基于FISST理论的多目标跟踪技术研究
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摘要
目标跟踪技术一直是一个备受关注的研究热点,其在军事、民用领域都发挥着巨大的作用,有着重要的应用价值和广阔的发展前景。有限集统计学(Finite Set Statistics: FISST)理论在最近十多年开始应用于目标跟踪领域,由于其表现出来的对问题的直观描述性、理论推导的严谨性等特点,受到各国学者广泛关注和深入研究。针对该理论框架下最优多目标Bayes滤波器极高的复杂度问题,近年来先后有学者提出基于FISST理论的近似多目标跟踪算法,如概率假设密度(Probability Hypothesis Density: PHD)滤波、带有势分布的概率假设密度(Cardinalized Probability Hypothesis Density: CPHD)滤波等。尽管如此,概率假设密度类滤波器的运算复杂度在密集杂波背景下仍然过高;而另一方面,基于FISST理论的多目标跟踪算法通常未能给出前后时刻多目标状态估计的关联关系。
本文在对PHD滤波、CPHD滤波进行深入研究的基础上,重点研究了密集杂波背景下PHD粒子滤波实现的改进算法、多模型CPHD滤波技术以及PHD多目标跟踪算法中的航迹形成等问题。具体研究内容如下:
针对密集杂波背景下PHD滤波的粒子近似实现算法运算复杂度过高的缺点,借鉴传统跟踪算法中跟踪门限的思想提出了一种改进算法。该算法通过添加门限滤除杂波以降低滤波过程中的运算量。实验结果表明,在不影响滤波结果的情况下,改进的PHD滤波粒子近似实现算法提高了滤波效率。
针对多机动目标的跟踪问题,本文提出了一种多模型扩展的CPHD滤波算法。该算法将传统的多模型方法与CPHD滤波相结合,在给出该算法详细的理论推导后,给出了该算法的粒子近似实现方法。实验结果表明,该算法对于多机动目标跟踪问题能够提供优越的性能。
最后,本文针对基于FISST理论的多目标跟踪算法无法给出目标航迹的问题,提出了一种改进的通过添加粒子标签的航迹形成方法。与现有方法相比,该方法能够更好的处理存在衍生目标、目标交叉、杂波等复杂场景的航迹形成问题。实验结果验证了上述结论。
Target tracking technique is a vital research topic for a long time, especially in the military and civilian areas. This technique has important application value and broad development prospects. Since the past ten years, Finite set statistics (FISST) theory has been beginning to be used for target tracking widely. Due to its demonstrated intuitive description to the problem and rigorous derivation, the FISST theory has attracted many research interests. Restricted to the computational intractability of the optimal Bayes filter in the FISST framework, some scholars have proposed many approximate algorithms based on the FISST theory for tracking multiple targets, such as the probability hypothesis density (PHD) filter, the Cardinalized probability hypothesis density (CPHD) filter, etc. Nevertheless, their computational complexity is still high in dense clutter environment. On the other hand, multi-target tracking algorithms based on the FISST theory always fail to give the track-value of the estimated targets.
In this paper, based on the in-depth study on the PHD and CPHD filters, we give the improved algorithm for particle PHD filter in a dense cluttered environment, multiple model extension of the CPHD filter and improved tracks-value estimation algorithm for the PHD filter. The specific research contents are as follows: When the clutter is dense, the computational complexity of approximation particle algorithm for the PHD filter is too high. Inspired by the idea of threshold in traditional tracking algorithm, we propose an improved particle algorithm. The proposed algorithm reduces the amount of computation by adding threshold to filter the clutter. The experimental results show that, the improved particle PHD filter improves the filtering efficiency, without affecting the filtering results.
Aiming at the tracking problem of multiple maneuvering targets, this paper presents a multiple model CPHD filter. The introduced filter combines the traditional multiple model method and the CPHD filter. After giving detailed theoretical derivation, we achieve the particle approximation method of the multiple model CPHD filter. Experimental results show that, the filter can provide superior performance for tracking multiple maneuvering targets.
Finally, to account for the point that multi-target tracking algorithms based on the FISST theory can not give the tracks, we propose an improved track-value estimation method by adding the label to particles. Compared to the existing methods, the improved method treats complex scenes better, as spawning targets, target crossings and/or clutter. Experimental results validate the above conclusions.
本文在对PHD滤波、CPHD滤波进行深入研究的基础上,重点研究了密集杂波背景下PHD粒子滤波实现的改进算法、多模型CPHD滤波技术以及PHD多目标跟踪算法中的航迹形成等问题。具体研究内容如下:
针对密集杂波背景下PHD滤波的粒子近似实现算法运算复杂度过高的缺点,借鉴传统跟踪算法中跟踪门限的思想提出了一种改进算法。该算法通过添加门限滤除杂波以降低滤波过程中的运算量。实验结果表明,在不影响滤波结果的情况下,改进的PHD滤波粒子近似实现算法提高了滤波效率。
针对多机动目标的跟踪问题,本文提出了一种多模型扩展的CPHD滤波算法。该算法将传统的多模型方法与CPHD滤波相结合,在给出该算法详细的理论推导后,给出了该算法的粒子近似实现方法。实验结果表明,该算法对于多机动目标跟踪问题能够提供优越的性能。
最后,本文针对基于FISST理论的多目标跟踪算法无法给出目标航迹的问题,提出了一种改进的通过添加粒子标签的航迹形成方法。与现有方法相比,该方法能够更好的处理存在衍生目标、目标交叉、杂波等复杂场景的航迹形成问题。实验结果验证了上述结论。
Target tracking technique is a vital research topic for a long time, especially in the military and civilian areas. This technique has important application value and broad development prospects. Since the past ten years, Finite set statistics (FISST) theory has been beginning to be used for target tracking widely. Due to its demonstrated intuitive description to the problem and rigorous derivation, the FISST theory has attracted many research interests. Restricted to the computational intractability of the optimal Bayes filter in the FISST framework, some scholars have proposed many approximate algorithms based on the FISST theory for tracking multiple targets, such as the probability hypothesis density (PHD) filter, the Cardinalized probability hypothesis density (CPHD) filter, etc. Nevertheless, their computational complexity is still high in dense clutter environment. On the other hand, multi-target tracking algorithms based on the FISST theory always fail to give the track-value of the estimated targets.
In this paper, based on the in-depth study on the PHD and CPHD filters, we give the improved algorithm for particle PHD filter in a dense cluttered environment, multiple model extension of the CPHD filter and improved tracks-value estimation algorithm for the PHD filter. The specific research contents are as follows: When the clutter is dense, the computational complexity of approximation particle algorithm for the PHD filter is too high. Inspired by the idea of threshold in traditional tracking algorithm, we propose an improved particle algorithm. The proposed algorithm reduces the amount of computation by adding threshold to filter the clutter. The experimental results show that, the improved particle PHD filter improves the filtering efficiency, without affecting the filtering results.
Aiming at the tracking problem of multiple maneuvering targets, this paper presents a multiple model CPHD filter. The introduced filter combines the traditional multiple model method and the CPHD filter. After giving detailed theoretical derivation, we achieve the particle approximation method of the multiple model CPHD filter. Experimental results show that, the filter can provide superior performance for tracking multiple maneuvering targets.
Finally, to account for the point that multi-target tracking algorithms based on the FISST theory can not give the tracks, we propose an improved track-value estimation method by adding the label to particles. Compared to the existing methods, the improved method treats complex scenes better, as spawning targets, target crossings and/or clutter. Experimental results validate the above conclusions.
引文
[1]张洪建.基于有限集统计学的多目标跟踪算法研究[D].上海:上海交通大学. 2009.
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[2]I. R. Goodman, R. Mahler and H. Nguyen. Mathematics of Data Fusion[M]. Boston: Kluwer Academic Publishers, 1997.
[3]R. Mahler. Statistical Multisource Multitarget Information Fusion[M]. Norwood MA: Artech House, 2007.
[4]R. Mahler. Multitarget Bayes Filtering Via First-order Multitarget Moments[J]. IEEE Transactions on Aerospace and Electronics Systems, 2003, 39(3): 1152-1178.
[5]Y. Bar-Shalom and T E. Fortman. Tracking and Data Association[M]. New York, Academic Press, January 1988. [ 6 ]A.J. Jaffer and Y. Bar-Shalom. on Optimal Tracking in Multiple Target Environments[J]. Proceedings of the third Symposium on Non-Linear Estimation Theory and Its Applications, San Diego, CA, September, 1972, pp: 112-117.
[7]Y. Bar-Shalom, E. Tse. Tracking in a cluttered environment with probabilistic data association[J], Automatica, 1975, 11(5): 451-460.
[8]Y. Bar-Shalom. Extension of the Probabilistic Data Association Filter in Multitarget Tracking[J]. Proceeding of the Fifth Symposium on Non-Linear Estimation, 1974, pp: 16-21. [ 9 ]Dezert, Y. Bar-Shalom. Joint probabilistic data association for autonomous navigation[J], IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(4): 1275-1286.
[10]T.E. Fortman, Y. Bar-Shalom, M. Scheffe. Sonar Tracking of Multiple Targets Using Joint Probabilistic Data Association[J]. IEEE Journal of Oceanic Engineering, 1983, 8(3): 173-184.
[11]D.B. Reid. An Algorithm for Tracking Multiple Targets[C]. Proceedings of the 17th IEEE Conference on Decision and Control, 1978, pp: 1202-1211
[12]S.S. Blackman. Multiple hypothesis tracking for multiple target tracking[J]. IEEE Aerospace and Electronics Systems. 2004, 19(1): 5-18.
[13]周宏仁,敬忠良,王培德,机动目标跟踪[M].北京:国防工业出版社. 1991. [ 14 ]Y. Bar-Shalom. Multitarget-multisensor tracking: Advanced Applications[M]. Norwood MA: Artech House, 1990.
[15]S.S. Blackman and R.Popoli, Design and analysis of Modern Tracking System[M]. Norwood, MA: Artech House, 1999.
[16]L.D. Stone, C.A. Barlow and T.L. Corwin. Bayesian Multiple Target Tracking[M]. Norwood, MA: Artech House, 1999.
[17]M. Baudin. Multidimensional point processes and random closed sets[J]. Journal of Applied Prob., 21(1984), 173-178, 1984.
[18]D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes[M]. New York: Springer-Verlag, 1988.
[19]A.F. Karr. Point Processes and Their Statistical Inference (2nd ed.)[M]. Marcel Dekker, 1991.
[20]M. Vihola. Random sets for multitarget tracking and data fusion[D]. Licentiate Thesis, Tampere University of Technology. 2004.
[21]Y. Ho, R. Lee. A Bayesian approach to problems in stochastic estimation and control[J]. IEEE Transactions on Automatic Control. Volume 9, issue4, pp. 333-339, Oct 1964.
[22]R. Mahler. Global integrated data fusion[C]. In proceedings of the 7th National Symposium on Sensor Fusion, Vol.1, Sandia National Laboratories Albuquerque, NM, pp. 187-199, 1994.
[23]B.D. Ripley. Locally finite random sets: foundations for point process theory[J]. Annals of Probability, 4, 6(1976), 983-994.
[24]D.L. Snyder and M.I. Miller. Random Point Processes in Time and Space (2nd ed.)[M]. New York: Springer, 1991.
[25]D. Stoyan, W.S. Kendall and J. Meche. Stochastic Geometry and Its Applications (2nd ed.) [M]. New York: Wiley, 1995.
[26]B.-N. Vo, S. Singh, and A. Doucet. Sequential Monte Carlo implementation of the PHD filter for multi-target tracking[C]. In Proceedings of the International Conference on Information Fusion, Cairns, Australia, 2003, pp. 792-799.
[27]B.-N. Vo, S. Singh, and A. Doucet. Random finite sets and sequential Monte Carlo methods in multi-target tracking[C]. In Proceedings of the International Conference on Radar, Adelaide, Australia, Sept. 3-5, 2003, pp. 486-491.
[28]B.-T. Vo, and B.-N. Vo and S. Singh. Sequential Monte Carlo methods for static parameter estimation in random set models[C]. In Proceedings of the 2nd International Conference on Intelligent Sensors, Sensor Networks, and Information Processing, Melbourne, Australia, December. 5-8, 2004, pp. 313-318.
[29]B.-N. Vo, S. Singh, and A. Doucet. Sequential Monte Carlo methods for multi-target filtering with random finite sets[J]. IEEE Transactions on Aerospace and Electronics Systems. 2005, 41(4): 1224-1245.
[30]A. Johansen, S. Singh, A. Doucet and B.-N. Vo, Convergence of the SMC implementation of the PHD filter[J]. Methodol. Comput. Appl. Probab. , Vol. 8, No. 2, pp. 265-291, 2006.
[31]T. Zajic and R. Mahler. A particle-system implementation of the PHD multi-target tracking filter[J]. Proc. SPIE, Signal Processing, Sensor Fusion Target RecognitionXII, Vol. 5096, pp. 291-299, 2003.
[32]H. Sidenbladh, S.-L. Wirkander. Tracking random sets of vehicles in terrain[C]. In Proceedings of the 2nd IEEE Workshop on Multi-Object Tracking. Madison, WI, 2003.
[33]B.-N. Vo and W.-K. Ma. A closed-form solution for the probability hypothesis density filter[C]. In Proceedings of the 8th International Conference on Information Fusion, Philadelphia, PA, July 25-29, 2005, 856-863.
[34]B.-N. Vo and W.-K. Ma. The Gaussian Mixture Probability Hypothesis Density Filter[J]. IEEE Transactions on Signal Processing, 2006, 54(11): 4091-4104.
[35]D. Clark, B.-N. Vo. Convergence Analysis of the Gaussian Mixture PHD filter[J]. IEEE Transactions On Signal Processing, April 2007, 55(4): 1204-1211.
[36]D. Clark, B.-T. Vo, B.-N. Vo and S. Godsill. Gaussian Mixture Implementations of PHD Filters for Non-linear Dynamical Models[C]. Proc. of the IET Conf. , Birmingham, UK, April 15-16, 2008.
[37]B.-T. Vo, B.-N. Vo and A. Cantoni. The cardinalized probability hypothesis filter for linear Gaussian multi-target models[C]. In Proceedings of the 40th Annual Conference on Information Sciences & Systems, Princeton, NJ, Mar. 22-24, 2006.
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