GEOPHYSICALRF.•EARCHLETTERS,VOL. i9, NO. 2, PAGES131-134,JANUARY24, 1992
GLOBAL GEODESY USING GPS WITHOUT FIDUCIAL SITES
MichaelHerin, Willy Bertiger,
GeoffBlewitt,AdamFreedman,
KenHurst,SteveLichten,
U!fLindqwister,
Yvonne
Vigue,
Frank
Webb,
TomYunck,
andJames
Zumberge
JetPropulsion
Laboratory,
California
Institute
ofTechnology
Abstract. Baselinelengthsand geocentricradii havebeen
90•
determinedfrom GPS data without the use of fiducial sites.
•
...........
I' "i NALL
I
i"
I
Data from the first GPS experiment for the IERS and
Geodynamics
(GIG '91)havebeenanalyzed
witha no-fiducial
strategy.A baselinelengthdailyrepeatability
of 2 mm + 4
pansperbillionwasobtained
for baselines
in thenorthern
hemisphere.
Comparison
of baselinelengthsfromGPSand
theglobalVLBI solution
GLB659(Caprette
et al. 1990)show
rmsagreement
of 2.1 pansperbillion. The geocentric
radius
meandailyrepeatability
for all siteswas15 cm. Comparison
of geocentric
radii from GPS andSV5 (Murrayet al. 1990)
60
showrms agreementof 3.8 cm. Given n globallydistributed
stations,
the n(n - 1)/2 baselinelengthsandn geocentric
radii
-30
JPLM
ALGO
o
uniquely
definea rigidclosedpolyhedron
witha we!l-defined
centerof mass. Geodeticinformationcan be obtainedby
examining
the structureof thepolyhedronandits changewith
k
-60
I • -IART•
vYAR1
•
SANT
time.
Introduction
-180
The first GPS experimentfor the IERS andGeodynamics
(GIG '91) took place betweenJanuary22 andFebruary13,
1991. The global extent of the experimentpromptedan
analysisstrategy designedto investigatethe arnountof
geodeticinformationthat GPS can providewithoutusing
fiducialsites.We decidedto focuson the21 Roguereceivers
whichparticipated.A mapwith all 21 sitesis givenin Figure
1. Receiver names and locations are listed in Table 1.
A fiducial site is one with coordinates which are held fixed at
previouslydeterminedvaluesduring analysis. A fiducial
networkconsistingof severalfiducial sitescan be usedto
providea well-definedterrestrialreferenceframe. Fiducial
networkstrategyhas been discussedby Davidsonet al.
(1985),Malla andWu (1989), KornreichWolf et al. (1990),
Larsonet. al (1991), andmanyothers.A terrestrial
reference
-120
-60
0
60
120
180
longitude(deg)
Fig. 1. Roguereceiverlocations.
geoeentricradii as illustratedin Figure2. Intrinsicproperties
of the polyhedron such as the difference between two
geocentricradii, the openingangiebetweentwo geocentric
radii, andtheperpendicular
distancefrom thecenterof massto
a baseline can be examined without the use of fiducial sites.
The absolute orientation of the polyhedron is poorly
determinedwithoutfiducialsites. The directionsof the x-, y-,
andz-axesareconstrained
by placing10-kma priori standard
deviations on each station and initial satellite position
component.The directionof the z-axisis furtherconstrained
by the signatureof Earth'sdaily rotation. Mathernatically
framerequiresan origin,scale,andorientation.Fiducial speaking,theestimatedz-component
for eachsitewill havea
networks
arenotnecessary
to provideanoriginandscalefor
smallererrorthanthe estimatedx- andy-components
andall of
globalGPS measurements.The satelliteforcemodel implies
the errors will be correlatedso that rotationally invariant
anoriginat theEarth'scenterof mass.A scaleis impliedby
quantitiessuchas geocentricradiusand baselinelengthare
thesatelliteforcernodel,radiopropagation
model,andGPS well determined.The intrinsicstructureof the polyhedronis
data. Furthermore,the orientationprovidedby fiducial completelyindependent
of itsorientation.
coordinates
doesnot affectrotationallyinvariantquantities.
The followinganalysisdemonstrates
a no-fiducialapproach
Baseline
lengthandgeocentric
radiusarerotationally
invariant. to globalgeodesy.Baselinelengthsandgeocentricradii are
Givenn globallydistributed
stations,
then(n- 1)/2 baseline determinedbothpreciselyand accuratelywithoutthe useof
lengths
andn geocentric
radiicanbeusedtoconstruct
a rigid fiducial sites---the polyhedron is well defined. The
closed
polyhedron
with a centerof masswell-defined
by the polyhedroncan be orientedarbitrarily or with information
from other techniquessuchas SLR and VLBI. Consistent
informationfrom othertechniquessuchasSLR and VLBI can
Copyright
1992by theAmerican
Geophysical
Union.
be used to improve the no-fiducia! solution. Our analysis
focuseson geodeticparameters.Herring et al. (1991) have
Papernumber91GL02933
0094-8534/92/91GL-02933503.00
obtainedpolarmotionestimates
usinga no-fiducialapproach.
131
132
Herin et al.: Geodesy
WithoutFiducialSites
Table 1 Station Information And Geocentric Radii
NameIx>cation
20
Days Radius
(m) •R (m)
•
•
•
•
x
x xn
16
AI_DO Algonquin,Canada
CANB
FAIR
GOI•
HART
20
Canberra,Australia
19
Fairbanks, Alaska
20
Goldstone,California
20
Hartebeesthoek,S. Africa 16
HONE H0nefoss,Norway
16
JPLM Pasadena,California
KOKB Kokee, Hawaii
20
20
KOSG Kootwijk, Netherlands
MADR Madrid,Spain
MATE Matera,Italy
20
20
20
NALL NyJdesund,
Norway
20
PGC1
20
Victoria, Canada
PINY Pinyon,California
SANT Santiago,Chile
20
18
SCRI
La Jolla, California
16
TROM
USUD
WETB
YAR1
Troms0, Norway
Usuda,Japan
Wettzel,Germany
Yarragadee,
Australia
10
14
20
20
YFJ_I. Yellowknife, Canada
N (N - 1) / 2 Lengths
20
6367333.62
6371684.46
6360923.50
6371978.83
6375643.95
6362263.30
6371841.80
6376292.47
6364932.44
6370016.64
6369640.56
6357629.07
6366132.38
6372878.12
6372503.53
6371883.45
6359486.92
6372250.91
6366607.82
6373369.65
6361528.66
0.!7
0.!2
0.18
0.13
0.!9
0.19
0.13
0.08
0. !7
0.15
0.15
0.20
0.15
0.13
0.12
0.12
0.!5
0.12
0.16
0.14
0.19
N Radii
1
2
Constructed Polyhedron
o
Receiver
Geocenter
Baseline
Radius
x
x
.--12
O OOoCl
C• 0
...,..
O
OO
.e 8
-
O
O
0
---
0
O
O
0
_
0
2
4
6
8
10
12
14
baseline length (1000 km)
Fig. 3. Daily repeatabilityversusbaselinelength. A linearfit
to NN baselinesyields2 mm + 4 ppb. A meanvalueof 9 ppb
and 16 ppb was derived for the NS and SS baselines
respectively.
stationpositionswere heldfixed. All stationpositions,initial
satellitepositions,initial satellitevelocities,solarradiation
coefficientsfor eachsatellite,wet tropospheric
zenithdelays
for eachstation,carderphaseambiguities,
satelliteclocks,and
stationclocks except the one at GOLD were estimated. All
other parameters were held fixed. GIPSY processes
undifferenceddual frequencycarrierphaseand pseudorange
data. The assumednoisewas 1 cm for carder phasedataand
100 cm for pseudorange
data. All stationand initial satellite
positioncomponents
had a priori standarddeviationsof 10
km. Initial satellitevelocitycomponents
hada prioristandard
deviationsof 10-4 km/sec. White noise clock biaseswere
estimatedevery 6 minutes. Undifferenced carrier phase
ambiguitieswere estimatedas real valuedmodelparameters.
Theelevationanglecutoffwas 15o.
The Earth'sdynamicinertial orientationwas describedby
modelsof precession
andnutationalongwithmeasurements
of
UT1 andX andY polarmotionobtainedfrom IERS Bulletins
B37 and B38. The Williams (1970) solid Earth tide model
3
was used along with a standardpole tide model and the
Pagiatakis(1982) oceanloadingmodel. The Lanyi (1984)
tropospheric
elevationanglemappingfunctionwasused. Wet
Fig. 2. Given n globallydistributedstations,the n(n -1)/2
baseline
lengths
andn geocentric
radiiuniquelydefinea closed
polyhedron.
tropospheric
zenith delayswere modeledwith an a priori
standard deviation of 50 cm and a random walk constraint of 1
cm variationper hour. A nominaldry troposphericzenith
delay of 220 cm was usedat all sites. Ionosphericdelaywas
removedby taking a linearcombinationof the dual frequency
datameasurements.
Earth'sgravityfield wasdescribed
by the
Analysis
GEM-T2 multipoleexpansion
(Marshet al. 1990). Onlythe
first !2 momentsof GEM-T2 were used. The monopole
Analysis was carriedout with the GIPSY (GPS Inferred
momentor pointmasstermwascalculatedwith GM(IERS).
GEM-T2 is geocentric-Positioning
SYstem)software
developed
at theJetPropulsion Thedipolemomentwaszerobecause
Laboratory (Lichten and Border, 1987; Sovers and Border,
its originis at the Earth'scenterof mass. All higherorder
1990). That fact to no fiducia! siteswere usedmeansthat no
momentsutilized GM(GEM~T2). The IERS and GEM-T2
Herinetal.: Geodesy
Without
Fiducial
Sites
133
valuesfor GM are 398600.440km3/sec
2 and 398600.436
km3/sec
2respectively.
Solarradiation
pressure
onthesatellite
wascharacterized
by threesolarradiationcoefficients.The xandz-coefficients
areproportionality
constants
whichrelatethe
x- and z-solar flux componentsto the x- and z-satellite
acceleration
components.The y-coefficientrepresents
a
constantacceleration. Here x, y and z refer to a satellite-
centered
framewith the z-axispointingradiallytowardthe
Earth,thex-axisperpendicular
to the z-axisin the Sun-Earth-
satelliteplane pointingtoward the Sun, and the y-axis
perpendicular
tothex- andz-axesin a righthanded
sense.
Thefollowingsimplifieddescription
of modelprediction
illustrates the use of models described above.
Satellite
positions
and velocitiesare propagatedforwardin time
according
to theforcesof gravityandsolarradiation
pressure.
Receiver positions are adjusted for tidal effects and
-6
transformed
into earth-centered
inertialcoordinates
by the
precession,
nutation,andUTPM values. Satelliteto receiver
0
2
4
6
8
10
12
propagation
timeis calculated
fromtherelativeearth-centered
inertialpositions,
clockvalues,andatmospheric
delayin the
baselinelength(1000 km)
context
of generalrelativity.Tropospheric
delayis calculated
fromthe wet and dry troposphericzenith delaysand the
Fig.4. GPSbaseline
length
solutions
compared
withVLBi
tropospheric
elevationanglemapping
function.Pseudorange
solutionGLB659. Stations
JPLM,KOKB,PINY, WETB,
andcarrierphase
predictions
arederived
fromthepropagation and TROM were used.
time. Estimatedparametersare adjustedto make model
predictions
as consistentas possiblewith the datain a least
squares sense.
divided by the square root of the number of daily
measurements.
The weightedrmsof (GPS- VLBi)/lengthis
Results
2.1 pansper billion,assuming
a conservative
combinedVLBI
andsitetie errorof 5 mm. Thevalueof 2.5 pansper billionis
Dailyoutput
solutions
included
a vector
of all estimatednot changedby assuminga combinedVLBI andsitetie error
parameters
anda full covariance
matrixof errors.All days greaterthan 5 mm. Figure 5 comparesthe GPS and SV5
were processedexcept 1/31/91, 2/2/91, and 2/13/91. The
geocentricradii for six siteswith good ¾LB! or SLR ties:
dailypositionestimatevectorsand covariancematriceswere
JPLM, KOKB, KOSG, PINY, TROM, and WETB. Error
combinedto yield one final positionestimatevector and barsagainrepresent
repeatability
dividedby thesquarerootof
covariance
matrix. The cartesian
components
of eachsite the numberof daily measurements.The weightedrms of
position
hadlargeerrors,roughly5 m for x andy and4 cm
forz, whichwerehighlycorrelated.Baseline
lengthsand
geocentricradii were calculatedfrom the final estimatevector
(GPS - SVS) radii is 3.8 cm.
Conclusions
andcovariance
matrix. Figure3 showsrepeatability
asa
function
of baseline
lengthforall 210baselines.
Thebaselines Data from GIG '91 have beenanalyzedwith a no-fiducial
aredividedinto three types;thosewith both sitesin the strategy. A baselinelengthdaily repeatabilityof 2 mm + 4
northernhemisphere(NN), thosewith one site in each parts per billion was obtained for the NN baselines.
hemisphere
(NS), andthosewith bothsitesin the southern Comparisonof baselinelengthsfrom GPS and the global
hemisphere
(SS). The17sitesin thenorthern
hemisphereVLBI solutionGLB659(Capretteet al. 1990)showagreement
define 136 NN baselines. The 4 sites in the southern
of 2.1 partsper billion, assuminga combinedVLBI and site
tie error or 5 mm. The NS and SS baselineshad daily
hemisphere
define6 SSbaselines,
leaving
68NSbaselines.
A
linewasfit totheNN baselines,
yielding
a dailyrepeatability repeatabilitiesof 9 pansper billion and 16 partsper billion
of 2 mm+ 4 partsper billion. A line wasfit to theNN respectively,becausetherewere only four sitesin the southern
baselines
because
thereareenough
shortNN baselines
to hemisphereand commonsatellite visibility was therefore
determine
theoffset
of2 mm.Themean
valueofrepeatability limited at thosesites. The geocentricradius mean daily
overlengthwas9 pansperbillionfor NS baselines
and16 repeatability for all sites was 15 cm. Comparisonof
geocentric
radiifromGPSandSV5 (Murrayet al. 1990)show
rms agreement
of 3.8 cm. Baselinelengthsand geocentric
areonlyfoursitesin thesouthern
hemisphere
andcommon radiiderivedwithouttheuseof fiducialsiteswerebothprecise
satellite
visibility
is therefore
limitedatthosesites.Geocentric andaccurate.Given n globallydistributedstations,the n(nradiiuniquelydefinea
radiiandtheirdailyrepeatabilities
arelistedin Table1. The 1)/2 baselinelengthsandn geocentric
with a centerof masswell-definedby
geocentric
radiusmeandailyrepeatability
is 15cmforall sites. rigidclosedpolyhedron
radii. Geodeticinformationcanbe obtained
by
Figure4 compares
theGPSandVLBI (GLB659)baselines thegeocentric
of thepolyhedron
andits changewith
defined
by 5 siteswithgoodVLBI ties: JPLM,KOKB, examiningthestructure
PINY,TROM,andWETB.Errorbarsrepresent
repeatabilitytime. Intrinsicpropertiesof the polyhedronsuchas the
pansper billion for SS baselines. The NS and SS baselines
are not as well determined as the NN baselines because there
134
Herin et al.: Geodesy
WithoutFiducial
Sites
15
Davidson,
J. M., C. L. Thornton.,
C. J'.Vegos,L. E. Young,
and T. P. Yunck, The March 1985 demonstrationof the
v
fiducialnetworkfor GPSgeodesy:A preliminaryreport,
o10
Proceedings of the First International Symposiumon
PrecisePositioningwith GPS, 603-612, 1985.
,
5
•
0
Herring,ThomasA., DananDong,andRobertW. King,
Sub-milliarcsecond
determination
of polepositionusing
global positioningsystemdata, Geophys.Res. Lett, 18,
No. IO, 1893, !991.
.....
KornreichWolf, S., T. H. Dixon, andJ. T. Freymeuller,The
effectsof trackingnetworkconfigurationon GPS baseline
estimatesfor the CASA UNO experiment,Geophys.Res.
rO -5
Lett, 17, No. 5, 647-650, 1990.
Lichten,S. M., andJ. S. Border,Strategies
for highprecision
Global Positioning System orbit determination,J.
Geophys.Res., 92, 12751-127662, 1987.
Lanyi, G. E., Tropospheric Delay Effects in Radio
Interferometry,Telecommunications
and Data Acquisition
Progress Report 42-78, Jet PropulsionLaboratory,
o -10
-15
JPLM
KOKB
KOSG
PINY
TROM
WETB
Pasadena,CA, 152-159, 1984.
site name
Fig.5. GPSgeocentric
radiussolutions
compared
withSV5.
differencebetweentwo geocentricradii, the openingangle
betweentwo geocentricradii, and the perpendicular
distance
Larson,K. M., F. H. Webb, andD.C. Agnew, Application
of the Global PositioningSystemto CrustalDeformation
Measurement, part II: the Influence of Errors in Orbit
Determination Networks, J. Geophys. Res., In Press,
1991.
Malla, R. and S. Wu, GPS Inferred Geocentric Reference
from a baseline to the center of mass are all well determined.
Frame For Satellite PositioningAnd Navigation, Bull.
Satelliteorbitsarealsowelldetermined.Baseline
repeatability
Geod. 63, 263~279, 1989.
of 2 mm + 4 partsper billion requiresvery preciseorbits. Marsh, J. G., F. J. Lerch,B. H. Putney,T. L. Felsentreiger,
Initial consistency
checkshavebeenmadeby mappingGPS
B. V. Sanchez, S. M. Klosko, G. B. Patel, J. W. Robbins,
orbitsfromoneday to anotherandcomputing
nnsdifferences.
R. G. Williamson, T. L. Engelis, W. F. Eddy, N. L.
Thistestof orbitconsistency
showsa meansinglecomponent Chandler,D. S. Chinn, S. Kapoor, K. E. Rachlin, andL.
rms of 40 cm for February9 and 10.
E. Braatz,The GEM-T2 GravitationalModel, J. Geophys.
Res., 95, 22043-22071, 1990.
The polyhedronhas its own scale and origin. Fiducial
networksare not necessaryto providean originand scalefor
Murray, M. H., R. W. King, and P. J. Morgan, SV5: A
global GPS measurements.Any center of massand scale
terrestrial
reference
framefor monitoring
crustaldeformation
informationinherentin a given fiducial networkmay not be
consistentwith the centerof massand scaleimplied by the
satelliteforcemodel,radiopropagation
model,andGPSdata.
if the coordinates of two fiducials had been fixed in the above
analysis,thenthetwo fiducialgeocentric
radiiandonefiducial
baselinewould havelead to systematicerrorsunlesstheywere
consistentwithin 15 cm and 2 mm + 4 parts per billion
respectively. The no-fiducial approachalso avoids the
problemof usingseveraldifferentfiducialnetworksduringan
experiment
because
of missingdataat particularfiducialsites.
RegionalGPScampaigns
canutilize the no-fiducialapproach
byincludingdatafromglobaltrackingsitesin theiranalysis.
with the Global PositioningSystem,(Abstract)EOS Trans,
AGU, v. 71, 1274, 1990.
Pagiatakis,S. D., OceanTide Loading,Body Tide andPolar
Motion Effects on Very Long Baseline Interferometry,
Technical Report No. 92, Department of Surveying
Engineering, University of New Brunswick, Fredericton,
N.B., Canada, 1982.
Sovers, O. J., and J. S. Border, Observation Model and
Parameter Partials for the JPL Geodetic GPS Modeling
Software "GPSOMC", JPL Pub. 87-21, Rev. 2, Jet
PropulsionLaboratory,Pasadena,
CA, 1990.
Williams, J. G., Solid Earth Tides, IOM 391-109 (JPL
internal document),Jet PropulsionLaboratory,Pasadena,
Acknowledgements. This researchwas carried out by the
let Propulsion
Laboratory,CaliforniaInstituteof Technology,
under contractwith the National Aeronauticsand Space
Administration.
We thank the numerous institutions
and
individualswho helped make the GIG '91 experiment
successful.
References
Caprette,D. S., C. Ma, andJ. W. Ryan,CrustalDynamics
Project Data Analysis -- 1990, NASA Technical
Memorandum 100765, 4-1, 1990.
CA, 1970.
Willy Bertiger,Geoff Blewitt, AdamFreedman,Michael
Herin, Ken Hurst, SteveLichten, Ulf Lindqwister,Yvonne
Vigue, Frank Webb, Tom Yunck, andJamesZumberge,Jet
PropulsionLaboratory,MS 238-625,4800 Oak GroveDrive,
Pasadena,CA 91109
(ReceivedAugust16, 1991;
RevisedNovember7, 1991;
AcceptedNovember27, 1991)