多目標(biāo)跟蹤英文ppt(編輯修改稿)
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【文章內(nèi)容簡(jiǎn)介】 sen et. al. 06] Gaussian Mixture PHD filter Closedform solution to the PHD recursion exists for linear Gaussian multitarget model vk1( . |Z1:k1) vk(. |Z1:k) vk|k1(. |Z1:k1) ??? ??? 1| ?Fkk kY??? ??? 1| ?Fkk kY{wk1, mk1, Pk1} i=1 Jk1 (i) (i) (i) {wk|k1, mk|k1, Pk|k1} i=1 Jk|k1 (i) (i) (i) {wk, mk, Pk } i=1 Jk (i) (i) (i) PHD filter Gaussian Mixture (GM) PHD filter [Vo Ma 05, 06] Gaussian mixture prior intensity ? Gaussian mixture posterior intensities at all subsequent times Extended Unscented Kalman PHD filter [Vo Ma 06] Jump Markov PHD filter [Pasha et. al. 06] Track continuity [Clark et. al. 06] Cardinalised PHD Filter Drawback of PHD filter: High variance of cardinality estimate Relax Poisson assumption: allows arbitrary cardinality distribution Jointly propagate: intensity function probability generating function of cardinality. More plex PHD update step (higher putational costs) CPHD filter [Mahler 06,07] vk1(xk1|Z1:k1) vk(xk|Z1:k) vk|k1(xk|Z1:k1) ??? ??? intensity prediction intensity update pk1(n|Z1:k1) pk(n|Z1:k) pk|k1(n|Z1:k1) ??? ??? cardinality prediction cardinality update Gaussian Mixture CPHD Filter ??? ??? {wk1, xk1} i=1 Jk1 (i) (i) {wk|k1, xk|k1} i=1 Jk|k1 (i) (i) {wk, xk } i=1 Jk (i) (i) intensity prediction intensity update cardinality prediction cardinality update ??? ??? {pk1(n)} n=0 ? {pk|k1(n)} n=0 ? {pk(n)} n=0 ? Particle CPHD filter [Vo 08] Closedform solution to the CPHD recursion exists for linear Gaussian multitarget model Gaussian mixture prior intensity ? Gaussian mixture posterior intensities at all subsequent times [Vo et. al. 06, 07] ParticlePHD filter can be extended to the CPHD filter CPHD filter Demonstration 10 20 30 40 50 60 70 80 90 1000510T i m eCardinality StatisticsT r u eM e a nS t D e v10 20 30 40 50 60 70 80 90 1000510T i m eCardinality StatisticsT r u eM e a nS t D e v1000 MC trial average GMCPHD filter GMPHD filter CPHD filter Demonstration 1000 MC trial average Comparison with JPDA: linear dynamics, sv = 5, sh = 10, 4 targets, Sonar images CPHD filter Demonstration MeMBer Filter ??? ??? {(rk1, pk1)} i=1 Mk1 (i) (i) {(rk|k1, pk|k1)} i=1 Mk|k1 (i) (i) {(rk, pk )} i=1 Mk (i) (i) prediction update Valid for low clutter rate high probability of detection Multiobject Bayes filter pk1(Xk1|Z1:k1) pk(Xk|Z1:k) pk|k1(Xk|Z1:k1) prediction update ??? ??? (Multitarget MultiBernoulli ) MeMBer filter [Mahler 07], biased Approximate predicted/posterior RFSs by MultiBernoulli RFSs CardinalityBalanced MeMBer filter [Vo et. al. 07], unbiased CardinalityBalanced MeMBer Filter ??? ??? {(rk1, pk1)} i=1 Mk1 (i) (i) {(rk|k1, pk|k1)} i=1 Mk|k1 (i) (i) {(rk, pk )} i=1 Mk (i) (i) prediction update {(rP,k|k1, pP,k|k1)} ? {(r?,k, p?,k)} (i) (i) (i) (i) i=1 Mk1 i=1 M?,k rk1? pk1, pS,k? (i) (i) ? fk|k1(?|?), pk1 pS,k? (i) ?pk1, pS,k? (i) term for object births CardinalityBalanced MeMBer filter [Vo et. al. 07] ??? ??? {(rk1, pk1)} i=1 Mk1 (i) (i) {(rk|k1, pk|k1)} i=1 Mk|k1 (i) (i) {(rk, pk )} i=1 Mk (i) (i) prediction update {(rL,k, pL,k)} ? {(rU,k,(z), pU,k(z))} (i) (i) z?Zk i=1 Mk|k1 1? ?pk|k1, pD,k? (i) pk|k1(1? pD,k) (i) 1? rk|k1 ?pk|k1, pD,k? (i) (i) rk|k1(1? ?pk|k1, pD,k?) (i) (i) CardinalityBalanced MeMBer Filter rk|k1(1? rk|k1) ?pk|k1, pD,kgk(z|?)? 1? rk|k1 ?pk|k1, pD,k? (i) (i) rk|k1 ?pk|k1, pD,kgk(z|?)? (i) (i) i=1 Mk|k1 ? (1? rk|k1?pk|k1, pD,k?)2 (i) (i) (i) (i) (i) i=1 Mk|k1 ? k(z) + 1? rk|k1 (i) rk|k1 pk|k1 (i) (i) i=1 Mk|k1 ? pD,kgk(z|?) rk|k1?pk|k1, pD,kgk(z|?)? 1? rk|k1 (i) (i) (i) i=1 Mk|k1 ? CardinalityBalanced MeMBer filter [Vo et. al. 07] CardinalityBalanced MeMBer Filter Closedform (Gaussian mixture) solution [Vo et. al. 07], Particle implementation [Vo et. al. 07], ??? ??? {(rk1, pk1)} i=1 Mk1 (i) (i) {(rk|k1, pk|k1)} i=1 Mk|k1 (i) (i) {(rk, pk )} i=1 Mk (i) (i) prediction update {wk1, xk1} j=1 Jk1 (i,j) (i,j) j=1 Jk|k1 (i,j) (i,j) {wk|k1, xk|k1 } {wk, xk } j=1 Jk (i,j) (i,j) {wk1, mk1, Pk1} j=1 Jk1 (i,j) (i,j) (i,j) {wk|k1, mk|k1, Pk|k1} j=1 Jk|k1 (i,j) (i,j) (i,j) {wk, mk, Pk } j=1 Jk (i,j) (i,j) (i,j) More useful than PHD filters in highly nonlinear problems Performance parison Example: 10 targets max on scene, with births/deaths 4D states: xy position/velocity, linear Gaussian observations: xy position, linear Gaussian 1 0 0 0 8 0 0 6 0 0 4 0 0 2 0 0 0 200 400 600 800 1000 1 0 0 0 8 0 0 6 0 0 4 0 0 2 0 002004006008001000x coor dinate (m )ycoordinate (m)?/? start/end positions Dynamics constant velocit
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