IEEE粒子滤波PPT

RandomFiniteSetsinStochasticFilteringBa-NguVoEEEDepartmentUniversityofMelbourneAustralia(1894-1964)A.N.Kolmogorov(1903-1987)R.E.Kalman(1930-)1940’s:WienerfilterPioneeringworkbyWiener,Kolmogorov1950’s:KalmanfilterWorkbyBode&Shannon,Zadeh&Ragazzini,Levinson,Swerling,Stratonovich,etc.1970’s:AerospaceapplicationsSorenson&Alspach,Singer,Bar-Shalom,Reid,etc.1960’s:PublicationoftheKalmanfilter,Kalman-Bucyfilter,Schmidt’s1stimplementation–ApolloprogramLMSalgorithmbyWidrow&HoffParticleFilter(1990’s--)Computationaltoolsfornon-linearnon-GaussianfilteringGordon,Salmond&Smith,Doucet…RandomFiniteSet(1990’s--)Unifiedframeworkformulti-objectfiltering&controlProbabilityHypothesisDensity(PHD)filters,BernoullifilterPioneeringworkbyMahlerStochasticFiltering:ThePresentTheBayes(nonlinear)FilterPracticalChallengesMulti-ObjectFilteringRandomFiniteSetPHD/CPHDFilters&ApplicationsConclusionsOutlineTheBayes(nonlinear)Filterstate-vectorstatedynamicstatespaceobservationspacexkxk-1zk-1zkfk|k-1(xk|xk-1)MarkovTransitionDensityMeasurementLikelihoodgk(zk|xk)Objectivemeasurementhistory(z1,…,zk)posteriorpdfofthestatepk(xk|z1:k)SystemModelstate-vectorstatedynamicstatespaceobservationspacexkxk-1zk-1zkBayesfilterpk-1(xk-1|z1:k-1)pk|k-1(xk|z1:k-1)pk(xk|z1:k)predictiondata-updatepk-1(xk-1|z1:k-1)dxk-1fk|k-1(xk|xk-1)gk(zk|xk)pk|k-1(xk|z1:k-1)TheBayes(nonlinear)Filterfk|k-1(xk|xk-1)gk(zk|xk)gk(zk|xk)pk-1(xk-1|z1:k-1)dxkstate-vectorstatedynamicstatespaceobservationspacexkxk-1zk-1zkTheBayes(nonlinear)Filterfk|k-1(xk|xk-1)gk(zk|xk)pk-1(.|z1:k-1)pk|k-1(.|z1:k-1)pk(.|z1:k)predictiondata-updateBayesfilterN(.;mk-1,Pk-1)N(.;mk|k-1,Pk|k-1)N(.;mk,Pk)Kalmanfilteri=1N{wk|k-1,xk|k-1}i=1N(i)(i){wk,xk}i=1N(i)(i){wk-1,xk-1}(i)(i)Particlefilterstate-vectorstatedynamicstatespaceobservationspacexkxk-1zk-1zkPracticalChallengesfk|k-1(xk|xk-1)gk(zk|xk)Sofar,weassumedexactly1observationateachtimeHoldsonlyforasmallnumberofapplicationsPracticalmeasuringdevice:mayfailtodetecttrueobservation(detectionuncertainty)&picksupfalseobservations(clutter)PracticalChallengesNotdetectedDetectionuncertainty:DetectedFalseobservations(clutter)orNumberoffalseobservationsunknownrandomFalsePracticalChallengesNoinformationonwhichistheobservationofthestateNumberofobservationsisarandomvariable.‘+’Observation=NotdetectedDetectedFalsestate-vectorstatedynamicstatespaceobservationspacexkxk-1zk-1zkPracticalChallengesSummaryofpracticalchallenges:Numberofobservationsisrandom&timevaryingTrueobservationmaynotbepresentDonotknowwhichobservationsarefalse/trueOrderingofobservationsnotrelevantobservationproducedbyobjectsstatedynamicstatespaceobservationspace5objects3objectsXk-1XkObjective:Jointlyestimatethenumber&statesofobjectsNumerousapplications:defence,surveillance,robotics,biomed,…Challenges:RandomnumberofobjectsandmeasurementsDetectionuncertainty,clutter,associationuncertaintyMulti-ObjectFiltering0011X11'00XEstimateiscorrectbutestimationerror???TrueMulti-objectstateEstimatedMulti-objectstate||'||2XXHowcanwemathematicallyrepresentthemulti-objectstate?2objectsUsualpractice:stackindividualstatesintoalargevector!2objectsRemedy:use(')min||'||0permXXXFundamentalinconsistency:Multi-ObjectFiltering0011001111'00XTrueMulti-objectstate?XEstimatedMulti-objectState2objectsnoobjectTrueMulti-objectstate00XEstimatedMulti-objectState2objects1objectWhataretheestimationerrors?11'00XMulti-ObjectFiltering0011001100Miss-distance:errorbetweenestimateandtruestatemeasureshowcloseanestimateistothetruevaluewell-understoodforsingletarget:Euclideandistance,MSE,etcfundamentalinestimation/filtering&controlVectorrepresentationdoesn’tadmitmulti-objectmiss-distanceFinitesetrepresentationadmitsmulti-objectmiss-distance,e.g.Haussdorf,Wasserstein,OSPA[Schuhmacheret.al.08]Infactthe“distance”isadistanceforsetsnotvectors(')min||'||0permXXXMulti-ObjectFilteringMulti-ObjectFilteringstatesmulti-objectstatemulti-objectobservationXobservationsXZpk-1(Xk-1|Z1:k-1)pk(Xk|Z1:k)pk|k-1(Xk|Z1:k-1)predictiondata-updateReconceptualiseasafiniteset-valuedfilteringproblemMulti-objectstate&observationrepresentedbyfinitesetsBayesianframeworktreatsstate/observationasrandomvariablesBayesianmulti-objectfilteringrequiresrandomfiniteset(RFS)RandomFiniteSetThenumberofpointsisrandom,ThepointshavenoorderingandarerandomAnRFSisafiniteset-valuedrandomvariableAlsoknownas:pointprocessorrandompointpatternWhatisarandomfiniteset(RFS)?Example1:BernoulliRFSsampleu~uniform[0,1]ifur,samplex~p(.),end;EExample2:multi-BernoulliRFS=UnionofBernoulliRFSsRandomFiniteSetESamplen~Poiss(r),fori=1:n,samplexi~p(.),end;Example3:PoissonRFSESamplen~c(.),fori=1:n,samplexi~p(.),end;Example4:i.i.d.clusterRFSRandomFiniteSetNeedsuitablenotionsofdensity/integrationforfinitesetpk-1(Xk-1|Z1:k-1)pk(Xk|Z1:k)pk|k-1(Xk|Z1:k-1)predictiondata-update