Table Of Content(cid:2)
NonlinearFilters
(cid:2) (cid:2)
(cid:2)
(cid:2)
(cid:2) (cid:2)
(cid:2)
(cid:2)
Nonlinear Filters
Theory and Applications
Peyman Setoodeh
McMasterUniversity
Ontario,Canada
(cid:2) (cid:2)
Saeid Habibi
McMasterUniversity
Ontario,Canada
Simon Haykin
McMasterUniversity
Ontario,Canada
(cid:2)
(cid:2)
Thiseditionfirstpublished2022
©2022byJohnWiley&Sons,Inc.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,
ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingor
otherwise,exceptaspermittedbylaw.Adviceonhowtoobtainpermissiontoreusematerial
fromthistitleisavailableathttp://www.wiley.com/go/permissions.
TherightofPeymanSetoodeh,SaeidHabibi,andSimonHaykintobeidentifiedastheauthors
ofthisworkhasbeenassertedinaccordancewithlaw.
RegisteredOffice
JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,USA
EditorialOffice
111RiverStreet,Hoboken,NJ07030,USA
Fordetailsofourglobaleditorialoffices,customerservices,andmoreinformationaboutWiley
productsvisitusatwww.wiley.com.
Wileyalsopublishesitsbooksinavarietyofelectronicformatsandbyprint-on-demand.Some
contentthatappearsinstandardprintversionsofthisbookmaynotbeavailableinother
formats.
LimitofLiability/DisclaimerofWarranty
Thecontentsofthisworkareintendedtofurthergeneralscientificresearch,understanding,and
discussiononlyandarenotintendedandshouldnotberelieduponasrecommendingor
promotingscientificmethod,diagnosis,ortreatmentbyphysiciansforanyparticularpatient.In
viewofongoingresearch,equipmentmodifications,changesingovernmentalregulations,and
(cid:2) theconstantflowofinformationrelatingtotheuseofmedicines,equipment,anddevices,the (cid:2)
readerisurgedtoreviewandevaluatetheinformationprovidedinthepackageinsertor
instructionsforeachmedicine,equipment,ordevicefor,amongotherthings,anychangesinthe
instructionsorindicationofusageandforaddedwarningsandprecautions.Whilethepublisher
andauthorshaveusedtheirbesteffortsinpreparingthiswork,theymakenorepresentationsor
warrantieswithrespecttotheaccuracyorcompletenessofthecontentsofthisworkand
specificallydisclaimallwarranties,includingwithoutlimitationanyimpliedwarrantiesof
merchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedby
salesrepresentatives,writtensalesmaterialsorpromotionalstatementsforthiswork.Thefact
thatanorganization,website,orproductisreferredtointhisworkasacitationand/orpotential
sourceoffurtherinformationdoesnotmeanthatthepublisherandauthorsendorsethe
informationorservicestheorganization,website,orproductmayprovideorrecommendations
itmaymake.Thisworkissoldwiththeunderstandingthatthepublisherisnotengagedin
renderingprofessionalservices.Theadviceandstrategiescontainedhereinmaynotbesuitable
foryoursituation.Youshouldconsultwithaspecialistwhereappropriate.Further,readers
shouldbeawarethatwebsiteslistedinthisworkmayhavechangedordisappearedbetween
whenthisworkwaswrittenandwhenitisread.Neitherthepublishernorauthorsshallbe
liableforanylossofprofitoranyothercommercialdamages,includingbutnotlimitedto
special,incidental,consequential,orotherdamages.
LibraryofCongressCataloging-in-PublicationDataAppliedfor:
ISBN:9781118835814
CoverDesign:Wiley
CoverImage:©EmrahTurudu/GettyImages
Setin9.5/12.5ptSTIXTwoTextbyStraive,Chennai,India
10 9 8 7 6 5 4 3 2 1
(cid:2)
(cid:2)
TothememoryofRudolf
EmilKalman
(cid:2) (cid:2)
(cid:2)
(cid:2)
(cid:2) (cid:2)
(cid:2)
(cid:2)
vii
Contents
ListofFigures xiii
ListofTable xv
Preface xvii
Acknowledgments xix
Acronyms xxi
1 Introduction 1
1.1 StateofaDynamicSystem 1
(cid:2) (cid:2)
1.2 StateEstimation 1
1.3 ConstrualsofComputing 2
1.4 StatisticalModeling 3
1.5 VisionfortheBook 4
2 Observability 7
2.1 Introduction 7
2.2 State-SpaceModel 7
2.3 TheConceptofObservability 9
2.4 ObservabilityofLinearTime-InvariantSystems 10
2.4.1 Continuous-TimeLTISystems 10
2.4.2 Discrete-TimeLTISystems 12
2.4.3 DiscretizationofLTISystems 14
2.5 ObservabilityofLinearTime-VaryingSystems 14
2.5.1 Continuous-TimeLTVSystems 14
2.5.2 Discrete-TimeLTVSystems 16
2.5.3 DiscretizationofLTVSystems 17
2.6 ObservabilityofNonlinearSystems 17
2.6.1 Continuous-TimeNonlinearSystems 18
2.6.2 Discrete-TimeNonlinearSystems 21
2.6.3 DiscretizationofNonlinearSystems 22
(cid:2)
(cid:2)
viii Contents
2.7 ObservabilityofStochasticSystems 23
2.8 DegreeofObservability 25
2.9 Invertibility 26
2.10 ConcludingRemarks 27
3 Observers 29
3.1 Introduction 29
3.2 LuenbergerObserver 30
3.3 ExtendedLuenberger-TypeObserver 31
3.4 Sliding-ModeObserver 33
3.5 Unknown-InputObserver 35
3.6 ConcludingRemarks 39
4 BayesianParadigmandOptimalNonlinearFiltering 41
4.1 Introduction 41
4.2 Bayes’Rule 42
4.3 OptimalNonlinearFiltering 42
4.4 FisherInformation 45
4.5 PosteriorCramér–RaoLowerBound 46
4.6 ConcludingRemarks 47
(cid:2) (cid:2)
5 KalmanFilter 49
5.1 Introduction 49
5.2 KalmanFilter 50
5.3 KalmanSmoother 53
5.4 InformationFilter 54
5.5 ExtendedKalmanFilter 54
5.6 ExtendedInformationFilter 54
5.7 Divided-DifferenceFilter 54
5.8 UnscentedKalmanFilter 60
5.9 CubatureKalmanFilter 60
5.10 GeneralizedPIDFilter 64
5.11 Gaussian-SumFilter 65
5.12 Applications 67
5.12.1 InformationFusion 67
5.12.2 AugmentedReality 67
5.12.3 UrbanTrafficNetwork 67
5.12.4 CybersecurityofPowerSystems 67
5.12.5 IncidenceofInfluenza 68
5.12.6 COVID-19Pandemic 68
5.13 ConcludingRemarks 70
(cid:2)
