ii THE UNIVERSITY OF CALGARY Error Analysis and St

UCGEReportsNumber20194DepartmentofGeomaticsEngineeringErrorAnalysisandStochasticModelingofMEMSbasedInertialSensorsforLandVehicleNavigationApplications(URL:)byMinhaParkApril,2004iiTHEUNIVERSITYOFCALGARYErrorAnalysisandStochasticModelingofMEMSbasedInertialSensorsforLandVehicleNavigationApplicationsbyMinhaParkATHESISSUBMITTEDTOTHEFACULTYOFGRADUATESTUDIESINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEDEPARTMENTOFGEOMATICSENGINEERINGCALGARY,ALBERTAApril,2004MinhaPark2004iiiAbstractAlthoughGPSmeasurementsaretheessentialinformationforcurrentlydevelopedlandvehiclenavigationsystems(LVNS),thesituationwhenGPSsignalsareunavailableorunreliableduetosignalblockagesmustbecompensatedtoprovidecontinuousnavigationsolutions.Inordertoovercometheunavailabilityorunreliabilityprobleminsatellitebasednavigationsystemsandalsotobecosteffective,MicroElectroMechanicalSystems(MEMS)basedinertialsensortechnologyhaspushedthedevelopmentoflow-costintegratednavigationsystemsforlandvehiclenavigationandguidanceapplications.Inspiteoflowinherentcost,smallsize,lowpowerconsumption,andsolidreliabilityofMEMSbasedinertialsensors,theerrorsintheobservationsfromtheMEMS-basedsensorsmustbeappropriatelytreatedinordertoturntheobservationsintousefuldataforvehiclepositiondetermination.Theerroranalysiswouldbeconductedinthetimedomainspecifyingthestochasticvariationaswellaserrorsourcesofsystematicnature.ThisthesiswilladdresstheaboveissuesandpresentalgorithmstoidentifyandmodeltheerrorsourcesinMEMS-basedinertialsensors.AKalmanfilterwillbedescribedandappliedtoanalyzetheperformanceofaminimumconfiguredGPS/IMUsystemforvehiclenavigationapplications.TheperformanceofthetestingsystemhasbeenassessedviaacomparisontoPrecisePointPosition(PPP)referencedata.Thetestingresultsindicatetheeffectivenessofthediscussederroranalysisandmodelingmethod.iiiAcknowledgementsIwishtoexpressmysinceregratitudetomysupervisor,Dr.YangGaoforhiscontinuedsupportsandunderstanding.Heencouragedmetochallengenewideasandguidedmethroughallaspectsofthisthesis.Heprovidedthevaluableadvices,opportunitiesandassistancethatgreatlyenhancedalltheresearchesduringmygraduatestudies.Iwouldliketothanksomeofmycolleagues,especiallyJames(Jau-Hsiung)Wang,whoparticipatedinfieldtestingwithhisdataacquisitionprogram.KongzheChenisalsothankedforprovidingPPPsolutionfortheperformanceanalysisoffieldtesting.Especially,IwouldliketoacknowledgeEun-HwanShinforhiswillingnesstodiscussandtogivepreciousadvices.Andlast,Iwouldliketoextendmysincerethankstomylovelywife,CatherineHee-JinKimforhergenerousunderstandingandcontinuousdedication.ivContentsApprovalPage…………………………………………………………………………...iiAbstract………………………………………………………………………………….iiiAcknowledgements……………………………………………………………………...ivContents………………………………………………………………………………….vListofTables…………………………………………………………………………..viiiListofFigures…………………………………………………………………………...ixNotation…………………………………………………………………………………xiiAcronyms………………………………………………………………………………xiii1.Introduction……………………………………………………………………………11.1BackgroundandObjective……………………………………………………11.2ThesisOutline………………………………………………………………...42.Multi-SensorNavigationSystems……………………………………………………62.1ConceptsofMulti-SensorNavigationSystems………………………………72.1SatellitebasedNavigationMethod…………………………………………..102.2.1DescriptionsofGPS……………………………………………….102.2.2GPSObservablesandErrorBudgets………………………………132.2.3LimitationsofGPS………………………………………………...16v2.3DeadReckoning(DR)NavigationMethod………………………………….162.4MEMSTechnology………………………………………………………….212.5MEMSbasedInertialSensors……………………………………………….232.5.1MEMSbasedAccelerometers……………………………………..242.5.2MEMSbasedGyroscopes…………………………………………283.ErrorAnalysisofMEMSbasedInertialSensors………………………………….313.1ErrorModelsofMEMSbasedInertialSensors……………………………..323.1.1ErrorModelofMEMSbasedAccelerometer……………………..323.1.2ErrorModelofMEMSbasedGyroscope…………………………343.2ReviewofStochasticModeling……………………………………………..353.2.1StationaryStochasticProcess……………………………………...353.2.2LinearSystemModeling…………………………………………..393.2.3Gauss-MarkovProcesses………………………………………….413.3SpecialdiscreteParametricModelsofStochasticProcesses………………..443.4EstimationofParametersinAutoregressive(AR)Models………………….513.4.1AutocorrelationSequenceofARModelandLevinson-DurbinAlgorithm………………………………………………………….513.4.2Yule-WalkerMethodforARModelParameterEstimation………553.4.3BurgMethodforARModelParameterEstimation……………….563.4.4UnconstrainedLeast-SquaresMethodforARModelParameterEstimation…………………………………………………………583.5DeterminationofOrderoftheStochasticModels…………………………………..59vi4.EstimationofDeterministicErrorSourcesandStochasticModeling……………614.1EstimationPrinciples………………………………………………………...614.2EstimationofMEMSbasedAccelerometerDeterministicErrorSources…..634.3EstimationofMEMSbasedGyroscopeDeterministicErrorSources………684.4StochasticModelingofMEMSbasedAccelerometerandGyroscope……...725.PerformanceAnalysis……………………………………………………………….845.1StaticTestingandResults…………………………………………………...855.2KinematicTestingandResults……………………………………………....965.2.1KinematicTestingSyst