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1、ATutorialonParticleFilteringandSmoothing:FifteenyearslaterArnaudDoucetAdamM.JohansenTheInstituteofStatisticalMathematics,DepartmentofStatistics,4-6-7Minami-Azabu,Minato-ku,UniversityofWarwick,Tokyo106-8569,Japan.Coventry,CV47AL,UKEmail:Arnaud@ism.ac.jpEmail:A.M.Johansen@warwick.ac.ukFirstVersion1.0{
2、April2008ThisVersion1.1{December2008AbstractOptimalestimationproblemsfornon-linearnon-Gaussianstate-spacemodelsdonottypicallyadmitanalyticsolutions.Sincetheirintroductionin1993,particle lteringmethodshavebecomeaverypopularclassofalgorithmstosolvetheseestimationproblemsnumericallyinanonlinemanner,i.e
3、.recursivelyasobservationsbecomeavailable,andarenowroutinelyusedin eldsasdiverseascomputervision,econometrics,roboticsandnavigation.Theobjectiveofthistutorialistoprovideacomplete,up-to-datesurveyofthis eldasof2008.Basicandadvancedparticlemethodsfor lteringaswellassmoothingarepresented.Keywords:Centr
4、alLimitTheorem,Filtering,HiddenMarkovModels,MarkovchainMonteCarlo,Par-ticlemethods,Resampling,SequentialMonteCarlo,Smoothing,State-Spacemodels.1IntroductionThegeneralstatespacehiddenMarkovmodels,whicharesummarisedinsection2.1,provideanextremely
exibleframeworkformodellingtimeseries.Thegreatdescripti
5、vepowerofthesemodelscomesattheexpenseofintractability:itisimpossibletoobtainanalyticsolutionstotheinferenceproblemsofinterestwiththeexceptionofasmallnumberofparticularlysimplecases.Theparticle"methodsdescribedbythistutorialareabroadandpopularclassofMonteCarloalgorithmswhichhavebeendevelopedoverthep
6、ast fteenyearstoprovideapproximatesolutionstotheseintractableinferenceproblems.1.1PreliminaryremarksSincetheirintroductionin1993[22],particle ltershavebecomeaverypopularclassofnumericalmeth-odsforthesolutionofoptimalestimationproblemsinnon-linearnon-Gaussianscenarios.Incomparisonwithstandardapproxim
7、ationmethods,suchasthepopularExtendedKalmanFilter,theprincipalad-vantageofparticlemethodsisthattheydonotrelyonanylocallinearisationtechniqueoranycrudefunctionalapproximation.Thepricethatmustbepaidfort
