高斯混合扩展目标概率假设密度滤波器的收敛性分析

连峰; 韩崇昭; 刘伟峰; 元向辉

doi:10.3724/SP.J.1004.2012.01343

高斯混合扩展目标概率假设密度滤波器的收敛性分析

doi: 10.3724/SP.J.1004.2012.01343

1.
西安交通大学电子与信息工程学院智能网络与网络安全教育部重点实验室西安 710049;
2.
杭州电子科技大学自动化学院杭州 310018

详细信息

通讯作者:
连峰

计量
- 文章访问数: 2085
- HTML全文浏览量: 53
- PDF下载量: 803
- 被引次数: 0
出版历程
- 收稿日期: 2011-10-17
- 修回日期: 2012-01-20
- 刊出日期: 2012-08-20

Convergence Analysis of the Gaussian Mixture Extended-target Probability Hypothesis Density Filter

1.
Ministry of Education Key Laboratory for Intelligent Networks and Network Security (MOE KLINNS), School of Electronics and Information Engineering, Xi'an Jiaotong University, Xi'an 710049;
2.
School of Automation, Hangzhou Dianzi University, Hangzhou 310018

摘要

摘要: 研究了高斯混合扩展目标概率假设密度(Gaussian mixture extended-target probability hypothesis density, GM-EPHD)滤波器的收敛性问题, 证明了在杂波强度先验已知且扩展目标的期望测量个数连续有界的假设条件下, 若该 GM-EPHD 滤波器的 GM 项趋于无穷多, 那么它一致收敛于真实的 EPHD 滤波器. 并且, 本文还证明了该算法在弱非线性条件下的扩展卡尔曼(Extended Kalman, EK)滤波近似实现 —EK-GM-EPHD 滤波器, 在每个 GM 项的协方差趋于0时, 也一致收敛于真实的 EPHD 滤波器. 本文的研究目的在于从理论上给出 GM-EPHD 和 EK-GM-EPHD 滤波器的收敛性结果以及它们满足一致收敛性的条件.
- 扩展目标跟踪 /
- 概率假设密度滤波器 /
- 高斯混合方法 /
- 收敛性分析
Abstract: The convergence of the Gaussian mixture extended-target probability hypothesis density (GM-EPHD) filter is studied. Under the assumptions that the clutter intensity is known a priori and the expected number of measurements arising from an extended target is continuous and bounded, this paper proves that the GM-EPHD filter converges uniformly to the true EPHD filter as the number of GM terms tends to infinity. In addition, this paper also proves that the extended Kalman (EK) filter approximation of the algorithm in weak nonlinear condition, which is called EK-GM-EPHD filter, converges uniformly to the true EPHD filter as the covariance of each GM term tends to zero. The purpose of this paper is to theoretically present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which they satisfy uniform convergence.
- Extended target tracking (ETT) /
- probability hypothesis density (PHD) filter /
- Gaussian mixture (GM) method /
- convergence analysis

HTML全文

参考文献(1)

[1]

Waxmann M J, Drummond O E. A bibliography of cluster (group) tracking. Proceedings of Signal and Data Processing of Small Targets, SPIE, 2004, 5428: 551-560[2] Salmond D J, Parr M C. Track maintenance using measurements of target extent. IEE Proceedings on Radar, Sonar and Navigation, 2003, 150(6): 389-395[3] Koch J W. Bayesian approach to extended object and cluster tracking using random matrices. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(3): 1042-1059[4] Feldmann M, Franken D. Tracking of extended objects and group targets using random matrices —-A new approach. In: Proceedings of the 11th International Conference on Information Fusion. Cologne, Germany: IEEE, 2008. 242-249[5] Goodman I R, Mahler R P S, Nguye n H T. Mathematics of Data Fusion. Norwood, MA: Kluwer Academic, 1997[6] Mahler R P S. Statistical Multisource Multitarget Information Fusion. Norwood, MA: Artech House, 2007[7] Mahler R P S. Multitarget Bayes filtering via first-order multitarget moments. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1152-1178[8] Vo B N, Singh S, Doucet A. Sequential Monte Carlo methods for multi-target filtering with random finite sets. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(4): 1224-1245[9] Vo B N, Ma W K. The Gaussian mixture probability hypothesis density filter. IEEE Transactions on Signal Processing, 2006, 54(11): 4091-4104[10] Clark D E, Bell J. Convergence results for the particle PHD filter. IEEE Transactions on Signal Processing, 2006, 54(7): 2652-2661[11] Clark D E, Vo B N. Convergence analysis of the Gaussian mixture PHD filter. IEEE Transactions on Signal Processing, 2007, 55(4): 1204-1212[12] Mahler R. PHD filters for nonstandard targets, I: Extended targets. In: Proceedings of the 12th International Conference on Information Fusion. Seattle, WA, USA: IEEE, 2009. 915-921[13] Granstrm K, Lundquist C, Orguner U. A Gaussian mixture PHD filter for extended target tracking. In: Proceedings of the 13th International Conference on Information Fusion. Edinburgh, United Kingdom: EICC, 2010. 1-8[14] Li Hui-Ping, Xu De-Min, Zhang Fu-Bin, Yao Yao. Consistency analysis of EKF-based SLAM by measurement noise and observation times. Acta Automatica Sinica, 2009, 35(9): 1177-1184 (李慧平, 徐德民, 张福斌, 姚尧. 基于量测噪声和观测次数的EKF-SLAM一致性分析. 自动化学报, 2009, 35(9): 1177-1184)[15] Gilholm K, Maskell S, Salmond D, Godsill S. Poisson models for extended target and group tracking. Proceedings of Signal and Data Processing of Small Targets, SPIE, 2005, 5913: 230-241[16] Sorenson H W, Alspach D L. Recursive Bayesian estimation using Gaussian sums. Automatica, 1971, 7(4): 465-479[17] Anderson B D O, Moore J B. Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979

施引文献

资源附件(0)

访问统计