IEEE粒子濾波PPT

1、.au/staff/bv/2021/8/62N. Wiener (1894-1964) A. N. Kolmogorov (1903-1987)R. E. Kalman (1930-) 2021/8/632021/8/642021/8/65state-vectorstate dynamicstate spaceobservation spacexkxk-1zk-1zk fk|k-1(xk| xk-1)Markov Transition DensityMeasurement Likelihoodgk(zk| xk)Objectivemeasurem

2、ent history (z1, zk)posterior pdf of the statepk(xk | z1:k)System Model2021/8/66state-vectorstate dynamicstate spaceobservation spacexkxk-1zk-1zkBayes filterpk-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-1 fk|k-1(xk| xk-1)gk(zk| xk) pk|k-1(xk| z1:k-1) fk

3、|k-1(xk| xk-1)gk(zk| xk) gk(zk| xk)pk-1(xk-1| z1:k-1)dxk2021/8/67state-vectorstate dynamicstate spaceobservation spacexkxk-1zk-1zk fk|k-1(xk| xk-1)gk(zk| xk)pk-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

4、|k-1, xk|k-1i=1N(i)(i)wk, xk i=1 N(i)(i)wk-1, xk-1(i)(i)Particle filter2021/8/68state-vectorstate dynamicstate spaceobservation spacexkxk-1zk-1zk fk|k-1(xk| xk-1)gk(zk| xk)2021/8/69Not detectedDetectedor Number of false observationsunknown random False2021/8/610+Observation =Not detectedDetectedFals

5、e2021/8/611state-vectorstate dynamicstate spaceobservation spacexkxk-1zk-1zk2021/8/612observation produced by objectsstate dynamicstate spaceobservation space5 objects3 objectsXk-1XkObjective: Jointly estimate the number & states of objectsNumerous applications: defence, surveillance, robotics,

6、biomed, Challenges: Random number of objects and measurementsDetection uncertainty, clutter, association uncertainty2021/8/6130011X 1100X TrueMulti-object stateEstimatedMulti-object state| 2XX2 objects2 objects()min | 0perm XXX00 11 00 11 2021/8/6141100X TrueMulti-object state?X EstimatedMulti-objec

7、t State2 objectsno objectTrueMulti-object state00X EstimatedMulti-object State2 objects1 object 1100X 00 11 00 11 00 2021/8/615()min | 0perm XXX2021/8/616statesmulti-object statemulti-object observation X X observations X Z pk-1(Xk-1|Z1:k-1) pk(Xk|Z1:k) pk|k-1(Xk|Z1:k-1)predictiondata-update 2021/8/

8、617sample u uniform0,1if u r, sample x p(.),end;E2021/8/618ESample n Poiss(r), for i=1:n, sample xi p(.) ,end;ESample n c(.), for i=1:n, sample xi p(.) ,end;2021/8/619 pk-1(Xk-1|Z1:k-1) pk(Xk|Z1:k) pk|k-1(Xk|Z1:k-1)predictiondata-update |111:1(|)(|)k kkkkfXX pX ZdX|11:1|11:1(|)(|)(|)(|)kkkk kkkkkk k

9、kgZXpXZgZX pX ZdX?statesmulti-object statemulti-object observation X X observations X ZMulti-object Bayes filter2021/8/620Belief “density” of f : F(E) 0,) b (T ) = T f (X)dXBelief “distribution” of b (T ) = P( T ) , T EEProbability density of p : F(E) 0,) P (T ) = T p (X)m(dX)Probability distributio

10、n of P (T ) = P( T ) , T F(E)F(E) Collection of finite subsets of E State space Mahlers Finite Set Statistics (1994)Choquet (1968)TTConventional integralSet integralPoint Process Theory (1950-1960s)VSD (2005)2021/8/621 Computationally expensive!single-object Bayes filter multi-object Bayes filter st

11、ate of system: random vectorfirst-moment filter(e.g. a-b-g filter)state of system: random setfirst-moment filter(“PHD” filter) Single-object Multi-object pk-1(Xk-1|Z1:k-1) pk(Xk|Z1:k) pk|k-1(Xk|Z1:k-1)predictiondata-update |111:1(|)(|)k kkkkfXX pX ZXd|11:1|11:1(|)(|)(|)(|)kkkk kkkkkk kkgZXpXZgZX pX

12、ZXdMulti-object Bayes filter2021/8/622x0state spacev PHD (intensity function) of an RFS S v(x)dx = expected number of objects in SSv(x0) = density of expected number of objects at x02021/8/623state space vk vk-1 PHD filter Mahler 03 vk-1(xk-1|Z1:k-1)vk(xk|Z1:k) vk|k-1(xk|Z1:k-1)PHD predictionPHD upd

13、ate Multi-object Bayes filter pk-1(Xk-1|Z1:k-1) pk(Xk|Z1:k) pk|k-1(Xk|Z1:k-1)predictionupdate q Avoids data association!2021/8/624vk|k-1(xk |Z1:k-1) = fk|k-1(xk, xk-1) vk-1(xk-1|Z1:k-1)dxk-1 + gk(xk) intensity from previoustime-step term for spontaneousobject birthsfk|k-1(xk, xk-1) = ek|k-1(xk-1) fk

14、|k-1(xk|xk-1) + bk|k-1(xk|xk-1)Markovtransitionintensityprobabilityof objectsurvivalterm for objectsspawned byexisting objectsMarkov 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-12021/8/

15、625 vk(xk|Z1:k) zZkDk(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)dxBayes-updated intensitypredicted intensity (from previous time)intensity offalse alarmssensor likelihood functionprobabilityof detectionexpected number of objectsm

16、easurementvk Ykvk|k-1(Yka)(x) =zZk + kk(z) yk,z(x) + 1 pD,k(x)a(x) 2021/8/626 vk-1( . |Z1:k-1)vk(. |Z1:k) vk|k-1(. |Z1:k-1) 1| Fkk kY wk-1, xk-1j=1Jk-1(j)(j)j=1Jk|k-1(j)(j)wk|k-1, xk|k-1 wk, xk j=1 Jk(j)(j)wk-1, mk-1, Pk-1j=1Jk-1(j)(j)(j)wk|k-1, mk|k-1, Pk|k-1j=1Jk|k-1(j)(j)(j)wk, mk, Pk j=1 Jk(j)(j

17、)(j)2021/8/627 2021/8/628Data courtesy of Czyz et. al. 2021/8/629Data courtesy of K. Smith IDIAP Research Institute.2021/8/630 CPHD filter Mahler 06, 07, Gaussian Mixture CPHD filter VVC 06, 07 vk-1(xk-1|Z1:k-1)vk(xk|Z1:k) vk|k-1(xk|Z1:k-1)intensity predictionintensity update ck-1(n|Z1:k-1)ck(n|Z1:k

18、) ck|k-1(n|Z1:k-1)cardinality predictioncardinality update 2021/8/6312021/8/6322021/8/633Courtesy of Lockheed Martin2021/8/634Courtesy of Lockheed MartinOSPA distance (satisfies all metric axioms) = per target cardinality & state error0102030405060708090100050010001500TimeCardinality TrueEstimat

19、e1020304050607080901000102030TimeOSPA (km)1020304050607080901000102030TimeOSPA Loc (km)1020304050607080901000102030TimeOSPA Card (km)2021/8/6352021/8/636|11:11:101:1:10|11:11:10(|,)( ,|,)( ,|,)(|,)( ,|,)kkkkk kkkkkkkkkkkkkkk kkkkkkkg Zx M px MZuxp x MZuxg Zx M px MZuxM dxd|11: 11: 10|11111111: 11:20

20、11( ,|, )( ,|,)(,|, )kkkkkkkkkkkkkkkkkkkkpx M Zuxfx M xMupxMZuxM dxdRobot poseMapMeasurementsControlsMeasurement likelihoodSet integralTransition densityRFS-SLAM predictionRFS-SLAM updateSet integralRFS-SLAM Mullane et. al. 082021/8/637PHD of the posterior map RFS2021/8/6382021/8/639Experiment: Nany

21、ang Technological University Campus 2021/8/640Low clutter:All 3 algorithms can close the loopHigher clutter:Only PHD-SLAM can close the loopGround truth plotted in green2021/8/641Thank You!For more info please see .auSee also: .au/staff/bv/publi

22、cations.html2021/8/642BooksD. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes, Springer-Verlag, 1988.D. Stoyan, D. Kendall, J. Mecke, Stochastic Geometry and its Applications, John Wiley & Sons, 1995I. Goodman, R. Mahler, and H. Nguyen, Mathematics of Data Fusion. Kluwe

23、r Academic Publishers, 1997.R. Mahler, Statistical Multisource-Multitarget Information Fusion, ArtechHouse, 2007.M. Mallick, V. Krisnamurthy, B.-N. Vo (eds), Advanced Topics and Applications in Integrated Tracking, Classification, and Sensor Management, IEEE-Wiley (under review)PapersR. Mahler, “Mul

24、ti-target Bayes filtering via first-order multi-target moments,” IEEE Trans. AES, vol. 39, no. 4, pp. 11521178, 2003.B.-N. Vo, S. Singh, and A. Doucet, “Sequential Monte Carlo methods for multi-target filtering with random finite sets,” IEEE Trans. AES, vol. 41, no. 4, pp. 12241245, 2005.B.-N. Vo, and W. K. Ma, “The Gaussian mixture PHD filter