概率假设密度高斯混合实现的分量删减

闫小喜; 韩崇昭

doi:10.3724/SP.J.1004.2011.01313

概率假设密度高斯混合实现的分量删减

doi: 10.3724/SP.J.1004.2011.01313

闫小喜^,,
韩崇昭

1.
西安交通大学电子与信息工程学院综合自动化研究所智能网络与网络安全教育部重点实验室、机械制造系统工程国家重点实验室西安 710049

详细信息

通讯作者:
闫小喜西安交通大学电子与信息工程学院综合自动化研究所博士研究生. 主要研究方向为多源信息融合, 多目标跟踪和随机有限集.E-mail: yanxiaoxi1981@gmail.com

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出版历程
- 收稿日期: 2010-12-01
- 修回日期: 2011-07-01
- 刊出日期: 2011-11-20

Component Pruning in Gaussian Mixture Implementation of Probability Hypothesis Density

YAN Xiao-Xi^,,
HAN Chong-Zhao

1.
Ministry of Education Key Laboratory for Intelligent Networks and Network Security and State Key Laboratory for Manufacturing Systems Engineering, Institute of Integrated Automation, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049

摘要

摘要: 针对概率假设密度(Probability hypothesis density, PHD)高斯混合实现算法中的分量删减问题, 提出了基于Dirichlet分布的分量删减算法以改进概率假设密度高斯混合实现算法的性能. 算法采用极大后验准则估计混合参数, 采用仅依赖于混合权重的负指数Dirichlet分布作为混合参数的先验分布, 利用拉格朗日乘子推导了混合权重的更新公式. 算法利用负指数Dirichlet分布的不稳定性,在极大后验迭代过程中驱使与目标强度不相关的分量消亡. 该不稳定性还能够解决多个相近分量共同描述一个强度峰值的问题, 有利于后续多目标状态的提取. 仿真结果表明, 基于Dirichlet分布的分量删减算法优于典型高斯混合实现中的删减算法.
- 概率假设密度 /
- 高斯混合实现 /
- 分量删减 /
- Dirichlet分布 /
- 极大后验
Abstract: As far as component pruning in Gaussian mixture (GM) implementation of probability hypothesis density (PHD) is concerned, a component pruning algorithm based on Dirichlet distribution is proposed to improve the performance of Gaussian mixture implementation of probability hypothesis density. The maximum a posterior criterion is adopted for estimation of mixing parameters. Dirichlet distribution with negative exponent parameters, which only depends on mixing weights, is adopted as the prior distribution of mixing parameters. The update formulation of mixing weight is derived by Lagrange multiplier. The instability of Dirichlet distribution with negative exponent parameters is applied to driving the components irrelevant with target intensity to extinction during the maximum a posterior iteration. Besides, the problem that one peak of intensity is presented by several proximate mixing component, can be solved by this instability. It is useful for the following state extraction. Simulation results show that the component pruning algorithm based on Dirichlet distribution is superior to that of typical Gaussian mixture implementation.
- Probability hypothesis density (PHD) /
- Gaussian mixture implementation /
- component pruning /
- Dirichlet distribution /
- maximum a posterior (MAP)

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参考文献(1)

[1]

Pulford G E. Taxonomy of multiple target tracking methods. IET Proceedings of Radar, Sonar, and Navigation, 2005, 152(2): 291-304[2] Blackman S, Popoli R. Design and Analysis of Modern Tracking Systems. Boston: Artech House, 1999[3] Daley D, Vere-Jones D. An Introduction to the Theory of Point Processes (Second Edition). New York: Springer, 2002[4] Mahler R P S. Multi-target Bayes filtering via first-order multi-target moments. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1152-1178[5] Mahler R P S. Statistical Multisource-Multitarget Information Fusion. Norwood: Artech House, 2007[6] Erdinc O, Willett P, Bar-Shalom Y. The bin-occupancy filter and its connection to the PHD filters. IEEE Transactions on Signal Processing, 2009, 57(11): 4232-4246[7] Vo B N, Ma W K. The Gaussian mixture probability hypothesis density filter. IEEE Transactions on Signal Processing, 2006, 54(11): 4091-4104[8] Pasha S A, Vo B N, Tuan H D, Ma W K. A Gaussian mixture PHD filter for jump Markov system models. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(3): 919-936[9] 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[10] Whiteley N, Singh S, Godsill S. Auxiliary particle implementation of the probability hypothesis density filter. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(3): 1437-1454[11] Clark D E, Bell J. Convergence results for the particle PHD filter. IEEE Transactions on Signal Processing, 2006, 54(7): 2652-2661[12] Clark D E, Vo B N. Convergence analysis of the Gaussian mixture PHD filter. IEEE Transactions on Signal Processing, 2007, 55(4): 1204-1212[13] Mahler R P S. PHD filters of higher order in target number. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(4): 1523-1543[14] Vo B T, Vo B N, Cantoni A. The cardinality balanced multi-target multi-Bernoulli filter and its implementations. IEEE Transactions on Signal Processing, 2009, 57(2): 409-423[15] Franken D, Schmidt M, Ulmke M. "Spooky action at a distance" in the cardinalized probability hypothesis density filter. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(4): 1657-1664[16] Vo B T, Vo B N, Cantoni A. Analytic implementations of the cardinalized probability hypothesis density filter. IEEE Transactions on Signal Processing, 2007, 55(7): 3553-3567[17] Punithakumar K, Kirubarajan T, Sinha A. Multiple-model probability hypothesis density filter for tracking maneuvering targets. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(1): 87-98[18] Lian Feng, Han Chong-Zhao, Liu Wei-Feng, Yuan Xiang-Hui. Multiple-model probability hypothesis density smoother. Acta Automatica Sinica, 2010, 36(7): 939-950 (连峰, 韩崇昭, 刘伟峰, 元向辉. 多模型概率假设密度平滑器. 自动化学报, 2010, 36(7): 939-950)[19] Panta K, Clark D E, Vo B N. Data association and track management for the Gaussian mixture probability hypothesis density filter. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(3): 1003-1016[20] Vo B T, Vo B N, Cantoni A. A Bayesian filtering with random finite set observations. IEEE Transactions on Signal Processing, 2008, 56(4): 1313-1326[21] Rezaeian M, Vo B N. Error bounds for joint detection and estimation of a single object with random finite set observation. IEEE Transactions on Signal Processing, 2010, 58(3): 1493-1506[22] Wang Y D, Wu J K, Kassim A A, Huang W M. Data-driven probability hypothesis density filter for visual tracking. IEEE Transactions on Circuits and Systems for Video Technology, 2008, 18(8): 1085-1095[23] Maggio E, Taj M, Cavallaro A. Efficient multitarget visual tracking using random finite sets. IEEE Transactions on Circuits and Systems for Video Technology, 2008, 18(8): 1016-1027[24] Maggio E, Cavallaro A. Learning scene context for multiple object tracking. IEEE Transactions on Image Processing, 2009, 18(8): 1873-1884[25] Clark D E, Ruiz I T, Petilot Y, Bell J. Particle PHD filter multiple target tracking in sonar images. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(1): 409-416[26] Clark D E, Ristic B, Vo B N, Vo B T. Bayesian multi-object filtering with amplitude feature likelihood for unknown object SNR. IEEE Transactions on Signal Processing, 2010, 58(1): 26-37[27] Yan Xiao-Xi, Han Chong-Zhao. Multiple target tracking by probability hypothesis density based on Dirichlet distribution. Journal of Xi'an Jiaotong University, 2011, 45(2): 6-10 (闫小喜, 韩崇昭. 应用Dirichlet分布的概率假设密度多目标跟踪. 西安交通大学学报, 2011, 45(2): 6-10)[28] Figueiredo M A F, Jain A K. Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(3): 381-396[29] Hoffman J R, Mahler R P S. Multitarget miss distance via optimal assignment. IEEE Transactions on Systems, Man, and Cybernetics--Part A: Systems and Humans, 2004, 34(3): 327-336

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概率假设密度高斯混合实现的分量删减

doi: 10.3724/SP.J.1004.2011.01313

通讯作者:
闫小喜西安交通大学电子与信息工程学院综合自动化研究所博士研究生. 主要研究方向为多源信息融合, 多目标跟踪和随机有限集.E-mail: yanxiaoxi1981@gmail.com

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Component Pruning in Gaussian Mixture Implementation of Probability Hypothesis Density

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概率假设密度高斯混合实现的分量删减

doi: 10.3724/SP.J.1004.2011.01313

通讯作者: 闫小喜 西安交通大学电子与信息工程学院综合自动化研究所博士研究生. 主要研究方向为多源信息融合, 多目标跟踪和随机有限集.E-mail: yanxiaoxi1981@gmail.com

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Component Pruning in Gaussian Mixture Implementation of Probability Hypothesis Density

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出版历程

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通讯作者:
闫小喜西安交通大学电子与信息工程学院综合自动化研究所博士研究生. 主要研究方向为多源信息融合, 多目标跟踪和随机有限集.E-mail: yanxiaoxi1981@gmail.com