粒子滤波应用

ParticleFilteringPh.D.Coursework:ComputerVisionEricLehmannDepartmentofTelecommunicationsEngineeringResearchSchoolofInformationSciencesandEngineeringTheAustralianNationalUniversity,[e-mail]06,2003ContextTracking:•Probabilisticinferenceaboutthemotionofanobjectgivenasequenceofmeasurements•Applications:robotics,multimedia,military,videoconferencing,surveillance,etc.•Computervision:vehicletracking,human-computerinteraction,robotlocalisation,etc.Inpractice:•Noiseinmeasurements(images)•Backgroundmightbeheavilycluttered➱Robusttrackingmethod:state-spaceapproachPage1—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.State-SpaceApproachProblemdefinitions:•StatevariableXk:e.g.targetpositionandvelocityinstate-spaceattimekXk=[x,y,z,˙x,˙y,˙z]T•ObservationYk:measurementsobtainedfromprocessingcameraimagedata•Setofallobservations:Y1:k=[Y1,...,Yk]•Systemdynamics(transition)equation:Xk=g(Xk−1,vk−1)Aim:givenalldataY1:k,computeposteriorPDFp(Xk|Y1:k)➱BayesianfilteringproblemPage2—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.State-SpaceApproach•Bayesianfilteringsolution:ifposteriorPDFp(Xk−1|Y1:k−1)knownattimek−1,computecurrentposteriorPDFasfollows:Predict:p(Xk|Y1:k−1)=Zp(Xk|Xk−1)p(Xk−1|Y1:k−1)dXk−1Update:p(Xk|Y1:k)∝p(Yk|Xk)p(Xk|Y1:k−1)wherep(Yk|Xk)isthelikelihoodfunction(measurementPDF)•Problem:usuallynoclosed-formsolutionsavailableformanynaturaldynamicmodels•Currentapproximations:Kalmanfilter,extendedKalmanfilter,Gaussiansummethods,grid-basedmethods,etc.➱SequentialMonteCarlomethods,i.e.ParticleFilters(PF)Page3—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.State-SpaceApproach:SymbolicRepresentationCase:GaussiannoiseandlinearequationsFrom[Condensation–conditionaldensitypropagationforvisualtracking,IsardandBlake,Int.J.ComputerVision,1998]Page4—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.State-SpaceApproach:SymbolicRepresentationCase:non-Gaussiannoiseand/ornonlinearequationsFrom[Condensation–conditionaldensitypropagationforvisualtracking,IsardandBlake,Int.J.ComputerVision,1998]Page5—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.ParticleFiltering•Numericalmethodtosolvenonlinearand/ornon-GaussianBayesianfilteringproblems•Knownvariouslyas:bootstrapfiltering,condensationalgorithm,interactingparticleapproximations,survivalofthefittest,JetStream,etc.•Particleandweightrepresentationofposteriordensity:From[Condensation–conditionaldensitypropagationforvisualtracking,IsardandBlake,Int.J.ComputerVision,1998]Page6—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.BasicPFAlgorithmFrom[Novelapproachtononlinear/non-GaussianBayesianstateestimation,Gordonetal.,IEEProc.F.,1993]Assumption:asetofNstatesamplesandcorrespondingweights{X(i)k−1,w(i)k−1,i=1,...,N}representstheposteriordensityp(Xk−1|Y1:k−1)attimek−1Procedure:updatetheparticlesettorepresenttheposteriordensityp(Xk|Y1:k)forcurrenttimekaccordingtofollowingiterationsPage7—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.BasicPF:SymbolicRepresentation{X(i)k−1,w(i)k−1}∼p(Xk−1|Y1:k−1)⇐resampling{eX(i)k−1,1/N}∼p(Xk−1|Y1:k−1)⇐prediction{X(i)k,1/N}∼p(Xk|Y1:k−1)p(Yk|Xk)⇐measurement&updateXk{X(i)k,w(i)k}∼p(Xk|Y1:k)Page8—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.PFMethodsOverview•Algorithmdesignchoices:.Sourcedynamicsmodel:variousmodelsavailable.Observations:cameraimagedata.Likelihoodfunction:derivedfromobservations•LargenumberofenhancedPFversionstobefoundinliterature:auxiliaryPF,unscentedPF,ICondensation,hybridbootstrap,fastweightedbootstrap,annealedPF,etc.•PFmethods:specialcaseofSequentialImportanceSampling,see[OnsequentialMonteCarlosamplingmethodsforBayesianfiltering,Doucetetal.,Statist.Comput.,2000]•ExcellentreviewofcurrentPFmethodsin[Atutorialonparticlefiltersforonlinenonlinear/non-GaussianBayesianTracking,Arulampalametal.,IEEETrans.Sig.Proc.,2002]Page9—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.PFTrackingofaHeadOutlineStandardheadoutlinetemplate(parametricsplinecurve)usedfortracking.Measurementsareobtainedbydetectingmaximaofintensitygradientalonglinesnormaltotheheadcontour.From[Condensation–conditionaldensitypropagationforvisualtracking,IsardandBlake,Int.J.ComputerVision,1998]and[SequentialMonteCarlofusionofsoundandvisionforspeakertracking,Vermaaketal.,Proc.Int.Conf.onComputerVision,2001]Page10—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.PFTrackingofaHeadOutlineParticlerepresentationofshapedistributionFrom[Condensation–conditionaldensitypropagationforvisualtracking,IsardandBlake,Int.J.ComputerVision,1998]Page11—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.ApplicationExampleTrackingobjectsinheavyclutterhand.mpgdancemv.mpgleafmv.mpgFrom[Condensation–conditionaldensitypropagationforvisualtracking,IsardandBlake,Int.J.ComputerVision,1998]Page12—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.ApplicationExampleCombiningsoundandvisioninPFalgorithmpatjacoCout.aviFrom[SequentialMonteCarlofusionofsoundandvisionforspeakertracking,Vermaaketal.,Proc.Int.Conf.onComputerVision,2001]Page13—ComputerVision,Ph.D.courseworkEricLehmann,Tel.Eng.ApplicationExa