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1、PPTPPT文档演模板文档演模板OfficeOfficePPTPPT多目标跟踪英文多目标跟踪英文ppt2023/5/19多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTThe The BayesBayes(single-target)filter(single-target)filterMulti-target trackingMulti-target trackingSystem representationSystem representationRandom finite set&Bayesian Multi-target filteringRan
2、dom finite set&Bayesian Multi-target filteringTractable multi-target filtersTractable multi-target filtersProbability Hypothesis Density(PHD)filterProbability Hypothesis Density(PHD)filterCardinalizedCardinalized PHD filter PHD filterMulti-Bernoulli filterMulti-Bernoulli filterConclusionsConclusions
3、 Outline多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT The Bayes(single-target)Filter state-vectortarget motionstate spaceobservation spacexkxk-1zk-1zk fk|k-1(xk|xk-1)Markov Transition DensityMeasurement Likelihoodgk(zk|xk)Objectivemeasurement history(z1,zk)posterior(filtering)pdf of the statepk(xk|z1
4、:k)System Model多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTstate-vectortarget motionstate spaceobservation spacexkxk-1zk-1zkBayes filterpk-1(xk-1|z1:k-1)pk|k-1(xk|z1:k-1)pk(xk|z1:k)predictiondata-updatepk-1(xk-1|z1:k-1)dxk-1 fk|k-1(xk|xk-1)gk(zk|xk)K-1 pk|k-1(xk|z1:k-1)The Bayes(single-target)Filter
5、 多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTpk-1(.|z1:k-1)pk|k-1(.|z1:k-1)pk(.|z1:k)predictiondata-updateBayes filterN(.;mk-1,Pk-1)N(.;mk|k-1,Pk|k-1)N(.;(mk,Pk)Kalman filteri=1Nwk|k-1,xk|k-1i=1N(i)(i)wk,xk i=1 N(i)(i)wk-1,xk-1(i)(i)Particle filterstate-vectortarget motionstate spaceobservation spac
6、exkxk-1zk-1zk fk|k-1(xk|xk-1)gk(zk|xk)The Bayes(single-target)Filter 多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Multi-target tracking多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTobservation produced by targetstarget motionstate spaceobservation space5 targets3 targetsXk-1XkObjective:Jointly estimat
7、e the number and states of targetsChallenges:Random number of targets and measurementsDetection uncertainty,clutter,association uncertainty Multi-target tracking多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT System RepresentationEstimateiscorrectbutestimationerror?TrueMulti-targetstateEstimatedMulti-t
8、argetstateHowcanwemathematically represent the multi-target state?2targets2targetsUsual practice:stackindividualstatesintoalargevector!Problem:Remedy:use多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTTrueMulti-targetstateEstimatedMulti-targetState2targetsnotargetTrueMulti-targetstateEstimatedMulti-targ
9、etState2targets1target System RepresentationWhat are the estimation errors?多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTErrorbetweenestimateandtruestate(miss-distance)fundamentalinestimation/filtering&controlwell-understoodforsingletarget:Euclideandistance,MSE,etcinthemulti-targetcase:dependsonstater
10、epresentationFor multi-target state:vector representationdoesntadmitmulti-targetmiss-distancefinite set representation admitsmulti-targetmiss-distance:distance between 2 finite setsInfactthe“distance”isadistanceforsetsnotvectors System Representation多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTobserv
11、ation produced by targetstarget motionstate spaceobservation space5 targets3 targetsXk-1XkNumberofmeasurementsandtheirvaluesare(random)variablesOrderingofmeasurementsnotrelevant!Multi-target measurementisrepresentedbyafinite set System Representation多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT RFS&B
12、ayesian Multi-target Filteringtargetstarget setobserved setX X observationsXZNeedsuitablenotionsofdensity&integration pk-1(Xk-1|Z1:k-1)pk(Xk|Z1:k)pk|k-1(Xk|Z1:k-1)predictiondata-update Reconceptualizeasageneralizedsingle-targetproblemMahler94Bayesian:Modelstate&observationasRandomFiniteSetsMahler94多
13、目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT RFS&Bayesian Multi-target FilteringS NS(S)=|S S|point process or random counting measurerandom finite set or random point patternSstate space Estate space E多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTBelief“density”ofS fS:F(E)0,)bS(T)=T fS(X)dXBelief“distr
14、ibution”ofSbS(T)=P(S T),T EESProbability densityofS pS:F(E)0,)PS(T)=T pS(X)m(dX)Probability distributionofSPS(T)=P(S T ),T F(E)F(E)SCollectionoffinitesubsetsofEStatespaceMahlers Finite Set Statistics(1994)Choquet(1968)TTConventional integralSet integralVo et.al.(2005)Point Process Theory(1950-1960s)
15、RFS&Bayesian Multi-target Filtering多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTxxXxdeathcreationXxspawnmotion Multi-target Motion Model fk|k-1(Xk|Xk-1)Multi-object transition densityXk=Sk|k-1(Xk-1)Bk|k-1(Xk-1)kEvolution of each element x of a given multi-object state Xk-1多目标跟踪英文pptPPTPPT文档演模板文档演模板Of
16、ficeOfficePPTPPT Multi-target Observation Model gk(Zk|Xk)Multi-object likelihoodZk=Qk(Xk)Kk(Xk)xzxlikelihoodmisdetectionclutterstate spaceobservation space Observation process for each element x of a given multi-object state Xk多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT pk-1(Xk-1|Z1:k-1)pk(Xk|Z1:k)
17、pk|k-1(Xk|Z1:k-1)predictiondata-update Computationally intractable in generalNo closed form solutionParticle or SMC implementation Vo,Singh&Doucet03,05,Sidenbladh03,Vihola05,Maetal.06 Restricted to a very small number of targets Multi-target Bayes FilterMulti-targetBayesfilter多目标跟踪英文pptPPTPPT文档演模板文档
18、演模板OfficeOfficePPTPPT Particle Multi-target Bayes FilterAlgorithmAlgorithmfor i=1:N,%Initialise=Sample:Compute:end;normalise weights;for k=1:kmax,for i=1:N,%Update =Sample:Update:end;normalise weights;resample;MCMC step;end;多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT pk-1(Xk-1|Z1:k-1)pk(Xk|Z1:k)pk|
19、k-1(Xk|Z1:k-1)predictiondata-update Multi-target Bayes filter:very expensive!single-objectBayesfilter multi-objectBayesfilter stateofsystem:random vectorfirst-momentfilter(e.g.a-b-g filter)stateofsystem:random setfirst-momentfilter(“PHD”filter)Single-object Multi-object The PHD Filter多目标跟踪英文pptPPTPP
20、T文档演模板文档演模板OfficeOfficePPTPPTx0state spacevS PHD(intensity function)of a RFS S SvS(x0)=density of expected number of objects at x0 The Probability Hypothesis Density vS(x)dx=expected number of objects in SS=mean of,NS(S),the random counting measure at S多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Th
21、e PHD Filterstate space vk vk-1 PHD filter vk-1(xk-1|Z1:k-1)vk(xk|Z1:k)vk|k-1(xk|Z1:k-1)PHD predictionPHD update Multi-object Bayes filter pk-1(Xk-1|Z1:k-1)pk(Xk|Z1:k)pk|k-1(Xk|Z1:k-1)predictionupdate Avoids data association!多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT PHD Predictionvk|k-1(xk|Z1:k-1
22、)=fk|k-1(xk,xk-1)vk-1(xk-1|Z1:k-1)dxk-1+gk(xk)intensity from previoustime-step term for spontaneousobject births =intensity of kfk|k-1(xk,xk-1)=ek|k-1(xk-1)fk|k-1(xk|xk-1)+bk|k-1(xk|xk-1)Markovtransitionintensityprobabilityof objectsurvivalterm for objectsspawned byexisting objects=intensity of Bk(x
23、k-1)Markov transition densitypredictedintensityNk|k-1=vk|k-1(x|Z1:k-1)dxpredicted expected number of objects(Fk|k-1a)(xk)=fk|k-1(xk,x)a(x)dx+gk(xk)vk|k-1=Fk|k-1vk-1多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT PHD Update vk(xk|Z1:k)SzZkDk(z)+kk(z)pD,k(xk)gk(z|xk)+1-pD,k(xk)vk|k-1(xk|Z1:k-1)Dk(z)=pD,k
24、(x)gk(z|x)vk|k-1(x|Z1:k-1)dx Nk=vk(x|Z1:k)dxBayes-updated intensitypredicted intensity(from previous time)intensity offalse alarmssensor likelihood functionprobabilityof detectionexpected number of objectsmeasurementvk=Ykvk|k-1(Yka)(x)=zZk+kk(z)yk,z(x)+1-pD,k(x)a(x)S多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeO
25、fficePPTPPT Particle PHD filterParticle approximation of vk-1 Particle approximation of vk state spaceVo,Singh&Doucet03,05,Sidenbladh03,Mahler&Zajic03ThePHD(orintensityfunction)vk is not a probability densityThePHDpropagationequationis not a standard Bayesian recursionSequentialMCimplementationofthe
26、PHDfilterNeed to cluster the particles to obtain multi-target estimates多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Particle PHD filterAlgorithmAlgorithmInitialise;for k=1:kmax,for i=1:Jk,Sample:;compute:;end;for i=Jk+1:Jk+Lk-1,Sample:;compute:;end;for i=1:Jk+Lk-1,Update:;end;Redistribute total mass
27、 among Lk resampled particles;end;Convergence:Vo,Singh&Doucet05,Clark&Bell06,Johansenet.al.06多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Gaussian Mixture PHD filterClosed-formsolutiontothePHDrecursionexistsforlinear Gaussian multi-target model vk-1(.|Z1:k-1)vk(.|Z1:k)vk|k-1(.|Z1:k-1)wk-1,mk-1,Pk-1i
28、=1Jk-1(i)(i)(i)wk|k-1,mk|k-1,Pk|k-1i=1Jk|k-1(i)(i)(i)wk,mk,Pk i=1 Jk(i)(i)(i)PHDfilterGaussianMixture(GM)PHDfilterVo&Ma05,06GaussianmixturepriorintensityGaussianmixtureposteriorintensitiesatallsubsequenttimes Extended&UnscentedKalmanPHDfilterVo&Ma06JumpMarkovPHDfilterPashaet.al.06TrackcontinuityClar
29、ket.al.06多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Cardinalised PHD FilterDrawback of PHD filter:HighvarianceofcardinalityestimateRelax Poisson assumption:allowsarbitrarycardinalitydistributionJointly propagate:intensityfunction&probabilitygeneratingfunctionofcardinality.More complex PHD update s
30、tep(highercomputationalcosts)CPHDfilterMahler06,07 vk-1(xk-1|Z1:k-1)vk(xk|Z1:k)vk|k-1(xk|Z1:k-1)intensity predictionintensity update pk-1(n|Z1:k-1)pk(n|Z1:k)pk|k-1(n|Z1:k-1)cardinality predictioncardinality update 多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Gaussian Mixture CPHD Filterwk-1,xk-1i=1J
31、k-1(i)(i)wk|k-1,xk|k-1i=1Jk|k-1(i)(i)wk,xk i=1 Jk(i)(i)intensity predictionintensity update cardinality predictioncardinality update pk-1(n)n=0pk|k-1(n)n=0pk(n)n=0ParticleCPHDfilterVo08Closed-form solution to the CPHD recursion exists for linear Gaussian multi-target modelGaussian mixture prior inte
32、nsity Gaussian mixture posterior intensities at all subsequent times Voet.al.06,07Particle-PHD filter can be extended to the CPHD filter 多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT CPHD filter Demonstration1000MCtrialaverageGMCPHDfilterGMPHDfilter多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT CPHD fi
33、lter Demonstration1000MCtrialaverageComparison with JPDA:linear dynamics,Comparison with JPDA:linear dynamics,s sv v=5,=5,s sh h=10,=10,4 targets,4 targets,多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTSonar imagesSonar images CPHD filter Demonstration多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT MeMBe
34、r Filter(rk-1,pk-1)i=1Mk-1(i)(i)(rk|k-1,pk|k-1)i=1Mk|k-1(i)(i)(rk,pk )i=1 Mk(i)(i)prediction update Valid for low clutter rate&high probability of detectionMulti-objectBayesfilter pk-1(Xk-1|Z1:k-1)pk(Xk|Z1:k)pk|k-1(Xk|Z1:k-1)predictionupdate(Multi-targetMulti-Bernoulli)MeMBerfilter Mahler07,biasedAp
35、proximate predicted/posterior RFSs by Multi-Bernoulli RFSsCardinality-BalancedMeMBerfilter Voet.al.07,unbiased多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Cardinality-Balanced MeMBer Filter(rk-1,pk-1)i=1Mk-1(i)(i)(rk|k-1,pk|k-1)i=1Mk|k-1(i)(i)(rk,pk )i=1 Mk(i)(i)prediction update(rP,k|k-1,pP,k|k-1)(
36、r,k,p,k)(i)(i)(i)(i)i=1Mk-1i=1M,krk-1pk-1,pS,k(i)(i)fk|k-1(|),pk-1 pS,k(i)pk-1,pS,k(i)term for object birthsCardinality-BalancedMeMBerfilterVoet.al.07多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT(rk-1,pk-1)i=1Mk-1(i)(i)(rk|k-1,pk|k-1)i=1Mk|k-1(i)(i)(rk,pk )i=1 Mk(i)(i)prediction update(rL,k,pL,k)(rU,
37、k,(z),pU,k(z)(i)(i)z Zki=1Mk|k-11-pk|k-1,pD,k(i)pk|k-1(1-pD,k)(i)1-rk|k-1 pk|k-1,pD,k(i)(i)rk|k-1(1-pk|k-1,pD,k)(i)(i)Cardinality-Balanced MeMBer Filterrk|k-1(1-rk|k-1)pk|k-1,pD,kgk(z|)1-rk|k-1 pk|k-1,pD,k(i)(i)rk|k-1 pk|k-1,pD,kgk(z|)(i)(i)i=1Mk|k-1S(1-rk|k-1pk|k-1,pD,k)2(i)(i)(i)(i)(i)i=1Mk|k-1Sk(
38、z)+1-rk|k-1(i)rk|k-1 pk|k-1(i)(i)i=1Mk|k-1SpD,kgk(z|)rk|k-1pk|k-1,pD,kgk(z|)1-rk|k-1(i)(i)(i)i=1Mk|k-1SCardinality-BalancedMeMBerfilterVoet.al.07多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Cardinality-Balanced MeMBer FilterClosed-form(Gaussian mixture)solution Voet.al.07,Particle implementation Voe
39、t.al.07,(rk-1,pk-1)i=1Mk-1(i)(i)(rk|k-1,pk|k-1)i=1Mk|k-1(i)(i)(rk,pk )i=1 Mk(i)(i)prediction update wk-1,xk-1j=1Jk-1(i,j)(i,j)j=1Jk|k-1(i,j)(i,j)wk|k-1,xk|k-1 wk,xk j=1 Jk(i,j)(i,j)wk-1,mk-1,Pk-1j=1Jk-1(i,j)(i,j)(i,j)wk|k-1,mk|k-1,Pk|k-1j=1Jk|k-1(i,j)(i,j)(i,j)wk,mk,Pk j=1 Jk(i,j)(i,j)(i,j)Moreusefu
40、lthanPHDfiltersinhighlynon-linearproblems 多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Performance comparisonExample:Example:10targetsmaxonscene,withbirths/deaths 4Dstates:x-yposition/velocity,linearGaussianobservations:x-yposition,linearGaussian/start/endpositionsDynamicsconstantvelocitymodel:v=5ms
41、-2,survivalprobability:pS,k=0.99,ObservationsadditiveGaussiannoise:=10m,detectionprobability:pD,k=0.98,uniformPoissonclutter:c=2.5x10-6m-2多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTCardinality-BalancedRecursionMahlersMeMBerRecursion1000MCtrialaverage Gaussian implementation多目标跟踪英文pptPPTPPT文档演模板文档演模
42、板OfficeOfficePPTPPT Gaussian implementation1000MCtrialaverageCPHDFilterhasbetterperformance多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Particle implementation1000MCtrialaverageCB-MeMBerFilterhasbetterperformance多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT Concluding RemarksThank You!Random Finite S
43、et frameworkRandom Finite Set frameworkRigorousformulationofBayesianmulti-targetfilteringRigorousformulationofBayesianmulti-targetfilteringLeadstoefficientalgorithmsLeadstoefficientalgorithmsFuture research directions Future research directions Track before detect Track before detect Performance mea
44、sure for multi-object systems Performance measure for multi-object systems Numerical techniques for estimation of trajectories Numerical techniques for estimation of trajectoriesFormoreinfopleaseseehttp:/randomsets.ee.unimelb.edu.au/多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPT ReferencesD.Stoyan,D.K
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50、A.Cantoni,“OnMulti-BernoulliApproximationoftheMulti-targetBayesFilter,ICIF,Xian,2007.Seealso:http:/www.ee.unimelb.edu.au/staff/bv/publications.html多目标跟踪英文pptPPTPPT文档演模板文档演模板OfficeOfficePPTPPTOptimal Subpattern Assignment(OSPA)metric Schumacheret.al08FillupXwithn-mdummypointslocatedatadistancegreater