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FundamentalsofGPSforhigh-precisiongeodesy

M.A.FloydMassachusettsInstituteofTechnology,Cambridge,MA,USA

GPSDataProcessingandAnalysiswithGAMIT/GLOBKandtrackAddisAbabaUniversity,Ethiopia24–25&27–29November2017

http://geoweb.mit.edu/~floyd/courses/gg/201711_AAU/MaterialfromR.W.King,T.A.Herring,M.A.Floyd(MIT)andS.C.McClusky (nowatANU)

Outline

• GPSObservables:• GPSdataandthecombinationsofphaseandpseudo-rangeused

• Modelingtheobservations:Aspectsnotwellmodeled• Multipathandantennaphasecentermodels• Atmosphericdelaypropagation

• LimitsofGPSaccuracy• Monumenttypes• Loading(morelater)• Orbitquality

2017/11/24 FundamentalsofGPSforgeodesy 1

InstantaneouspositioningwithGNSSpseudoranges


Receiversolution,teqc +qc orsh_rx2apr• Pointposition(svpos):5–100m• Differential(svdiff):1–10m

Your location is:37o 23.323’ N

122o 02.162’ W

Precisepositioningusingphasemeasurements• High-precisionpositioningusesthephaseobservations• Long-sessionstatic:trackingofchangeinphaseovertimecarriesmostoftheinformation• Theshorterthespanthemoreimportantisambiguityresolution

2017/11/24 FundamentalsofGPSforgeodesy 5Each satellite (and station) has a different signature

20000000

21000000

22000000

23000000

24000000

25000000

16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0

C1_07_(m)Theory_(m)C1_28_(m)Theory_(m)C1_26_(m)Theory_(m)C1_11_(m)Theory_(m)C1_02_(m)Theory_(m)Ra

nge

(m)

Time_Hrs

Observablesindataprocessing

FundamentalobservationsL1phase=f1 × range(λ =19cm)L2phase=f2 × range(λ =24cm)C1orP1pseudorangeusedseparatelytogetreceiverclockoffset(time)

ToestimateparametersusedoublydifferencedLC=2.55L1− 1.98L2“ionosphere-freephasecombination”(L1cycles)PC=2.55P1−1.55P2 “ionosphere-freerangecombination”(meters)

Doubledifferencing(DD)cancelsclockfluctuations;LCcancelsalmostallofionosphere.BothDDandLCamplifynoise(useL1andL2directlyandindependentlyforbaselines<1km)

Auxiliarycombinationsfordataeditingandambiguityresolution:“geometry-freecombination(LG)”or“extrawide-lane”(EX-WL)

LG=L2−f2/f1 L1(usedinGAMIT)EX-WL=L1−f1/f2 L2(usedinTRACK)Removesallfrequency-independenteffects(geometric&atmosphere)butnot

multipathorionosphereMelbourne-Wubbena wide-lane(MW-WL):phase/pseudorange combinationthat

removesgeometryandionosphere;dominatedbypseudorangenoiseMW-WL=N1−N2=(L1−L2)−(Df/Sf)(P1+P2)=(L1−L2)−0.12(P1+P2)


Modeling theobservationsI.Conceptual/Quantitative

• Motionofthesatellites• Earth’sgravityfield(flatteningeffectapprox.10km;higherharmonics100m)• AttractionofMoonandSun(100m)• Solarradiationpressure(20m)

• MotionoftheEarth• IrregularrotationoftheEarth(5m)• Luni-solarsolid-Earthtides(30cm)• Loadingduetotheoceans,atmosphere,andsurfacewaterandice(10mm)

• Propagationofthesignal• Neutralatmosphere(dry6m;wet1m)• Ionosphere(10mbutLCcorrectstoafewmmmostofthetime)• Variationsinthephasecenters ofthegroundandsatelliteantennas(10cm)

*incompletelymodeled


Modeling theobservationsII.Softwarestructure

• Satelliteorbit• IGStabulatedephemeris(Earth-fixedSP3file)[track]• GAMITtabulatedephemeris(t-file):numericalintegrationbyarc ininertialspace,fittoSP3file,mayberepresentedbyitsinitialconditions(ICs)andradiation-pressureparameters;requirestabulatedpositionsofSunandMoon

• MotionoftheEarthininertialspace[model ortrack]• Analyticalmodelsforprecessionandnutation(tabulated);IERSobservedvaluesforpoleposition(wobble),andaxialrotation(UT1)

• Analyticalmodelofsolid-Earthtides;globalgridsofoceanandatmospherictidalloading

• Propagationofthesignal[model ortrack]• Zenithhydrostatic(dry)delay(ZHD)frompressure(met-file,VMF1,orGPT)• Zenithwetdelay(ZWD)[crudelymodeled andestimatedinsolve ortrack]• ZHDandZWDmappedtoline-of-sightwithmappingfunctions(VMF1gridorGMF)

• Variationsinthephasecentersofthegroundandsatelliteantennas(ANTEXfile)


Parameterestimation

• Phaseobservations[solve ortrack]• FormdoubledifferenceLCcombinationofL1andL2tocancelclocks&ionosphere

• Applyaprioriconstraints• Estimatethecoordinates,ZTD,andreal-valuedambiguities• FormM-WWLand/orphaseWLwithionosphericconstraintstoestimateandresolvetheWL(N2−N1)integerambiguities[autcln (orsolve),track]

• Estimateandresolvethenarrow-lane(NL)ambiguities[solve,track]• EstimatethecoordinatesandZTDwithWLandNLambiguitiesfixed

• Estimationcanbebatchleastsquares[solve]orsequential(Kalman filter)[track]

• Quasi-observationsfromphasesolution(h-file)[globk]• Sequential(Kalman filter)• Epoch-by-epochtestofcompatibility(χ2 increment)butbatchoutput


LimitsofGPSaccuracy

• Signalpropagationeffects• Signalscattering(antennaphasecenter/multipath)• Atmosphericdelay(mainlywatervapor)• Ionosphericeffects• Receivernoise

• Unmodeledmotionsofthestation• Monumentinstability• Loadingofthecrustbyatmosphere,oceans,andsurfacewater

• Unmodeledmotionsofthesatellites• Referenceframe


LimitsofGPSAccuracy


• Unmodeled motionsofthestation• Monumentinstability• Loadingofthecrustbyatmosphere,oceans,andsurfacewater

• Unmodeled motionsofthesatellites• Referenceframe


Multipathisinterferencebetweenthedirectandafar-fieldreflectedsignal(geometricopticsapply)


• Avoid Reflective Surfaces• Use a Ground Plane Antenna • Avoid near-ground mounts• Observe for many hours• Remove with average from many days

To mitigate the effects:

Simple geometry for incidence of a direct and reflected signal

Multipath contributions to observed phase for three different antenna heights [From Elosegui et al, 1995]

0.15 m

Antenna Ht

0.6 m

1 m


Antennaphasepatterns

Moredangerousarenear-fieldsignalinteractionsthatchangetheeffectiveantennaphasecenter withtheelevationandazimuthoftheincomingsignal

Figures courtesy of UNAVCO

Left: Examples of the antenna phase patterns determined in an anechoic chamber…BUT the actual pattern in the field is affected by the antenna mount

To avoid height and ZTD errors of centimeters, we must use at least a nominal model for the phase-center variations (PCVs) for each antenna type


The signal from each GPS satellite is delayed by an amount dependent on the pressure and humidity and its elevation above the horizon. We invert the measurements to estimate the average delay at the zenith (green bar).

(Figure courtesy of COSMIC Program)

Atmosphericdelay


Plot courtesy of J. Braun, UCAR

Zenithdelayfromwetanddrycomponentsoftheatmosphere

• Colors are for different satellites

• Total delay is ~2.5 meters• Variability mostly caused by wet

component

• Wet delay is ~0.2 meters• Obtained by subtracting the

hydrostatic (dry) delay

• Hydrostatic delay is ~2.2 meters

• Little variability between satellites or over time

• Well calibrated by surface pressure


One-way (undifferenced) LC phase residuals projected onto the sky in 4-hr snapshots. Spatially repeatable noise is multipath; time-varying noise is water vapor.

Red is satellite track. Yellow and green positive and negative residuals purely for visual effect. Red bar is scale (10 mm).

Multipathandwatervaporeffectsintheobservations


LimitsofGNSSaccuracy





Monuments Anchored to Bedrock are Critical for Tectonic Studies (not so much for atmospheric studies)

Good anchoring:Pin in solid rockDrill-braced (left) in fractured rock Low building with deep foundation

Not-so-good anchoring:Vertical rodsBuildings with shallow foundation Towers or tall building (thermal effects)


FromDongetal.J.Geophys.Res.,107,2075,2002

Atmosphere (purple)2-5 mm

Water/snow (blue/green)2-10 mm

Nontidal ocean (red)

2-3 mm

Annual Component of Vertical Loading


GPS Satellite

Limits to model are non-gravitational accelerations due to solar and Earth radiation, unbalanced thrusts, and outgassing; and non-spherical antenna pattern

Modeling of these effects has improved, but for global analyses remain a problem


Quality of IGS Final Orbits 1994-2017/0620 mm = 1 ppb Source:http://acc.igs.org


Analysiscentersnow<15mmRMSdifference2000/1/1Week1042

Referenceframes

• BasicIssue:Howwellcanyourelateyourpositionestimatesovertimeto:1. Asetofstationswhosemotioniswellmodeled?2. A blockofcrustthatallowsyoutointerpretthe

motions?

• Implementation:HowtousetheavailabledataandthefeaturesofGLOBKtorealizetheframe(s)

• Bothquestionstobeaddressedindetailinlaterlectures


Effect of Orbital and Geocentric Position Error/Uncertainty

•

High-precision GPS is essentially relative !

Baseline error/uncertainty ~ Baseline distance x geocentric SV or position errorSV altitude

SV errors reduced by averaging:Baseline errors are ~ 0.2 • orbital error / 20,000 kme.g. 20 mm orbital error = 1 ppb or 1 mm on 1000 km baseline

Network (“absolute”) position errors less important for small networkse.g. 5 mm position error ~ 1 ppb or 1 mm on 1000 km baseline10 cm position error ~ 20 ppb or 1 mm on 50 km baseline

* But SV and position errors are magnified for short sessions


Summary

• GPSObservables:• GPSdataandthecombinationsofphaseandpseudo-rangeused

• Modelingtheobservations:Aspectsnotwellmodeled• Multipathandantennaphasecentermodels• Atmosphericdelaypropagation

• LimitsofGPSaccuracy• Monumenttypes• Loading(morelater)• Orbitquality:Since2000lessthan40mmcorrespondingto2ppb.HardtoimproveontheIGSorbits.


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