THE UNIVERSITY OF CALGARY IONOSPHERE WEIGHTED GLOB

UCGEReportsNumber20155DepartmentofGeomaticsEngineeringIonosphereWeightedGlobalPositioningSystemCarrierPhaseAmbiguityResolution(URL:)ByGeorgeChiaLiuDecember2001Calgary,Alberta,CanadaTHEUNIVERSITYOFCALGARYIONOSPHEREWEIGHTEDGLOBALPOSITIONINGSYSTEMCARRIERPHASEAMBIGUITYRESOLUTIONbyGEORGECHIALIUATHESISSUBMITTEDTOTHEFACULTYOFGRADUATESTUDIESINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEDEPARTMENTOFGEOMATICSENGINEERINGCALGARY,ALBERTAOCTOBER,2001cGEORGECHIALIU2001AbstractIntegerAmbiguityconstraintisessentialinpreciseGPSpositioning.Theperfor-manceandreliabilityoftheambiguityresolutionprocessarebeinghamperedbythecurrentculmination(Y2000)oftheeleven-yearsolarcycle.Thetraditionalapproachtomitigatethehighionosphericeffecthasbeeneithertoreducetheinter-stationseparationortoformionosphere-freeobservables.Neitherissatisfactory:thefirstrestrictstheoperatingrange,andthesecondnolongerpossessesthe”integerness”oftheambiguities.Athirdgeneralizedapproachisintroducedherein,wherebythezeroionosphereweightconstraint,orpseudo-observables,withanappropriateweightisaddedtotheKalmanFilteralgorithm.TheweightcanbetightlyfixedyieldingthemodelequivalenceofanindependentL1/L2dual-bandmodel.Attheotherextreme,aninfinitefloatedweightgivestheequivalenceofanionosphere-freemodel,yetperservestheambiguityintegerness.Astochasticallytuned,orweighted,modelprovidesacompromisebetweenthetwoex-tremes.Thereliabilityofambiguityestimatesreliesonmanyfactors,includinganaccuratefunctionalmodel,arealisticstochasticmodel,andasubsequentefficientintegersearchalgorithm.Theseareexaminedcloselyinthisresearch.TwodaysofselectedSwedishGPSNetworkdatasetsfromionosphericallyactive(upto15ppm)andmoderate(upto4ppm)days,formingamaximumbaselinelengthof400km,havebeenanalyzed.Allthreeionosphereweightmodelsyieldeda90%rangeofcorrectwidelaneambiguitieswithinthreeminutes,regardlessofinter-iiistationdistance.Ofthethreeionosphericweightingschemesanalyzed,theweightedmodelappearstobetheoptimalchoice,withsmallerinstantaneousestimateerrorsandpossessingtheconvergencecharacteristic.Uponparameterremovaloftheresolvedwidelaneambiguities,theprecisionofL1ambiguityestimatesimprovedbetweenafewprecentto59percentforbaselinesoveronehundredkilometres.However,theimprovementisnotsufficientforresolvingtheL1ambiguities.ivAcknowledgementsFirstandforemost,IwishtothankmanyindividualsattheGeomaticsDepartmentattheUniversityofCalgary.Withoutthecontinuousencouragementandsupportfrommysupervisor,ProfessorG.Lachapelle,thisthesiswouldnothavebeenpos-sible.Furthergratitudeextentstomycolleague,Luiz-PauloFortes,andDr.SusanSkoneformanyconstructivediscussions.Second,IwouldliketothankDr.StefanSchaerattheAstronomicalInstituteattheUniversityofBerne,forrespondingtomanyofmyemailquestionsrelatedtoionospheremodelling.Hispromptandunequivocalrepliesaremuchappreciated.IwouldalsoliketothankProfessorPeterTeunissenattheDelftUniversityofTechnol-ogyforhisvaluableadviserelatedtotheintegerambiguityresolutionandprovidingtheMatlabversionoftheLAMBDAcode.Lastly,furtheracknowledgementsextendtotheSwedishNationalGeodeticSur-veyforprovidingtheGPSdatasets,theOnsalaAstronomicalInstituteforthewatervapourradiometerandmeteorologicaldata,theScrippsInstituteofOceanographyfortheorbitdata,andtheAstronomicalInstituteoftheUniversityofBernefortheGlobalIonosphereModels.vTableofContentsApprovalPageiiAbstractiiiAcknowledgementsvTableofContentsviNotationsxiii1Introduction11.1Background................................11.2Motivation.................................41.3Objectives.................................71.4Outline...................................92GPSSignals,Observables,andErrors122.1SignalStructure..............................122.2SignalProcessing.............................162.2.1Antenna..............................172.2.2RFSection............................192.3GPSObservationModels.........................222.3.1FundamentalGPSObservationEquations...........222.3.2FormingDifferences........................242.3.3LinearlyCombinedObservations................263AtmosphericEffectsAndModelling323.1Ionosphere.................................333.1.1IonizationProcesses.......................333.1.2IonosphericEffectsonGPSSignals...............373.1.3TECModellingAndParameterization.............403.1.4ApplicationofIonosphereModels................493.2Troposphere................................503.2.1TroposphereModelling......................533.2.2InverseGPSMethod.......................55vi4Implementation574.1OverviewoftheKalmanFilter......................574.2Non-LinearMeasurementModel.....................604.3RandomProcesses............................614.4FunctionalModel.............................634.5StochasticModel.............................654.5.1SystemNoise...........................654.5.2MeasurementNoise........................664.5.3Measurement(Co)VarianceMatrix,R.............694.6AmbiguityResolution:TheLAMBDAMethod.............724.6.1DecorrelationTransformation..................724.6.2Integer