IEEE粒子滤波课件VIP

RandomFiniteSetsinStochasticFiltering,Ba-NguVoEEEDepartmentUniversityofMelbourneAustralia,.au/staff/bv/,IEEEVictorianChapterJuly28,2009,StochasticFilteringHistory,1940s:WienerfilterPioneeringworkbyWiener,Kolmogorov,1950s:KalmanfilterWorkbyBodemk-1,Pk-1),N(.;mk|k-1,Pk|k-1),N(.;mk,Pk),Kalmanfilter,7,学习交流PPT,state-vector,statedynamic,statespace,observationspace,xk,xk-1,zk-1,zk,PracticalChallenges,fk|k-1(xk|xk-1),gk(zk|xk),Sofar,weassumedexactly1observationateachtimeHoldsonlyforasmallnumberofapplicationsPracticalmeasuringdevice:mayfailtodetecttrueobservation(detectionuncertainty),E,Example2:multi-BernoulliRFS=,UnionofBernoulliRFSs,17,学习交流PPT,RandomFiniteSet,E,SamplenPoiss(r),fori=1:n,samplexip(.),end;,Example3:PoissonRFS,E,Samplenc(.),fori=1:n,samplexip(.),end;,Example4:i.i.d.clusterRFS,18,学习交流PPT,RandomFiniteSet,Needsuitablenotionsofdensity/integrationforfiniteset,pk-1(Xk-1|Z1:k-1),pk(Xk|Z1:k),pk|k-1(Xk|Z1:k-1),prediction,data-update,?,?,states,multi-objectstate,multi-objectobservation,X,observations,X,Z,Multi-objectBayesfilter,19,学习交流PPT,RandomFiniteSet,Belief“density”ofSfS:F(E)0,)bS(T)=TfS(X)dX,Belief“distribution”ofSbS(T)=P(ST),TE,E,S,ProbabilitydensityofSpS:F(E)0,)PS(T)=TpS(X)m(dX),ProbabilitydistributionofSPS(T)=P(ST),TF(E),F(E),S,CollectionoffinitesubsetsofE,Statespace,MahlersFiniteSetStatistics(1994),Choquet(1968),T,T,Conventionalintegral,Setintegral,PointProcessTheory(1950-1960s),VSD(2005),20,学习交流PPT,Computationallyexpensive!,single-objectBayesfilter,multi-objectBayesfilter,stateofsystem:randomvector,first-momentfilter(e.g.a-b-gfilter),stateofsystem:randomset,first-momentfilter(“PHD”filter),Single-object,Multi-object,ThePHDFilter,pk-1(Xk-1|Z1:k-1),pk(Xk|Z1:k),pk|k-1(Xk|Z1:k-1),prediction,data-update,Multi-objectBayesfilter,21,学习交流PPT,ThePHDFilter,x0,statespace,vPHD(intensityfunction)ofanRFS,S,v(x)dx=expectednumberofobjectsinS,S,v(x0)=densityofexpectednumberofobjectsatx0,22,学习交流PPT,ThePHDFilter,statespace,vk,vk-1,PHDfilterMahler03,vk-1(xk-1|Z1:k-1),vk(xk|Z1:k),vk|k-1(xk|Z1:k-1),PHDprediction,PHDupdate,Multi-objectBayesfilter,pk-1(Xk-1|Z1:k-1),pk(Xk|Z1:k),pk|k-1(Xk|Z1:k-1),prediction,update,Avoidsdataassociation!,ThePHDFilter:Prediction,vk|k-1(xk|Z1:k-1)=fk|k-1(xk,xk-1)vk-1(xk-1|Z1:k-1)dxk-1+gk(xk),fk|k-1(xk,xk-1)=ek|k-1(xk-1)fk|k-1(xk|xk-1)+bk|k-1(xk|xk-1),probabilityofobjectsurvival,termforobjectsspawnedbyexistingobjects,Markovtransitiondensity,24,学习交流PPT,ThePHDFilter:Update,vk(xk|Z1:k),S,zZk,Dk(z)+kk(z),pD,k(xk)gk(z|xk),+1-pD,k(xk)vk|k-1(xk|Z1:k-1),Dk(z)=pD,k(x)gk(z|x)vk|k-1(x|Z1:k-1)dx,Nk=vk(x|Z1:k)dx,Bayes-updatedintensity,predictedintensity(fromprevioustime),intensityoffalsealarms,sensorlikelihoodfunction,probabilityofdetection,expectednumberofobjects,measurement,25,学习交流PPT,ThePHDFilter,GaussianMixturePHDFilterVM05,06,ParticlePHDFilterVSD03,05,Mahler&Zajic03,Sidenbladh03,wk-1,xk-1,j=1,Jk-1,(j),(j),j=1,Jk|k-1,(j),(j),wk|k-1,xk|k-1,wk,xk,j=1,Jk,(j),(j),wk-1,mk-1,Pk-1,j=1,Jk-1,(j),(j),(j),wk|k-1,mk|k-1,Pk|k-1,j=1,Jk|k-1,(j),(j),(j),wk,mk,Pk,j=1,Jk,(j),(j),(j),26,学习交流PPT,ThePHDfilter,Extended&UnscentedKalmanPHDfilterVM06JumpMarkovPHDfilterPashaet.al.06TrackcontinuityClarket.al.06ConvergenceClarket.al.07BritishPetrolium(Pipelinetracking)07VisualtrackingPhamet.al.07CelltrackingJuanget.al.09,BistaticradarTobias&Lanterman05TracklabellingtrackassociationPantaet.al.07,Linet.al06ConvergenceVDS05,Johansenetal07,Clark&Bell06,ComputervisionMaggioet.al.07,Wanget.al.2008,AuxiliaryparticlePHDfilterWhitleyet.al.07TrafficintensityestimationBattistelliet.al.08,Particle-PHDfilterVSD03,05,GM-PHDfilterVM05,06,27,学习交流PPT,ThePHDfilter,Videodata:trackingfootballplayersPhametal.07,DatacourtesyofCzyzet.al.,28,学习交流PPT,ThePHDfilter,Videotrackingofpeoplewalking(340frames)Phametal.07,DatacourtesyofK.SmithIDIAPResearchInstitute.,29,学习交流PPT,TheCardinalisedPHDFilter,DrawbackofPHDfilter:Highvarianceofcardinalityestimate,RelaxPoissonassumption:allowsanycardinalitydistribution,Jointlypropagate:intensityfunction&cardinalitydistribution.,HighercomputationalcostthanPHDStillcheaperthanstate-of-the-arttraditionaltechniques,CPHDfilterMahler06,07,GaussianMixtureCPHDfilterVVC06,07,30,学习交流PPT,GMTIRadarUlmkeet.al.07TestedbyFGAN(NATOBoldAvengerexercise)07,AcousticsourcetrackingPhamet.al.08TestedonMSTWGandSEABARDatasetsErdincet.al.08ComparisonwithMHTSvenssonetal.09ConvoytrackingPollardet.al.09TrackingfromaerialimagePollardet.al.09LockheedMartin(SpaceFence)09.,GM-CPHDfilterVVC05,06,TheCardinalisedPHDFilter,31,学习交流PPT,Sonarimages,TheCardinalisedPHDFilter,32,学习交流PPT,Largescalemultipletargettrackingwithsmallfalsealarmrate,CourtesyofLockheedMartin,TheCardinalisedPHDFilter,33,学习交流PPT,Upto1500closelyspacedtargetsonastandardlaptop!,CourtesyofLockheedMartin,OSPAdistance(satisfiesallmetricaxioms)=pertargetcardinality&stateerror,TheCardinalisedPHDFilter,34,学习交流PPT,SLAM(SimultaneousLocalisationandMapping),Objective:Jointlyestimaterobotpose&map(setoflandmarks),ThePHDFilterinSLAM,35,学习交流PPT,ThePHDFilterinSLAM,Robotpose,Map,Measurements,Controls,Measurementlikelihood,Setintegral,Transitiondensity,RFS-SLAMprediction,RFS-SLAMupdate,(Feature)Map=finitesetoflandmarksBayesianSLAMrequiresmodellingthemapbyanRFS,Setintegral,RFS-SLAMMullaneet.al.08,36,学习交流PPT,Mapping:specialcaseofSLAMwithknownrobotposes,PHDapproximation:propagate1stmomentofthemapRFS,PHDoftheposteriormapRFS,ThePHDFilterinSLAM,37,学习交流PPT,Mapping:specialcaseofSLAMwithknownrobotposes,ThePHDFilterinSLAM,38,学习交流PPT,Experiment:NanyangTechnologicalUniversityCampus,PHDSLAM(approximationofRFS-SLAMrecursion):AugmentlandmarkswiththevehicleposeRepresentsetofaugmentedlandmarksasamarkedpointprocessPropagatePHDofthemarkedpointprocess,ThePHDFilterinSLAM,39,学习交流PPT,Lowclutter:All3algorithmscanclosetheloop,Higherclutter:OnlyPHD-SLAMcanclosetheloop,Groundtruthplottedingreen,ThePHDFilterinSLAM,40,学习交流PPT,ConcludingRemarks,ThankYou!,RandomFiniteSetFilteringBorneoutofpractical&fundamentalnecessitySignificanttheoreticalextensionofclassicalfilteringYieldsefficientalgorithmssuchasthePHDfiltersBeyondthePHDfiltersMulti-Bernoulli,Gauss-PoissonfiltersFilteringwithimagedataRobustnessStochasticcontrol,Formoreinfopleasesee.auSeealso:.au/staff/bv/publications.html,41,学习交流PPT,SomeReferences,BooksD.DaleyandD.Vere-Jones,AnIntroductiontotheTheoryofPointProcesses,Springer-Verlag,1988.D.Stoyan,D.Kendall,J.Mecke,StochasticGeometryanditsApplications,JohnWiley&Sons,1995I.Goodman,R.Mahler,andH.Nguyen,MathematicsofDataFusion.KluwerAcademicPublishers,1997.R.Mahler,StatisticalMultisource-MultitargetInformationFusion,ArtechHouse,2007.M.Mallick,V.Krisnamurthy,B.-N.Vo(eds),AdvancedTopicsandApplicationsinIntegratedTracking,Classification,andSensorManagement,IEEE-Wiley(underreview)PapersR.Mahler,“Multi-targetBayesfilteringviafirst-ordermulti-targetmoments,”IEEETrans.AES,vol.39,no.4,pp.11521178,2003.B.-N.Vo,S.Singh,andA.Doucet,“SequentialMonteCarlomethodsformulti-targetfilteringwithrandomfinitesets,”IEEETrans.AES,vol.41,no.4,pp.12241245,2005.B.-N.Vo,andW.K.Ma,“TheGaussianmixturePHDfilter,”IEEETrans.SignalProcessing,IEEETrans.SignalProcessing,Vol.54,No.11,pp.4091-4104,2006.R.Mahler,“PHDfilterofhigherorderintargetnumber,”IEEETrans.Aerospace&ElectronicSystems,vol.43,no.4,pp.15231543,2007B.T.Vo,B.-N.Vo,andA.Cantoni,AnalyticimplementationsoftheCardinalizedProbabilityHypothesisDensityFilter,IEEETrans.SignalProcessing,Vol.55,No.7,Part2,pp.3553-3567,2007.B.-T.Vo