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ANANALYSISOFANEWNONLINEARESTIMATIONTECHNIQUE: THESTATE-DEPENDENTRICATTIEQUATIONMETHOD By CRAIGM.EWING ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1999 ACKNOWLEDGMENTS Iwouldliketothankmyadvisor.Dr.NormanFitz-Coy,forhiseffortsin continuallypushingmetodevelopabetterdissertation.IagreeitisnowsomethingIcan lookuponwithpride.IalsothankDr.JamesCloutier,themanbehindtheidea.Without hishelpandguidancethisworkcouldneverhavebeenwritten.Iwouldespeciallyliketo thankmywife,Darsi,forhernever-endingsupportthroughtheseyearsofwork.She neverletmegiveup. 3 TABLEOFCONTENTS page ACKNOWLEDGMENTS ii LISTOFTABLES v LISTOFFIGURES vi ABSTRACT x CHAPTERS 1 INTRODUCTION 1 2 LITERATURESURVEY 4 3 SCOPEOFWORK 8 4 EXOATMOSPHERIC-GUIDANCE-PROBLEMENGAGEMENTSCENARIO 10 5 EXOATMOSPHERIC-GUIDANCE-PROBLEMFILTERDEVELOPMENT 1 5.1EKFDerivation 14 5.2BootstrapEstimatorDerivation 19 5.3SDREFDerivation 22 6 EXOATMOSPHERIC-GUIDANCE-PROBLEMSIMULATIONRESULTS 49 6.1BaselinePerformance 49 6.2PDFDistributionComparison 54 6.3SensitivityAnalysis 64 6.4SDREFClosedLoopPerformance 79 6.5SummaryofExoatmosphericGuidanceProblem 87 7 PENDULUMPROBLEMFILTERDEVELOPMENT 88 7.1SDREFDerivation 90 7.2EKFDevelopment 91 8 PENDULUMPROBLEMSIMULATIONRESULTS 92 m 1 9 MSDREFDEVELOPMENT 103 9.1MSDREFDerivation 103 9.2StabilityProof 104 10 MSDREFPROBLEMSIMULATIONRESULTS 112 1 CRITICALANALYSISOFRESULTS 119 REFERENCES 122 BIOGRAPHICALSKETCH 125 LISTOFTABLES Table page 1. Filtersimulationparametersbaselineconditions 50 2. EKFandSDREFparametersone-percentinitializationerror 65 3. EKFandSDREFparametersfive-percentinitializationerror 69 4. EKFandSDREFmeasurementnoiseparameterslevel-1 72 5. EKFandSDREFmeasurementnoiseparameterslevel-2 72 6. Maneuveringtargetparameters 76 7. Head-onsimulationparameters 81 8. 90-degreebeamshotsimulationparameters 81 9. Tail-chasesimulationparameters 82 10. Missdistanceperformanceforvaryingscenarios 83 11. Missdistanceperformanceforstressingtargetmaneuvers 84 12. Missdistanceperformanceforvaryingmeasurementnoise 85 13.Missdistanceperformanceforvaryinginitializationerror 86 . 1 LISTOFFIGURES Figure page 1. Genericinterceptvehicle 1 2. Guidancesystemblockdiagram 12 3. EKFpositionerrorwith+3<7standarddeviations 52 4. SDREFpositionerrorwith±3crstandarddeviations 52 5. Bootstrappositionerrorwith±3<7standarddeviations 52 6. CofmopraYripsoosintioofnEKFandSDREFcovariance±3astandarddeviations 53 7. ExpandedviewofFigure6 53 8. PofsotrerXiopropsriotbiaobnilitydensityfunctionsattime=1,5,and9seconds 55 9. PofsotrerYiopropsriotbiaobnilitydensityfunctionattime=1,5,and9seconds 56 10. MosnetceonCdasrlfoorpXostpeorsiiotriopnrobabilitydensityfunctionsattime=1,5,and9 58 11 MosnetceonCdasrlfoorpYostpeorsiiotriopnrobabilitydensityfunctionsattime=1,5,and9 59 12. EKFestimatedandtrueacceleration 61 13. SDREFestimatedandtrueacceleration 61 14. Bootstrapestimatedandtrueacceleration 61 15. MosnetceonCdasrlfoorptohsrtuesrtiocrutp-roofbfaXbilpiotsyitdieonnsityfunctionsattime=2,2.5,and3 62 16. MosnetceonCdasrfloorptohsrtuesrticourtp-roofbfaYbilpiotsyitdieonnsityfunctionsattime=2,2.5,and3 63 17. EKFpositionerrorswith±3<7standarddeviationsfor1-percent initializationerrors 67 18. SDREFpositionerrorswith±3ffstandarddeviationsfor1-percent initializationerrors 67 19. EKFpositionerrorswith±3<7standarddeviationsfor5-percent initializationerrors 68 20. SDREFpositionerrorswith±3c7standarddeviationsfor5-percent initializationerrors 68 21. SDREFpositionerrorswith±3crstandarddeviationsafternewinitialization method,1-percenterror 70 22. SDREFvelocityerrorswith±3astandarddeviationsafternewinitialization method,1-percenterror 70 23. SDREFaccelerationerrorswith±3<Tstandarddeviationsafternewinitialization method,1-percenterror 70 24. SDREFpositionerrorswith±3<7standarddeviationsafternewinitialization method,5-percenterror 71 25. SDREFvelocityerrorswith±3tTstandarddeviationsafternewinitialization method,5-percenterror 71 26. SDREFaccelerationerrorswith±3crstandarddeviationsafternewinitialization method,5-percenterror 71 27. EK1F00pmosiictrioornadeirraonrserwriotrhin±Y3eransdtaZndarddeviations1-percenterrorinX, 74 28. SD1R00EFmipcorsoirtaidoinanererrorrsorwiinthY±a3n<dTZstandarddeviations1-percenterrorinX, 74 29. EK5F00pmosiictrioornadeirraonrserwriotrhin±Y3cransdtaZndarddeviations10-percenterrorinX, 75 30. SD50R0EFmipcorsoirtaidoinanererrorrsorwiinthY±a3ncdrZstandarddeviations10-percenterrorinX, 75 .. 31 EKFpositionerrorswith±3crstandarddeviationsfor10deg/secrotating targetmaneuver 77 32. SDREFpositionerrorswith+3<7standarddeviationsfor10deg/secrotating targetmaneuver 77 33. EKFpositionerrorswith±3<rstandarddeviationsfordoglegtargetmaneuver 78 34. SDREFpositionerrorswith±3(7standarddeviationsfordoglegtargetmaneuver.78 35. Aspectangledescription 80 36. Pendulumset-up 88 37. EKFandSDREFestimatesvs.truethetawithnoinitializationerror 93 38. EKFandSDREFestimatesvs.truetheta-dotwithnoinitializationerror 93 39. EKFandSDREFestimationerrorforthetawithnoinitializationerror 94 40. EKFandSDREFestimationerrorfortheta-dotwithnoinitializationerror 94 41 MotnitmeeC=ar0l.o5psreocbabilitydensityfunctionfortheta,withnoinitializationerror, 95 42. MonteCarloprobabilitydensityfunctionfortheta-dot,withnoinitialization error,time=0.5sec 95 43. MonteCarloprobabilitydensityfunctionfortheta,withnoinitializationerror, time=2.0sec 96 44. MonteCarloprobabilitydensityfunctionfortheta-dot,withnoinitialization error,time=2.0sec 96 45. MonteCarloprobabilitydensityfunctionfortheta,withnoinitializationerror, time=3.0sec 97 46. MonteCarloprobabilitydensityfunctionfortheta-dot,withnoinitialization error,time=3.0sec 97 47. EKFandSDREFthetaestimationerrorwithinitializationerror 99 48. EKFandSDREFtheta-dotestimationerrorwithinitializationerror 99 49. MonteCarloprobabilitydensityfunctionfortheta,withinitializationerror, time=0.5sec 100 . 50. MonteCarloprobabilitydensityfunctionfortheta-dot,withinitialization error,time=0.5sec 100 51 MotnitmeeC=ar2l.o0psreocbabilitydensityfunctionfortheta,withinitializationerror, 101 52. MonteCarloprobabilitydensityfunctionfortheta-dot,withinitializationerror, time=2.0sec 101 53. MotnitmeeC=ar3l.o0psreocbabilitydensityfunctionfortheta,withinitializationerror, 102 54. MotnitmeeC=ar3l.o0psreocbabilitydensityfunctionfortheta-dot,withinitializationerror, 102 55. Truevs.estimatedXIstate 117 56. Truevs.estimatedX2state 117 57. Truevs.estimatedXIstate,non-zeroinitialconditions 118 58. Truevs.estimatedX2state,non-zeroinitialconditions 118 AbstractofDissertationPresentedtotheGraduateSchool ofTheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ANANALYSISOFANEWNONLINEARESTIMATIONTECHNIQUE: THESTATE-DEPENDENTRICATTIEQUATIONMETHOD By CraigM.Ewing August1999 Chairman:NormanFitz-Coy MajorDepartment:AerospaceEngineering,Mechanics,andEngineeringScience Researchintononlinearestimationtechniquesforterminalhomingmissileshas beenconductedformanydecades.Theterminalstateestimator,alsocalledtheguidance filter,isresponsibleforprovidingaccurateestimatesoftargetmotionforuseinguiding themissiletoacollisioncoursewiththetarget.Someformoftheextended-Kalmanfilter (EKE)hasbecomethestandardestimationtechniqueemployedinmostmodernweapon guidancesystems.EKFlinearizationofnonlineardynamicsand/ormeasurementscan causeproblemsofdivergencewhenconfrontedbyhighlynonlinearconditions. The objectiveofthisdissertationistoanalyzeanewnonlinearestimationtechniquethatis basedontheparameterizationofthenonlinearities.Thisparameterizationconvertsthe nonlinearestimationproblemintotheformofasteady-statecontinuousKalmanfiltering problemwithstate-dependentcoefficients.

Analysis of a new nonlinear estimation technique : the state-dependent Ricatti equation method PDF

139 Pages·1999·3.1 MB·English

by Ewing, Craig M

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