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1、MANUSCRIPT1BayesianFiltering:FromKalmanFilterstoParticleFilters,andBeyondZHECHENAbstractInthisself-containedsurvey/reviewpaper,wesystem-IVBayesianOptimalFiltering9aticallyinvestigatetherootsofBayesian?lteringaswellasitsrichIV-AOptimalFiltering....................
2、.10leavesintheliterature.Stochastic?lteringtheoryisbrie?yreviewedIV-BKalmanFiltering.....................11withemphasisonnonlinearandnon-Gaussian?ltering.FollowingIV-COptimumNonlinearFiltering..............13theBayesianstatistics,di?erentBayesian?lteringtechnique
3、sarede-IV-C.1Finite-dimensionalFilters............13velopedgivendi?erentscenarios.UnderlinearquadraticGaussiancircumstance,thecelebratedKalman?ltercanbederivedwithintheVNumericalApproximationMethods14Bayesianframework.Optimal/suboptimalnonlinear?lteringtech-nique
4、sareextensivelyinvestigated.Inparticular,wefocusourat-V-AGaussian/LaplaceApproximation............14tentionontheBayesian?lteringapproachbasedonsequentialMonteV-BIterativeQuadrature...................14Carlosampling,theso-calledparticle?lters.ManyvariantsoftheV-CM
5、ulitgridMethodandPoint-MassApproximation..14particle?lteraswellastheirfeatures(strengthsandweaknesses)areV-DMomentApproximation.................15discussed.RelatedtheoreticalandpracticalissuesareaddressedinV-EGaussianSumApproximation..............16detail.Inaddit
6、ion,someother(new)directionsonBayesian?lteringV-FDeterministicSamplingApproximation.........16arealsoexplored.V-GMonteCarloSamplingApproximation.........17IndexTermsStochastic?ltering,Bayesian?ltering,V-G.1ImportanceSampling..............18Bayesianinference,parti
7、cle?lter,sequentialMonteCarlo,V-G.2RejectionSampling................19sequentialstateestimation,MonteCarlomethods.V-G.3SequentialImportanceSampling........19V-G.4Sampling-ImportanceResampling.......20V-G.5Strati?edSampling................21“Theprobabilityofanyeve
8、ntistheratiobetweentheV-G.6MarkovChainMonteCarlo...........22valueatwhichanexpectationdependingonthehappeningoftheeventoughttobecomputed,andthevalueoftheV-G.7H
