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

139 Pages·1999·3.1 MB·English

by  Ewing, Craig M

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.