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1、IEEETRANSACTIONSONSIGNALPROCESSING,VOL.49,NO.3,MARCH2001613ParticleFiltersforStateEstimationofJumpMarkovLinearSystemsArnaudDoucet,NeilJ.Gordon,andVikramKrishnamurthy,SeniorMember,IEEEAbstract—JumpMarkovlinearsystems(JMLS)arelinearMCMCmethodsaresimulation-ba
2、sedalgorithmsthathaveledsystemswhoseparametersevolvewithtimeaccordingtoafinitetopowerfulnumericalmethodsforcomputationoflikelihoods,stateMarkovchain.Inthispaper,ouraimistorecursivelycom-posteriordistributions,andestimatesderivedfromthem.Mostputeoptimalstate
3、estimatesforthisclassofsystems.WepresentofthedevelopmentinMCMCmethodssofarhasfocusedefficientsimulation-basedalgorithmscalledparticlefilterstosolvetheoptimalfilteringproblemaswellastheoptimalfixed-lagonoff-linealgorithmsthatoperateonafixedbatchofdata.smooth
4、ingproblem.Ouralgorithmscombinesequentialimpor-Theaimofthispaperistoproposeandanalyzerecursivetancesampling,aselectionscheme,andMarkovchainMonte(on-line)simulation-basedalgorithms.ThesealgorithmsCarlomethods.Theyuseseveralvariancereductionmethodstocombinese
5、quentialimportancesamplingandMCMCalgo-makethemostofthestatisticalstructureofJMLS.rithms.MotivatedbyseveralapplicationsinsignalprocessingComputersimulationsarecarriedouttoevaluatetheperfor-manceoftheproposedalgorithms.Theproblemsofon-linede-outlinedbelow,wef
6、ocusonderivingrecursivealgorithmsconvolutionofimpulsiveprocessesandoftrackingamaneuveringforoptimalstateestimationofjumpMarkovlinearsystemstargetareconsidered.Itisshownthatouralgorithmsoutperform(JMLS)—whichisawell-knownNP-hardproblem.thecurrentmethods.Let,
7、denoteadiscretetimeMarkovchainwithIndexTerms—Filteringtheory,MonteCarlomethods,statees-knowntransitionprobabilities.AjumpMarkovlinearsystemtimation,switchingsystems.canbemodeledasNOMENCLATURE(1)dimensionofanarbitraryvector.discretetime.(2)iterationnumberoft
8、hevariousiterativealgorithms.wheredenotesaknownexogenousinput,andanddenoteindependentwhiteGaussiannoisesequences.AjumpFor.T.Markovlinearsystemcanbeviewedasalinearsystemwhoseparameters(,,,,,)evolveGauss