(-91.2)
(-94.6)
(-98.7)
(- !02.5)
(-!04.9)
(-108.1)
-1.0 + 0.2 (-! 11.0)
2.0 + 0.3 (! !4.0)
biases,PMX andPMY showa variabilityover3 weeksof--5
-0.7 + 0.2 (- 114.1)
1.9 + 0.3 (115.8)
masand ~2 mas,respectively,with respectto the smoothed 02-09-91
reference series.
02-10-9!
0.! +0.2 (-!16.4)
2.2+0.3 (1!8.0)
In the free network case, the fiducial constraints were
02-1!-91
0.0 + 0.3 (-1 !9.6)
2.2 _+0.3 (!20.2)
removed. The filled triangles in Figure 2 show the pole
positionsfor theno fiducialcase,wherea meanbiashasbeen 02-12-91
1.2 + 0.3 (-121.4)
2.3 ñ 0.3 (122.6)
added so that the two GPS solutions are aligned. The
02-!3-91
-0.1
+
0.3
(-125.7)
2.0+_0.3 (124.7)
reference frame is indeterminate for the free network solution
andthe pole biasesare arbitrary.The rms agreementbetween
Note:all epochsare at noonUTC andthe Bulletin-Bnominfl
the two caseswas -0.08 mas for each pole component.It is
clearfrom geometricalargumentsandborneout by the above values were obtained from B37 and B38, 1991.
resultsthat polar motionvariabilityin time is invariantunder
smallrigid rotationsof thereferenceframeandthatany such coordinatetransformationwould only add constantbiases
to
thepole parameters.
To specify fiducial coordinatesfor a GPS stationit is
[] PMY fiducial
necessaryto know (1) the coordinatesof a nearbyVLBI or
O PMX fiducial
SLR stationin a knownreferenceframe, (2) the ground
tie
ß
between the two station monuments, and (3) the site vector
between the GPS monument and the GPS antennaphase
free network
center.For theGIG'91experiment
only7 stations
haveatthe
time of this analysisbeencollocatedwith VLBI andSLR.
Any errors in the above three collocation measurements
would limit how well these stations are tied into the SV5
reference
frame.To studythisquestion,
polarmotionseries
o
:•
0
were obtainedwith two different setsof three-stationfiducial
networks. Shown in Table 2 are mean biases obtained
-
Table2. Meanbiasesbetween
polarmotionseries
obtained
fromvariousgeodetic
techniques
for twofiducialstrategies.
a, -2..
Shown in brackets are offsets for PMX
respectivelyin unitsof mas.
4
26 Jan
3 ! Jan
5 Feb
10 Feb
and PMY
Fiducial A
Fiducial B
[-0.5, 2.5]
[0.4,-0.9]
[2.7, 1.01
[0.6, 4.7]
[-0.7,-3.1]
[1.6, - 1.2]
Date
Fig. 2. A comparisonof polar motion estimatesfor the
fiducialversusthe free networkcases.The opencirclesand
rectanglesrepresent the day-to-day x-pole and y-pole
positionestimatesfor the fiducialcase.The filled triangles
representthe free network caseafter the additionof a biasto
alignthe two GPS solutions.
(GPS - IERS)
(SLR - GPS)
(VLBI - GPS)
Fiducial Network A: Goldstone,Tromso, Wettzell.
FiducialNetwork B: Goldstone,Kootwijk, Kokee.
Lindqwister
et al.:Measuring
PolarMotionwithGPS
between
GPS and IERS determinedpolarmotionseriesfor
fiducia!s
at eitherGoldstone,Tromso,andWettzell (CaseA)
orGoldstone,
Kootwijk(Holland),andKokee(HI) (CaseB).
TheA networkappearsto produceon averagesmallerbiases
'•9-Jan
•4an
847
5-F•
12-Feb
compared
to B, suggesting
that the GPS monuments
at
TromsoandWettzell are more accuratelytied to the SV5
framethanthoseat Kootwijkor Kokee.
Sensitivity
Analysis
A numberof sensitivity studies [Bierman, 1977] were
performed
todetermine
thebiases
in poleposition
estimates
due to possible systematic errors in fiducia! station
coordinatesand in geocenteroffset. Fiducia! errors were
I
i
i
assumedto be 3 cm in each of the three station coordinates
for Goldstone,Kootwijk and Kokee, and 10 cm for eachof
thegeocenter
components.
The root-sum-square
(rss)polar
motion
biasesdueto errorsin thefiducia!components
at each
sitearerepresented
by cross-hatched
columnsin Figure3,
whilegeocenter-induced
biasesare shownby the solidblack
column.Systematicfiducialand geocentererrors(of order3
2
2
o
cm and 10 cm) induce biases of order 1 mas and 2 mas in
PMX and PMY, respectively,for fiducial network B. The
observed
polarmotionbiasesrelativeto IERS for caseA are
1-2masandfor caseB 1-5 mas,with PMY roughlytwiceas
largeasPMX, aspredictedfrom the sensitivityanalysis.
Pan
of thebiasmay be accountedfor by offsetsbetweenthe SV5
•-2
-2
andIERS (Bulletin-B) reference frames, which are known to
bemisaligned
at the mas level. Independent
GPS analyses
haveshownthatfiducialoffsetsare largestat Goldstone(3-4
cm)andsmallerat the otherfixed sites(1-2 cm) and thatthe
geocenter
offsetfor SV5 is a few cm. Note that the pole
position
biasesinducedby thesensitivity
errorsscalelinearly
withthe input value, suchthat a few cm geocenteroffset
wouldreducethe inducedpole positionbiasesshownin
Figure3 by a factor of 2 or more. The observedbiasesare
hencelikely to be dominatedby fiducial errors,i.e., sitefie
errorsandSVS-IERSreferenceframemisalignment.
Fig. 4. Estimates
of polepositionwith GPS, VLBI, andSLR.
Bulletin B values have been subtractedfrom all the estimates,
and mean differences with GPS have been removed from the
VLBI and SLR data. The polar motion seriesfrom these
spacegeodetictechniquesagree within their formal errors
(-0.5 mas).
GPSversusVLBI andSLREstimatesof Pole Position
Solutions
fromnineVLBI experiments
havebeenobtained Each solution was obtained from 24 hours of measurements
spanning
January23 to February12 [Herring,eta!., 1991]. on one of several VLBI networks utilizing typically 4-5
stations.To removeunevenness
in network geometries,the
2
,
Goldstone
,-, . •5• Kootwijk
!•
'
[• KokeePk
•
' I
Geocentei
station coordinates were fixed
at values determined
from
-1300 experiments.
A concisedescriptionof the analysisis
givenby Herring,et al., [199!]. The VLBI solutionepochs
occurredat varyingtimesfor eachdaily solution,whereasthe
GPS epochsoccurred at 12:00 noon, UTC, each day
(obtainedfrom a 24 hoursolutionrunningfrom midnightto
the following midnight). In order to compute the rms
differencesat the same epoch, the GPS pole position
estimateswere linearlyinterpolatedto the timesof the VLBI
measurements(which introducessome small error). The GPS
and VLBI estimatesare shown in Figure 4, where a mean
bias has been removedfor each pole parameterfrom the
VLBI solutions with respect to GPS to show the close
correlation between the two polar motion series. The
resultingrms agreementsbetween GPS and VLBI, after
removingthe meanbiases,were 0.4 mas for PMX and 0.5
masfor PMY. The formalerrorsfor the GPS pole position
estimatesrangedfrom 0.2-0.4 mas, while the VLBI formal
errorsrangedfrom 0.1-0.4 mas. Hence the GPS and VLBI
,,
0-
..0
PMX
PMY
solutions were consistent with each other to within
their
respectiveerror bars (similar to the result obtainedby
Herring, et al., 1991). The biasesbetweenGPS (using
Fig.3. Effect
ofsystematic
errors
onpolar
motion
estimates.fiducial network A) and VLBI
Thecross-hatched
bars
show
theinduced
poleposition
biases mas for PMY, where the
were 2.7 mas in PMX and 1.0
mean of the (VLBI-GPS)
based
ona 3-cmerrorin eachfiducialstationcoordinate, differenceshave been computed for nine points. For
whilethesolidblackbar showsthe total biasdueto 10-cm
completeness,
the biasesbetweenVLBI and networkB are
offsets
ineach
geocenter
component.
also shown in Table 2.
Lindqwister
etal.'Measuring
Polar
Motion
withGPS
848
SLR data were obtained from the CSR 91 L 02 series
producedby the Centerfor SpaceResearch,Universityof
Texas at Austin [IERS, 1990; 1991]. Each data point
representsthe mean of approximatelythreedaysworthof
SLR measurements.The SLR estimatesare shownin Figure
4 together with the GPS and VLBI results, where mean
biases have been removed
from the SLR solutions with
Acknowledgments.
Theauthors
wishtothank
TomHerring
for providingtheVLBI solutions
andRichardEanesforthe
SLRdata.Discussions
withR. Gross,
A. Steppe,
S.Lichten,
andT. Yunckweremuchappreciated.
Theworkdescribed
in
thisletterwascarried
outbytheJetPropulsion
Laboratory,
CaliforniaInstituteof Technology,undercontractwiththe
NationalAeronauticsand SpaceAdministration.
respectto GPS to showtheclosecorrelation
betweenall three
polarmotionseries.The rmsagreements
betweenGPS and
SLR, afterremovingthe biases,were0.3 masfor PMX and
0.4 mas for PMY. The mean biases for the (SLR-GPS)
differences were 0.4 mas for PMX and -0.9 mas for PMY
usingnetworkA (seeTable 2). Thereportederrorsfor the
SLR data average-0.8 mas, hencethe computedpolar
motionseriesfrom all threespacegeodetictechniques
are
consistent
with eachother(afterremovingconstant
biases).
Discussion and Conclusions
References
Bierman, G. J., FactorizationMethodsfor Discrete
Sequential
Estimation,V128, Mathematics
in Science
and
EngineeringSeries,AcademicPress,1977.
Blewitt, G., An AutomaticEditingAlgorithmfor GPSdata
GRL., 17, pp. 199-202,March 1990.
Freedman,A. P., S. M. Lichten, W. G. Melbourne,andS.
Pogorelc,
A GPSCampaign
to Assess
HighFrequency
EarthRotationVariability,(Abstract)
EOS,Trans.,AGU,
43, p. 1272, 1990.
The above results show that the GPS techniquecan, at
Gross,R. S., andU. J. Lindqwister,AtmosphericExcitation
least in the short-term,determinepole positionvariations
of Polar Motion During the GIG'91 Measuremere
independent
from, andat a level comparable
to, estimates
Campaign,GRL, thisissue,1992.
obtainedfrom either VLBi or SLR. Also importantare the Herin, M., W. Bertiger,G. Blewitt, A. Freedman,K. Hurst,
absolute
polepositionestimates.
Thesmallpolebiasesimply
S. Lichten,U. Lindqwister,Y. Vigue, F. Webb,T. Yunck,
anupperlimit on theerrorsin theGPSfiducialcoordinates and J. Zumberge,Global GeodesyUsing GPS Without
(andgeocenter
errors).According
to thesensitivity
analysis,
Fiducial Sites,GRL, 19, p. 131-134, 1992.
a 1-2 mas bias would be the result of at most a station error
Herring, T. A., D. Dong, and R. W. King, Subof 3 cmpercomponent,
whichwouldsuggest
thatthefiducial
MilliarcsecondDeterminationof Pole PositionUsing
coordinates for network A are known to •-3 cm. In addition,
Global PositioningSystemData, GRL, 18, 1893-6,1991.
the small pole biasesobtainedwhencomparinggeodetic IERS, IERS Technical Note 5, Central Bureau of IERS,
techniques
implythatthe internalsystematic
errorsin GPS
Observatoire de Paris, June, 1990.
mustbe small,placingan upperlimit of sucherrorsat the IERS, IERS Annual Report for 1990, Central Bureauof
levelof ~1 mas(~5 ppb).Theseerrorsincludesatelliteorbit
IERS, Observatoire
de Paris,July, 1991.
errors, atmospheric delay mismodeling, and antenna Lichten,S. M., andJ. S. Border,Strategiesfor High Precision
multipatherrors.The fact thatthemeanpoleoffsetbetween
Global Positioning System Orbit Determination,J.
eachtechniqueis smallindicatesthat eachreferenceframe
Geophys.Res.,92, pp. 12751-12762,1987.
mustbecloselyaligned.Thisis notsurprising,
sincetheGPS McCarthy, D. D., IERS Standards,IERS TechnicalNote3,
frameis definedthroughstationcoordinates
in theSV5 frame
Central Bureau of IERS, Observatoire de Paris, 1989.
and the SV5 referenceis a compositeof recentSLR and Munk, M. H., and G.I. MacDonald, The Rotation of the
VLBI solutions(CSR8902 andGLB659 respectively)aligned
Earth, CambridgeUniversityPress,1975.
withiTRF. Absolutepolepositionestimates
in a well defined Murray, M. H., R. W. King, and P. J. Morgan, SV5: A
referenceframe are also useful for studyingthe long term
Terrestrial Reference Frame for Monitoring Crustal
variationsin polar motion. For example,if the pole biases
Deformation With the Global Positioning System,
due to reference frame errors are assumed to remain constant
(Abstract)EOSTrans,AGU, 71, p. 1274, 1990.
whenan identicalfiducial strategyis employed,a drift in the Thomas,J. B., Functional
Description
of SignalProcessing
in
polarmotionbiasfrom experimentto experimentwouldthen
the RogueGPS Receiver,JPL Pub. 88-15, JetPropulsion
imply either true polar motiondrift or unmodeledtectonic
Laboratory,Pasadena,
June,1988.
motionat the observingsites,ratherthan systematic
errorsin
GPSdataprocessing.
From the above discussionand comparisonwith other
techniques,
daily variationsin polarmotionlargerthan-0.5
mas observedwith GPS as comparedwith the Bulletin-B
valuesmust be significant.For this 3 week study,variations
of 2-5 mas were observed over-7 days. Gross and
Lindqwister [!992] have interpretedthese polar motion
variations in terms of atmospheric wind and pressure
fluctuations by using available atmospheric angular
momentum
Z-functions.
U. Lindqwister,
A. Freedman,
andG. Blewitt,MS:238624,JetPropulsion
Laboratory,
CaliforniaInstitute
of
Technology,
Pasadena,
CA 91109.
(Received October 22, 1991;
revisedJanuary9, 1992;
acceptedMarch 5, !992.)