基于贝塔高斯概率假设密度的扩展目标跟踪
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摘要
基于二项分布的扩展目标概率假设密度(extended target probability hypothesis density based on binominal distribution,BET-PHD)算法能够获得比泊松ET-PHD更好的跟踪性能。然而,BET-PHD中作为先验信息的检测概率和量测数目最大值在实际应用中是未知的。参数严重不匹配会导致算法性能急剧下降。鉴于已有文献给出量测数目最大值的估计方法,提出一种能够在线估计检测概率的贝塔高斯ET-PHD(beta Gaussian ET-PHD,BG-ET-PHD)滤波器。首先采用二项分布的共轭先验贝塔分布估计检测概率,并与BET-PHD相结合得到BG-ET-PHD。仿真结果表明,BG-ET-PHD滤波器能够准确估计检测概率,能够获得比基于泊松模型的伽马高斯ET-PHD(gamma Gaussian ET-PHD,GG-ET-PHD)更好的跟踪性能。
The extended target probability hypothesis density(BET-PHD)method based on binominal distribution has shown better tracking performance than the Poisson ET-PHD method.However,the detection probability and measurement number maximum as prior information in BET-PHD are unknown in practical applications.Significant mismatches in these parameters make the method's performance decline sharply.In view of the method to estimate the measurement number maximum already being presented by some literature,this paper proposes a beta Gaussian ET-PHD(BG-ET-PHD)filter for online estimating the detection probability.Firstly,use the conjugate prior,beta distribution of binominal distribution to estimate the detection probability,and then the BG-ET-PHD is obtained by combing beta distribution with BET-PHD.Finally,simulated results show that the BG-ET-PHD filter has good estimates for the detection probability and can obtain better tracking performance compared with gamma Gaussian ET-PHD(GG-ET-PHD)based on a Poisson model.
The extended target probability hypothesis density(BET-PHD)method based on binominal distribution has shown better tracking performance than the Poisson ET-PHD method.However,the detection probability and measurement number maximum as prior information in BET-PHD are unknown in practical applications.Significant mismatches in these parameters make the method's performance decline sharply.In view of the method to estimate the measurement number maximum already being presented by some literature,this paper proposes a beta Gaussian ET-PHD(BG-ET-PHD)filter for online estimating the detection probability.Firstly,use the conjugate prior,beta distribution of binominal distribution to estimate the detection probability,and then the BG-ET-PHD is obtained by combing beta distribution with BET-PHD.Finally,simulated results show that the BG-ET-PHD filter has good estimates for the detection probability and can obtain better tracking performance compared with gamma Gaussian ET-PHD(GG-ET-PHD)based on a Poisson model.
引文
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[2]BEARD M,VO B T,VO B N.Bayesian multi-target tracking with merged measurements using labelled random finite sets[J].IEEE Trans.on Signal Processing,2015,63(6):1433-1447.
[3]LI S Q,YI W,HOSEINNEZHAD Y,et al.Robust distributed fusion with labeled random finite sets[J].IEEE Trans.on Signal Processing,2018,66(2):278-293.
[4]VO B,SINGH S,DOUCENT A.Sequential Monte Carlo methods for multi-target filtering with random finite sets[J].IEEE Trans.on Aerospace and Electronic Systems,2005,41(4):1224-1245.
[5]PAPI F,KIM D Y.A particle multi-target tracker for superpositional measurements using labeled random finite sets[J].IEEE Trans.on Signal Processing,2015,63(16):4348-4358.
[6]FERNANDEZ A.Track-before-detect labeled multi-Bernoulli particle filter with label switching[J].IEEE Trans.on Aerospace and Electronic Systems,2016,52(5):2123-2138.
[7]VO B,MA W.The Gaussian mixture probability hypothesis density filter[J].IEEE Trans.on Signal Processing,2006,54(11):4091-4104.
[8]LI W L,JIA Y M.Nonlinear Gaussian mixture PHD filter with an H∞criterion[J].IEEE Trans.on Aerospace and Electronic Systems,2016,52(4):2004-2016.
[9]DEHKORDI M Y,AZIMIFAR Z.Novel N-scan GM-PHDbased approach for multi-target tracking[J].IET Signal Processing,2016,10(5):493-503.
[10]MAHLER R.Multi target Bayes filtering via first-order multi target moments[J].IEEE Trans.on Aerospace and Electronic Systems,2003,39(4):1152-1178.
[11]ABDULLAHI D,GONG Y,LAMBOTHARAN S,et al.Kalman-gain aided particle PHD filter for multitarget tracking[J].IEEE Trans.on Aerospace and Electronic Systems,2017,53(5):2251-2265.
[12]SCHLANGEN I,DELANDE E D,HOUSSINEAU J,et al.A second-order PHD filter with mean and variance in target number[J].IEEE Trans.on Signal Processing,2018,66(1):48-63.
[13]LI C,SHI Z G,CHEN J M.Hardware architecture and optimisation of FPP particle PHD filter for multi-target tracking in cyberphysical systems[J].IET Control Theory&Applications,2017,11(11):1830-1837.
[14]GILHOLM K,SALMOND D.Spatial distribution model for tracking extended objects[J].IET Radar,Sonar&Navigation,2005,152(5):364-371.
[15]ZONG P,BARBARY M.Improved multi-Bernoulli filter for extended stealth targets tracking based on sub-random matrices[J].IEEE Sensors Journal,2016,16(5):1428-1447.
[16]LAN J,LI X R.Tracking of extended object or target group using random matrix:new model and approach[J].IEEE Trans.on Aerospace and Electronic Systems,2016,52(6):2973-2989.
[17]VIVONE G,GRANSTROM K,BRACA P,et al.Multiple sensor measurement updates for the extended target trackingrandom matrix model[J].IEEE Trans.on Aerospace and Electronic Systems,2017,53(5):2544-2558.
[18]MAHLER R.PHD filters for nonstandard targets I:extended targets[C]∥Proc.of the International Conference on Information Fusion,2009:915-921.
[19]GRANSTROM K,LUNDQUIST C,ORGUNER U.Extended target tracking using a Gaussian mixture PHD filter[J].IEEE Trans.on Aerospace and Electronic Systems,2012,48(4):3268-3286.
[20]李文娟,顾红,苏卫民.基于多伯努利概率假设密度的扩展目标跟踪方法[J].电子与信息学报,2016,38(12):3114-3121.LI W J,GU H,SU W M.Extended target tracking method based on multi-Bernoulli probability hypothesis density[J].Journal of Electronics&Information Technology,2016,38(12):3114-3121.
[21]盛骤,谢式千,潘承毅.概率论与数理统计[M].4版.北京:高等教育出版社,2008.SHENG Z,XIE S Q,PAN C Y.Probability and mathematical statistics[M].4th ed.Beijing:Press of Advanced Education,2008.
[22]RISTIC B,SHERRAH J.Bernoulli filter for detection and tracking of an extended object in clutter[J].IET Radar,Sonar&Navigation,2013,7(1):26-35.
[23]MAHLER R,VO B T,VO B N.CPHD filtering with unknown clutter rate and detection profile[J].IEEE Trans.on Signal Processing,2011,59(8):3497-3513.
[24]GRANSTROM K,ORGUNER U.Estimation and maintenance of measurement rate for multiple extended target[C]∥Proc.of the International Conference of Information Fusion,2012:2170-2176.
[25]Bishop C.Pattern recognition and machine learning[M].New York:Springer-Verlag,2006.
[26]BEARD M,REUTER S,GILHOLM K,et al.Multiple extended target tracking with labeled random finite sets[J].IEEE Trans.on Signal Processing,2016,64(7):1638-1653.
[27]GRANSTROM K,ORGUNER U.A PHD filter for tracking multiple extended targets using random matrices[J].IEEE Trans.on Signal Processing,2012,60(11):5657-5671.
[28]ZHOU Y Q,ZHOU S L,ZOU H X,et al.Probability hypothesis density filter with adaptive estimation of target birth intensity[J].IET Radar,Sonar&Navigation,2016,10(5):901-911.
[29]CHOI B,PARK S,KIM E.A newborn track detection and state estimation algorithm using Bernoulli random finite sets[J].IEEE Trans.on Signal Processing,2016,64(10):2660-2674.
[30]KOCH W.Bayesian approach to extended object and cluster tracking using random matrices[J].IEEE Trans.on Aerospace and Electronic Systems,2008,44(3):1042-1059.