基于概率假设密度滤波方法的多目标跟踪技术综述

杨峰; 王永齐; 梁彦; 潘泉

doi:10.3724/SP.J.1004.2013.01944

基于概率假设密度滤波方法的多目标跟踪技术综述

doi: 10.3724/SP.J.1004.2013.01944

1.
西北工业大学自动化学院西安 710072

基金项目:

国家自然科学基金(61374159,61203224,61135001,61074179),中国航空科学基金(20125153027)资助

详细信息

作者简介:
杨峰西北工业大学副教授. 主要研究方向为信息融合, 目标跟踪, 雷达数据处理. E-mail: yangfeng@nwpu.edu.cn

计量
- 文章访问数: 2342
- HTML全文浏览量: 154
- PDF下载量: 3116
- 被引次数: 0
出版历程
- 收稿日期: 2013-07-01
- 修回日期: 2013-08-28
- 刊出日期: 2013-11-20

A Survey of PHD Filter Based Multi-target Tracking

1.
School of Automation, Northwestern Polytechnical University, Xi'an 710072

Funds:

Supported by National Natural Science Foundation of China (61374159, 61203224, 61135001, 61074179), Aviation Science Foundation of China (20125153027)

摘要

摘要: 概率假设密度 (Probability hypothesis density, PHD) 滤波方法在多目标跟踪、交通管制、图像处理以及多传感器管理等领域得到了广泛关注. 本文对基于PHD滤波方法的多目标跟踪技术的产生、发展及研究现状进行了综述, 主要包括PHD滤波器、PHD执行方法、峰值提取及航迹提取技术、多传感器多目标跟踪及多传感器管理、 PHD平滑器以及多目标跟踪性能评价指标等, 并对PHD滤波器的相关应用进行介绍. 最后, 基于现有PHD滤波进展, 提出了PHD滤波技术在多目标跟踪领域需要重点关注的若干问题.
- 概率假设密度 /
- 多目标跟踪 /
- 贝叶斯滤波 /
- 峰值及航迹提取
Abstract: Probability hypothesis density (PHD) filter has attracted much attention in multi-target tracking, traffic control, image processing, multi-sensor management and other fields. An overview of the emergence, the development and the present research situation of the PHD filter in target tracking is presented here. Special attention is paid to the following areas: PHD filter, its implementation method, the peak and track extraction technology, multi-sensor multi-target tracking, multi-sensor management, PHD smoother, the assessment metrics of multi-target tracking performance, and also the relevant applications. Finally, based on the progress of existing PHD filters, some key issues which need to be focused on for PHD filters in multi-target tracking are introduced.
- Probability hypothesis density (PHD) /
- multi-target tracking /
- Bayesflter /
- peak and track extraction

HTML全文

参考文献(111)

[1]	Mahler R P S. Multitarget Bayes fltering via frst-order multitarget moments. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1152-1178
[2]	Mahler R P. Statistical Multisource-Multitarget Informa-tion Fusion. Norwood: Artech House, 2007
[3]	Bar-Shalom Y. Tracking and Data Association. San Diego: Academic Press, 1988
[4]	Bar-Shalom Y, Kirubarajan T, Lin X. Probabilistic data association techniques for target tracking with applications to sonar, radar and EO sensors. IEEE Aerospace and Elec-tronic Systems Magazine, 2005, 20(8): 37-56
[5]	Musicki D, Evans R. Joint integrated probabilistic data association: JIPDA. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(3): 1093-1099
[6]	Blackman S S. Multiple hypothesis tracking for multiple target tracking. IEEE Aerospace and Electronic Systems Magazine, 2004, 19(1): 5-18
[7]	Erdinc O, Willett P, Bar-Shalom Y. A physical-space ap-proach for the probability hypothesis density and cardinal-ized probability hypothesis density flters. In: Proceedings of the 2006 Signal and Data Processing of Small Targets. Orlando, FL: SPIE, 2006. 623619-623619-12
[8]	Erdinc O, Willett P, Bar-Shalom Y. Probability hypoth-esis density flter for multitarget multisensor tracking. In: Proceedings of the 8th International Conference on Infor-mation Fusion. Philadelphia, PA: IEEE, 2005. 25-29
[9]	Mahler R. A theory of PHD flters of higher order in tar-get number. In: Proceedings of the 2006 Signal and Data Processing of Small Targets. Orlando, FL: SPIE, 2006.62350K-62350K-12
[10]	Mahler R. PHD flters of higher order in target number. IEEE Transactions on Aerospace and Electronic Systems,2007, 43(4): 1523-1543
[11]	Vo B T, Vo B N, Cantoni A. Performance of PHD based multi-target flters. In: Proceedings of the 9th Interna-tional Conference on Information Fusion. Florence: IEEE,2006. 1-8
[12]	Mahler R. The multisensor PHD flter: I. General solution via multitarget calculus. In: Proceedings of the 2009 SPIE Defense, Security, and Sensing on International Society for Optics and Photonics. Orlando, FL: SPIE, 2009. 73360D-73360D-12
[13]	Mahler R, Lockheed Martin M S, Eagan M N. Second-generation PHD/CPHD flters and multitarget calculus. In: Proceedings of the 2009 Signal and Data Processing of Small Targets. Orlando, FL: SPIE, 2009, 7445: 74450I
[14]	Vo B N, Singh S, Boucet A. Sequential Monte Carlo meth-ods for multi-target fltering with random fnite sets. IEEE Transactions on Aerospace and Electronic Systems. 2005,41(4): 1224-1245
[15]	Vo B N, Ma W K. The Gaussian mixture probability hy-pothesis density flter. IEEE Transactions on Signal Pro-cessing, 2006, 54(11): 4091-4104
[16]	Clark D, Vo B T, Vo B N. Gaussian particle implemen-tations of probability hypothesis density flters. In: Pro-ceedings of the 2007 IEEE Aerospace Conference. Big Sky, MT: IEEE, 2007. 1-11
[17]	Ouyang C, Ji H B. Weight over-estimation problem in GMP-PHD flter. Electronics Letters, 2011, 47(2):139-141
[18]	Nandakumaran N, Sutharsan S, Tharmarasa R, Lang T, Kirubarajan T, Kirubarajan T. Rao-blackwellised approx-imate conditional mean probability hypothesis density fl-tering. In: Proceedings of the 2009 Signal and Data Pro-cessing of Small Targets. Orlando, FL: SPIE, 2009, 7445:74450J-1
[19]	Melzi M, Ouldali A. Joint multiple target tracking and classifcation using the unscented Kalman particle PHD fl-ter. In: Proceedings of the 9th International New Circuits and Systems Conference. Bordeaux: IEEE, 2011. 534-537
[20]	Pace M, Zhang H L. Grid based PHD fltering by fast Fourier transform. In: Proceedings of the 14th Interna-tional Conference on Information Fusion. Chicago, IL: IEEE, 2011. 1-8
[21]	Clark D E, Bell J. Convergence results for the particle PHD flter. IEEE Transactions on Signal Processing, 2006,54(7): 2652-2661
[22]	Johansen A M, Singh S S, Doucet A, Vo B N. Convergence of the SMC implementation of the PHD flter. Methodol-ogy and Computing in Applied Probability, 2006, 8(2):265-291
[23]	Clark D E, Vo B N. Convergence analysis of the Gaussian mixture PHD flter. IEEE Transactions on Signal Process-ing, 2007, 55(4): 1204-1212
[24]	Ristic B, Clark D E, Vo B N. Improved SMC implemen-tation of the PHD flter. In: Proceedings of the 13th In-ternational Conference on Information Fusion. Edinburgh, UK: IEEE, 2010. 1-8
[25]	Pace M, Del Moral P, Caron F. Comparison of implemen-tations of Gaussian mixture PHD flters. In: Proceedings of the 13th International Conference on Information Fu-sion. Edinburgh, UK: IEEE, 2010. 1-8
[26]	Fearnhead P, Clifford P. On-line inference for hidden Markov models via particle flters. Journal of the Royal Statistical Society: Series B (Statistical Methodology),2003, 65(4): 887-899
[27]	Mahler R. Linear-complexity CPHD flters. In: Proceed-ings of the 13th International Conference on Information Fusion. Edinburgh, UK: IEEE, 2010. 1-8
[28]	Macagnano D, Freitas de Abreu G T. Adaptive gating for multitarget tracking with Gaussian mixture flters. IEEE Transactions on Signal Processing, 2012, 60(3):1533-1538
[29]	Clark D, Ristic B, Vo B N, Vo B T. Bayesian multi-object fltering with amplitude feature likelihood for unknown ob-ject SNR. IEEE Transactions on Signal Processing, 2010,58(1): 26-37
[30]	Lin L, Bar-Shalom Y, Kirubarajan T. Data association combined with the probability hypothesis density flter for multitarget tracking. In: Proceedings of the the 2004 SPIE conference on Signal and Data Processing on Small Tar-gets. Orlando, Florida: SPIE, 2004. 464-475
[31]	Panta K, Vo B N, Singh S, Doucet A. Probability hypoth-esis density flter versus multiple hypothesis tracking. In: Proceedings of the 2004 SPIE Conference on Signal Pro-cessing, Sensor Fusion and Target Recognition. Orlando, FL: SPIE, 2004. 284-295
[32]	Papi F, Battistelli G, Chisci L, Morrocchi S, Farina A, Graziano A. Multitarget tracking via joint PHD fltering and multiscan association. In: Proceedings of the 12th International Conference on Information Fusion. Seattle, WA: IEEE, 2009. 1163-1170
[33]	Lin L, Bar-Shalom Y, Kirubarajan T. Track labeling and PHD flter for multitarget tracking. IEEE Transactions on Aerospace and Electronic Systems, 2006, 42(3): 778-795
[34]	Danu D G, Lang T, Kirubarajan T. Assignment-based par-ticle labeling for PHD particle flter. In: Proceedings of the2009 SPIE conference on Signal and Data Processing on Small Targets. Orlando, FL: SPIE, 2009, 7445: 74450D-1
[35]	Clark D E, Bell J. Multi-target state estimation and track continuity for the particle PHD flter. IEEE Transac-tions on Aerospace and Electronic Systems, 2007, 43(4):1441-1453
[36]	Erdinc O, Willett P, Bar-Shalom Y. The bin-occupancy flter and its connection to the PHD flters. IEEE Trans-actions on Signal Processing, 2009, 57(11): 4232-4246
[37]	Dunne D, Kirubajaran T. Weight partitioned probability hypothesis density flters. In: Proceedings of the 14th In-ternational Conference on Information Fusion. Chicago, IL: IEEE, 2011. 1-8
[38]	Panta K, Clark D E, Vo B N. Data association and track management for the Gaussian mixture probability hypoth-esis density flter. IEEE Transactions on Aerospace and Electronic Systems, 2009, 45(3): 1003-1016
[39]	Streit R L. Multisensor multitarget intensity flter. In: Pro-ceedings of the 11th International Conference on Informa-tion Fusion. Cologne: IEEE, 2008. 1-8
[40]	Streit R L, Stone L D. Bayes derivation of multitarget in-tensity flters. In: Proceedings of the 11th International Conference on Information Fusion. Cologne, Germany: IEEE, 2008. 1-8
[41]	Mahler R. The multisensor PHD flter: II. Erroneous solu-tion via `Poisson magic'. In: Proceedings of the 2009 SPIE Defense, Security, and Sensing on International Society for Optics and Photonics. Orlando, FL: SPIE, 2009. 73360D-73360D-12
[42]	Schikora M, Bender D, Koch W, Cremers D. Multitarget, multisensor localization and tracking using passive anten-nas and optical sensors on UAVs. In: Proceedings of the2010 Security and Defence on International Society for Op-tics and Photonics. Bellingham, WA: SPIE, 2010. 783305-783305-9
[43]	Liu W F, Wen C L. A linear multisensor PHD flter using the measurement dimension extension approach. In: Pro-ceedings of the 2nd International Conference on Advances in Swarm Intelligence. Berlin, Heidelberg: Springer, 2011.486-493
[44]	Delande E, Duflos E, Vanheeghe P, Heurguier D. Multi-sensor PHD: construction and implementation by space partitioning. In: Proceedings of the 2011 IEEE Interna-tional Conference on Acoustics, Speech, and Signal Pro-cessing. Prague, Czech Republic: IEEE, 2011. 3632-3635
[45]	Meng F B, Hao Y L, Xia Q X, Ouyang T S, Zou W. A particle PHD flter for multi-sensor multi-target tracking based on sequential fusion. In: Proceedings of the 2009 International Conference on Information Engineering and Computer Science. Wuhan, China: IEEE, 2009. 1-5
[46]	Mahler R. Approximate multisensor CPHD and PHD fl-ters. In: Proceedings of the 13th International Conference on Information Fusion. Edinburgh, UK: IEEE, 2010. 1-8
[47]	Anderson B D O, Moore J B. Optimal Filtering. Engle-wood Cliffs, NJ: Prentice-Hall, 1979
[48]	Harvey A C. Forecasting, Structural Time Series Models and the Kalman Filter. New York: Cambridge University Press, 1989
[49]	Bar-Shalom Y, Li X R. Multitarget-Multisensor Tracking: Principles and Techniques. Storrs, CT: University of Con-necticut, 1995
[50]	Bar-Shalom Y, Li X R, Kirubarajan T. Estimation with Applications to Tracking and Navigation. New York: Wi-ley, 2001
[51]	Clark D. Joint target-detection and tracking smoothers. In: Proceedings of the 2009 SPIE Defense, Security, and Sensing on International Society for Optics and Photonics. Orlando, FL: SPIE, 2009. 73360G-73360G-11
[52]	Mahler R P S. Statistical Multisource-Multitarget Infor-mation Fusion. Norwood: Artech House, 2007
[53]	Vo B T. Random Finite Sets in Multi-Object Filtering [Ph. D. dissertation], University ofWestern Australia, Aus-tralia, 2008
[54]	Vo B N, Vo B T, Mahler R P S. Closed-form solutions to forward-backward smoothing. IEEE Transactions on Sig-nal Processing, 2012, 60(1): 2-17
[55]	Clark D E, Vo B T, Vo B N. Forward-backward sequen-tial Monte Carlo smoothing for joint target detection and tracking. In: Proceedings of the 12th International Con-ference of Information Fusion. Seattle, WA: IEEE, 2009.899-906
[56]	Nandakumaran N, Punithakumar K, Kirubarajan T. Im-proved multi-target tracking using probability hypothesis density smoothing. In: Proceedings of the 2007 Signal and Data Processing of Small Targets. San Diego, CA: SPIE,2007, 6699: 66990M
[57]	Nandakumaran N, Kirubarajan T. Maneuvering target tracking using probability hypothesis density smoothing. In: Proceedings of the 2009 SPIE conference on Signal Pro-cessing, Sensor Fusion, and Target Recognition. Orlando, FL: SPIE, 2009, 7336: 73360F-1
[58]	Clark D E. First-moment multi-object forward-backward smoothing. In: Proceedings of the 13th International Con-ference of Information Fusion. Edinburgh: IEEE, 2010.1-6
[59]	Nagappa S, Clark D E. Fast sequential Monte Carlo PHD smoothing. In: Proceedings of the 14th International Con-ference of Information Fusion. Chicago, IL: IEEE, 2011.1-7
[60]	Rothrock R L, Drummond O E. Performance metrics for multiple-sensor multiple-target tracking. In: Proceedings of the 2000 International Society for Optics and Photonics. Orlando, FL: SPIE, 2000. 521-531
[61]	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
[62]	Schuhmacher D, Vo B T, Vo B N. A consistent met-ric for performance evaluation of multi-object flters. IEEE Transactions on Signal Processing, 2008, 56(8):3447-3457
[63]	Ristic B, Vo B N, Clark D. Performance evaluation of multi-target tracking using the OSPA metric. In: Proceed-ings of the 13th International Conference of Information Fusion. Edinburgh: IEEE, 2010. 1-7
[64]	Ristic B, Vo B N, Clark D, Vo B T. A metric for per-formance evaluation of multi-target tracking algorithms. IEEE Transactions on Signal Processing, 2011, 59(7):3452-3457
[65]	Nagappa S, Clark D E, Mahler R. Incorporating track uncertainty into the OSPA metric. In: Proceedings of the 14th International Conference of Information Fusion. Chicago, IL: IEEE, 2011. 1-8
[66]	Granstrom K, Lundquist C, Orguner U. A Gaussian mix-ture PHD flter for extended target tracking. In: Proceed-ings of the 13th International Conference on Information Fusion. Edinburgh: IEEE, 2010. 1-8
[67]	Sidenbladh H. Multi-target particle fltering for the proba-bility hypothesis density. In: Proceedings of the 6th Inter-national Conference of Information Fusion. Cairns, Aus-tralia: IEEE, 2003. 800-806
[68]	Ulmke M, Erdinc O, Willett P. GMTI tracking via the Gaussian mixture cardinalized probability hypothesis den-sity flter. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(4): 1821-1833
[69]	Kohlleppel R. Ground moving target tracking of PAMIR detections with a Gaussian mixture-PHD flter. In: Pro-ceedings of the 2011 International Radar Symposium. Leipzig: IEEE, 2011. 193-198
[70]	Sidenbladh H, Wirkander S L. Tracking random sets of vehicles in terrain. In: Proceedings of the 2003 Conference on Computer Vision and Pattern Recognition Workshop. Madison, Wisconsin, USA: IEEE, 2003. 98
[71]	Punithakumar K, Kirubarajan T, Sinha A. A sequential Monte Carlo probability hypothesis density algorithm for multitarget track-before-detect. In: Proceedings of the2005 SPIE. San Diego, California: SPIE, 2005, 5913:59131S
[72]	Tong H S, Zhang H, Meng H D, Wang X Q. Multitarget tracking before detection via probability hypothesis den-sity flter. In: Proceedings of the 2010 International Con-ference on Electrical and Computer Engineering. Wuhan, China: IEEE, 2010. 1332-1335
[73]	Habtemariam B K, Tharmarasa R, Kirubarajan T. PHD flter based track-before-detect for MIMO radars. Signal Processing, 2012, 92(3): 667-678
[74]	Punithakumar K, Kirubarajan T, Sinha A. A multiple-model probability hypothesis density flter for tracking ma-neuvering targets. In: Proceedings of the 2004 Signal and Data Proceedings of Small Targets. Orlando, FL: SPIE,2004. 113-121
[75]	Pasha A, Vo B, Tuan H D, Ma W K. Closed form PHD fltering for linear jump Markov models. In: Proceedings of the 9th International Conference on Information Fusion. Sunnyvale, CA: IEEE, 2006. 1-8
[76]	Pasha S A, Vo B N, Tuan H D, Ma W K. A Gaussian mixture PHD flter for jump Markov system models. IEEE Transactions on Aerospace and Electronic Systems, 2009,45(3): 919-936
[77]	Wood T M. Interacting methods for manoeuvre handling in the GM-PHD flter. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(4): 3021-3025
[78]	Ahlberg S, Hörling P, Jöred K, Mårtenson C, Neider G, Schubert J, Sidenbladh H, Svenson P, Svensson P, Undén, Walter J. The IFD03 information fusion demonstrator. In: Proceedings of the 7th International Conference on Infor-mation Fusion. Sunnyvale, CA: IEEE, 2004. 936-943
[79]	Clark D, Godsill S. Group target tracking with the Gaus-sian mixture probability hypothesis density flter. In: Pro-ceedings of the 3rd International Conference on Intelligent Sensors, Sensor Networks and Information. Melbourne, Qld.: IEEE, 2007. 149-154
[80]	Wang Y D, Wu J K, Kassim A A, Huang W M. Tracking a variable number of human groups in video using probabil-ity hypothesis density. In: Proceedings of the 18th Inter-national Conference on Pattern Recognition. Hong Kong, China: IEEE, 2006. 1127-1130
[81]	Gilholm K, Godsill S, Maskell S, Salmond D. Poisson mod-els for extended target and group tracking. In: Proceedings of the 2005 SPIE conference on Signal and Data Process-ing on Small Targets. San Diego, California, USA: SPIE,2005, 5913: 59130R
[82]	Mahler R. PHD flters for nonstandard targets, I: extended targets. In: Proceedings of the 12th International Con-ference on Information Fusion. Seattle, WA: IEEE, 2009.915-921
[83]	Subramaniam M, Tharmarasa R, McDonald M, Kirubara-jan T. Passive tracking with sensors of opportunity using passive coherent location. In: Proceedings of the 2008 In-ternational Society for Optics and Photonics. Orlando, FL: SPIE, 2008. 69691F-69691F-12
[84]	Kemper J, Hauschildt D. Passive infrared localization with a probability hypothesis density flter. In: Proceedings of the 7th Workshop on Positioning Navigation and Commu-nication. Dresden: IEEE, 2010. 68-76
[85]	Tobias M, Lanterman A D. Probability hypothesis density-based multitarget tracking with bistatic range and Doppler observations. IEE Proceedings-Radar, Sonar, and Naviga-tion, 2005, 152(3): 195-205
[86]	Balakwmar B, Sinha A, Kirubarajan T, Reilly J P. PHD fltering for tracking an unknown number of sources using an array of sensors. In: Proceedings of the 13th Workshop on Statistical Signal Processing. Novosibirsk: IEEE, 2005.43-48
[87]	Maggio E, Taj M, Cavallaro A. E±cient multitarget visual tracking using random fnite sets. IEEE Transactions on Circuits and Systems for Video Technology, 2008, 18(8):1016-1027
[88]	Pham N T, Huang W M, Ong S H. Tracking multiple ob-jects using probability hypothesis density flter and color measurement. In: Proceedings of the 2007 IEEE Inter-national Conference on Multimedia and Expo. Beijing, China, IEEE, 2007. 1511-1514
[89]	Juang R R, Levchenko A, Burlina P. Tracking cell motion using GM-PHD. In: Proceedings of the 2009 IEEE Inter-national Symposium on Biomedical Imaging: From Nano to Macro. Boston, MA: IEEE, 2009. 1154-1157
[90]	Battistelli G, Chisci L, Morrocchi S, Papi F, Benavoli A, Di Lallo A, Farina A, Graziano A. Tra±c intensity estimation via PHD fltering. In: Proceedings of the 2008 European Radar Conference. Amsterdam: IEEE, 2008. 340-343
[91]	Guerriero M, Coraluppi S, Willett P. Analysis of scan and batch processing approaches to static fusion in sensor net-works. In: Proceedings of the 2008 International Soci-ety for Optics and Photonics. Orlando, FL: SPIE, 2008.69690Z-69690Z-10
[92]	Mahler R. Multitarget sensor management of dispersed mobile sensors. Theory and Algorithms for Cooperative Systems, New York: Springer, 2005
[93]	Mahler R. Sensor management with non-ideal sensor dy-namics. In: Proceedings of the 2004 International Confer-ence on Information Fusion. Sunnyvale, CA: IEEE, 2004
[94]	El-Fallah A, Zatezalo A, Mahler R K, Donatelli D. Space-based sensor management and geostationary satellites tracking. In: Proceedings of the 2007 International Soci-ety for Optics and Photonics. Orlando, FL: SPIE, 2007.65670R-65670R-12
[95]	Zatezalo A, El-Fallah A, Mahler R K, Pham K. Joint search and sensor management for geosynchronous satel-lites. In: Proceedings of the 2008 International Society for Optics and Photonics. Orlando, FL: SPIE, 2008. 69680O-69680O-12
[96]	El-Fallah A, Zatezalo A, Mahler R K, Donatelli D. Dy-namic sensor management of dispersed and disparate sen-sors for tracking resident space objects. In: Proceedings of the 2008 International Society for Optics and Photonics. Orlando, FL: SPIE, 2008. 69680P-69680P-11
[97]	Zatezalo A, El-Fallah A, Mahler R K, Brown J. Dispersed and disparate sensor management for tracking low earth orbit satellites. In: Proceedings of the 2009 International Society for Optics and Photonics. Orlando, FL: SPIE,2009. 73360I-73360I-12
[98]	Mahler R, El-Fallah A. Unifed sensor management in un-known dynamic clutter. In: Proceedings of the 2010 Inter-national Society for Optics and Photonics. Orlando, FL: SPIE, 2010. 769811-769811-12
[99]	Tian Shu-Rong, Wang Guo-Hong, He You. Multi-target tracking with probability hypothesis density particle flter. Journal of Naval Aeronautical Engineering Institute, 2007,22(4): 417-420, 430 (田淑荣, 王国宏, 何友. 多目标跟踪的概率假设密度粒子滤波. 海军航空土程学院学报, 2007, 22(4): 417-420, 430)
[100]	Zhuang Ze-Sen, Zhang Jian-Qiu, Yin Jian-Jun. Rao-Blackwellized particle probability hypothesis density fl-ter. Acta Aeronautica et Astronautica Sinica, 2009, 30(4):698-705 (庄泽森, 张建秋, 尹建君. Rao-Blackwellized 粒子概率假设密度滤波算法. 航空学报, 2009, 30(4): 698-705)
[101]	Yin Y J, Zhang J Q, Zhuang Z S. Gaussian sum PHD flter-ing algorithm for nonlinear non-Caussian models. Chinese Journal of Aeronautics, 2008, 21(4): 341-351
[102]	Zhou Cheng-Xing, Liu Gui-Xi, Hou Lian-Yong, Zhong Xing-Zhi. Modifed Gaussian particle probability hypothe-sis density fltering algorithm. Control Theory and Appli-cations, 2011, 30(4): 1005-1008 (周承兴, 刘贵喜, 侯连勇, 钟兴质. 改进的高斯粒子概率假设密度滤波算法. 控制理论与应用, 2011, 30(4): 1005-1008)
[103]	Lian Feng, Han Chong-Zhao, Liu Wei-Feng, Yuan Xiang-Hui. Multiple-model probability hypothesis density smoother. Acta Automatica Sinica, 2010, 30(4): 939-950 (连峰, 韩崇绍, 刘伟峰, 元向辉. 多模型概率假设密度平滑器. 自动化学报, 2010, 30(4): 939-950)
[104]	Meng Fan-Bin, Hao Yan-Ling, Zhou Wei-Dong, Sun Feng. Sequential particle PHD flter algorithm based on radar and infrared sensor. Journal of Huazhong University of Science and Technology (Nature Science Edition), 2010,38(4): 14-17 (孟凡彬, 郝燕玲, 周卫东, 孙枫. 基于雷达和红外的序贯粒子PHD 滤波融合算法. 华中科技大学学报(自然科学版), 2010, 38(4):14-17)
[105]	Wu Jing-Jing, Hu Shi-Qiang. Probability hypothesis den-sity flter based multi-target visual tracking. Control and Decision, 2010, 25(12): 1861-1865 (吴静静, 胡士强. 基于概率假设密度的多目标视频跟踪算法. 控制与决策, 2010, 25(12): 1861-1865)
[106]	Huang Zhi-Bei, Sun Shu-Yan, Wu Jian-Kang. Multiple hy-potheses detection with Gaussian mixture probability hy-pothesis density flter for multi-target trajectory tracking. Journal of Electronics and Information Technology, 2010,32(6): 1289-1294 (黄志蓓, 孙树岩, 吴健康. 多元假设检验GMPHD 轨迹跟踪. 电子与信息学报, 2010, 32(6): 1289-1294)
[107]	Tan Shun-Cheng, Wang Guo-Hong, Wang Na, Jia Shu-Yi. Multi-target tracking based on PHD flter and data association. Systems Engineering and Electronics, 2011,33(4): 734-737 (谭顺成, 王国宏, 王娜, 贾舒宜. 基于PHD 滤波和数据关联的多目标跟踪. 系统工程与电子技术, 2011, 33(4): 734-737)
[108]	Wang Xiao, Han Chong-Zhao. A probability hypothesis density flter with multiple models for maneuvering tar-get tracking. Journal of Xi0an Jiaotong University, 2011,45(12): 1-5 (王晓, 韩崇昭. 用于机动目标跟踪的多模型概率假设密度滤波器. 西安交通大学学报, 2011, 45(12): 1-5)
[109]	Yan Xiao-Xi, Han Chong-Zhao. Multiple target tracking algorithm based on online estimation of target birth inten-sity. Acta Automatica Sinica, 2011, 37(8): 963-972 (闫小喜, 韩崇昭. 基于目标出生强度在线估计的多目标跟踪算法. 自动化学报, 2011, 37(8): 963-972)
[110]	Wang Pin, Xie Wei-Xin, Liu Zong-Xiang, Guo Dong. The course angle aided Gaussian mixture PHD fuzzy flter. Sig-nal Processing, 2011, 27(9): 1319-1324 (王品, 谢维信, 刘宗香, 郭栋. 航向角辅助的高斯混合PHD 模糊滤波方法. 信号处理, 2011, 27(9): 1319-1324)
[111]	Lian Feng, Han Chong-Zhao, Liu Wei-Feng, Yuan Xiang-Hui. Convergence analysis of the Gaussian mixture extended-target probability hypothesis density flter. Acta Automatica Sinica, 2012, 38(8): 1343-1352 (连峰, 韩崇昭, 刘伟峰, 元向辉. 高斯混合扩展目标概率假设密度滤波器的收敛性分析. 自动化学报, 2012, 38(8): 1343-1352)