Inertial Navigation

StochasticConstraintsforVision-AidedInertialNavigationbyDavidD.DielSubmittedtotheDepartmentofMechanicalEngineeringinpartialfulfillmentoftherequirementsforthedegreeofMastersofScienceinMechanicalEngineeringattheMASSACHUSETTSINSTITUTEOFTECHNOLOGYJanuary2005c2005DavidD.Diel.Allrightsreserved.TheauthorherebygrantstoMITpermissiontoreproduceanddistributepubliclypaperandelectroniccopiesofthisthesisdocumentinwholeorinpart.Author.............................................................DepartmentofMechanicalEngineeringJanuary27,2005Certifiedby.........................................................PaulDeBitettoSeniorMemberofDraperTechnicalStaffThesisSupervisorCertifiedby.........................................................DerekRowellProfessorofMechanicalEngineeringThesisSupervisorAcceptedby.........................................................ProfessorLallitAnandChairman,CommitteeonGraduateStudiesStochasticConstraintsforVision-AidedInertialNavigationbyDavidD.DielSubmittedtotheDepartmentofMechanicalEngineeringonJanuary27,2005,inpartialfulfillmentoftherequirementsforthedegreeofMastersofScienceinMechanicalEngineeringAbstractThisthesisdescribesanewmethodtoimproveinertialnavigationusingfeature-basedcon-straintsfromoneormorevideocameras.TheproposedmethodlengthenstheperiodoftimeduringwhichahumanorvehiclecannavigateinGPS-deprivedenvironments.Ourapproachintegrateswellwithexistingnavigationsystems,becauseweinvokegeneralsen-sormodelsthatrepresentawiderangeofavailablehardware.Theinertialmodelincludeserrorsinbias,scale,andrandomwalk.Anycameraandtrackingalgorithmmaybeused,aslongasthevisualoutputcanbeexpressedasrayvectorsextendingfromknownlocationsonthesensorbody.AmodifiedlinearKalmanfilterperformsthedatafusion.UnliketraditionalSimultane-ousLocalizationandMapping(SLAM/CML),ourstatevectorcontainsonlyinertialsensorerrorsrelatedtoposition.Thischoiceallowsuncertaintytobeproperlyrepresentedbyacovariancematrix.Wedonotaugmentthestatewithfeaturecoordinates.Instead,imagedatacontributesstochasticepipolarconstraintsoverabroadbaselineintimeandspace,re-sultinginimprovedobservabilityoftheIMUerrorstates.Theconstraintsleadtoarelativeresidualandassociatedrelativecovariance,definedpartlybythestatehistory.Navigationresultsarepresentedusinghigh-qualitysyntheticdataandrealfisheyeimagery.ThesisSupervisor:PaulDeBitettoTitle:SeniorMemberofDraperTechnicalStaffThesisSupervisor:DerekRowellTitle:ProfessorofMechanicalEngineeringAcknowledgmentsLetmenotforgetthosewhohelpedmeonthisjourney.Fromaveryyoungage,mymothergavememanythingstoobserve,andthepowerofobservationisstillmymostvaluedpossession.Myfathernevertiredofansweringmytechnicalquestions,soIneverstoppedaskingthem.Icannotforgetthegreatteacherswholaidmyearlymathematicalfoundations:Mrs.Habel,Mrs.Pierce,Mrs.Geoielli,Mr.Frongello,MikeBouch,andLarryBrown,whotaughtuntilhediedintheserviceofhisstudents.FromtheUniversityofCentralFlorida,IwouldliketothankMadiDogariu,JamalNayfeh,RichardZarda,andNielsdaVitoriaLoboforperceivingthatIcouldhaveacareerinresearchbeforeIhadanyinterestinsuchathing.Inthepursuitofthisthesis,severalpeoplehavehelpedmedirectly.SpecialthankstoJamesDonnaandBrentApplebyfordescribingclassicalinertialnavigationmodelsandconcepts;J.-J.SlotineandRamiMangoubiforinsightsonnonlinearitiesanderrorprojec-tions;BrockBoseforintroducingmetosphericalharmonics;JohnLeonardandAndrewPatrikalakisforuseoftheirgantry;andScottRasmussenforhisinvaluablehardwareassis-tance.ThankstoPaulDeBitetto,SethTeller,andDerekRowellfortheiradvisement,andforlisteningtomewhileIrambledonaboutissuesunrelatedtomywork.Finally,Isendbrotherlylovetomyeditors,FrankGoergenandJeremyParks.SoliDeoGloria!DisclaimerThisthesiswaspreparedatTheCharlesStarkDraperLaboratory,Inc.,andsupportedbyIn-ternalCompanySponsoredResearchProjectC5058,NavigationandMapping.Anyopin-ions,findingsandconclusionsorrecommendationsexpressedinthisthesisarethoseoftheauthorsanddonotnecessarilyreflecttheviewsofDraper.Itispublishedfortheexchangeandstimulationofideas..........................................Contents1Introduction191.1NavigationProblem..............................201.2UnifiedNotation...............................211.3ChapterDescriptions.............................212Approach252.1SensorConfigurations.............................252.1.1GyroscopeReliance.........................262.2AppliedMachineVision...........................272.2.1Trackingvs.Flow..........................272.3DataFusion..................................272.3.1AnAlternativetoSLAM.......................292.3.2SystemBlockDiagram........................313InertialMeasurements333.1AccelerometerError.............................343.1.1DiscreteImplementation.......................363.1.2HardwareCost............................373.2GeologicalEffects...............................373.2.1WGS84GeoidModel........................373.2.2GeoidRotationandApparentGravity................404VisualMeasurements434.1ImageFormation...............................444.1.1Calibration..............................444.2RotationCompen