針對一些具有高度非線性模型, 以及非高斯雜訊的目標物追蹤環境之下, 粒子濾波器(Particle Filter) 的追蹤精準度都比擴展卡爾曼濾波器(Extended Kalman Filter)好, 又加上設計簡單, 因此相當適用於現實環境。惟因其粒子濾波器相當依靠於雜訊的機率模型, 所以只要雜訊的資訊錯誤, 其追蹤精準度將大幅下降。而基於成本函數之粒子濾波器(Cost Function-Based Particle Filter) 雖然犧牲了一點追蹤性能, 但由於其不需要雜訊的機率假設, 所以在任何環境的強健性更高。單目標追蹤系統中, 估測器由感測器所得到的單一筆量測資料, 不需判斷就可知道此量測為此目標物所被觀測到的訊號。但在多目標追蹤系統中, 感測器同一時間點接收到好幾筆量測資料, 並無法直接知道其量測值與目標物的歸屬關係, 因此需要資料關聯(Data Association) 技術來決定其歸屬性。將基於成本函數之粒子濾波器應用於多機動目標追蹤(Multiple Maneuvering Target Tracking), 由於不需要依靠雜訊的任何模型,能適用於無雜訊假設之環境。但其困難在於資料關聯與估測器之間的連結。因為經由大多數資料關聯的演算法, 得出的是一個概似機率函數(likelihood function) 來表示量測值與目標物的歸屬關係。而在基於成本函數之粒子濾波器中, 都是運用成本函數來做粒子的移動與權重更新, 並沒有運用到機率假設, 所以概似機率函數無法幫助基於成本函數之粒子濾波器來判斷量測值與目標物的歸屬關係。因此本篇論文除了會將基於成本函數之粒子濾波器應用於機動目標追蹤系統, 包括單目標物追蹤與多目標物追蹤, 在不同環境下做分析研究以外, 另一個重點就在於如何將資料關聯技術與基於成本函數之粒子濾波器做結合, 使多目標物追蹤系統不需要雜訊機率假設模型, 整個系統能更具有強健性(robust)。

For the environment of target tracking with highly non-linear models and non-Gaussian noise, the tracking performance of the particle filter is better than extended Kalman filter; in addition, the design of particle filter is simpler, so it is quite suitable for the realistic environment. However, particle filter depends on the probability model of the noise. If the knowledge of the noise is incorrect, the tracking performance of the particle filter will degrade severely. To tackle the problem, cost function-based particle filters have been studied. Though suffering from minor degradation on the performance, the cost function-based particle filters do not need probability assumptions of the noises. The application of cost function-based particle filters will be more robust in any realistic environment. Cost function-based particle filters will enable maneuvering multiple target tracking to be suitable for any environment because it does not depend on the noise model. The difficulty lies in the link between the estimator and data association. The likelihood function are generally obtained from the algorithm of the data association; while cost functions are used in the cost function-based particle filter for moving the particles and update the corresponding weights without probability assumptions on the noises. The thesis is focused on the combination of data association and cost function-based particle filter, in order to make the algorithm of multiple target tracking more robust in noisy environments.

1 緒論1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 全文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 機動目標追蹤的模型環境與問題4
2.1 單機動目標追蹤的模型環境. . . . . . . . . . . . . . . . . . . . . . 4
2.2 多機動目標追蹤的模型環境與問題. . . . . . . . . . . . . . . . . . . 6
2.2.1 模型環境與問題. . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 資料關聯的相關技術. . . . . . . . . . . . . . . . . . . . . . 7
3 針對機動目標物追蹤可用的估測演算法9
3.1 擴展式卡爾曼濾波器(Extended Kalman Filter) . . . . . . . . . . . 9
3.2 粒子濾波器(Particle Filter) . . . . . . . . . . . . . . . . . . . . . 10
3.2.1 蒙地卡羅取樣(Monte Carlo Sampling) . . . . . . . . . . . 11
3.2.2 貝斯重要性取樣(Bayesian Importance Sampling) . . . . . . 12
3.2.3 順序重要性取樣(Sequence Importance Sampling) . . . . . 14
3.2.4 重取樣(Resampling) . . . . . . . . . . . . . . . . . . . . . 14
3.2.5 粒子濾波器演算法綜述. . . . . . . . . . . . . . . . . . . . . 16
3.2.6 粒子濾波器優缺點. . . . . . . . . . . . . . . . . . . . . . . 18
3.3 基於成本函數之粒子濾波器(Cost Function-Based Particle Filter) . 19
3.3.1 成本參考之粒子濾波器(Cost Reference Particle Filter) . . . 20
3.3.2 成本參考之粒子濾波器綜述. . . . . . . . . . . . . . . . . . 25
3.3.3 成本參考之粒子濾波器的優缺點. . . . . . . . . . . . . . . . 27
4 成本參考之粒子濾波器應用於多目標物追蹤系統28
4.1 最近鄰法(Nearest Neighbor) . . . . . . . . . . . . . . . . . . . . . 28
4.2 結合最近鄰法與成本參考之粒子濾波器於多目標追蹤系統之應用. . . 30
4.2.1 最近鄰法之改進. . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.2 k-權重最近鄰法之結合成本參考之粒子濾波器. . . . . . . . . 32
5 電腦模擬分析與討論38
5.1 單機動目標追蹤環境之模擬. . . . . . . . . . . . . . . . . . . . . . 38
5.1.1 訊號模型與模擬環境設置. . . . . . . . . . . . . . . . . . . 38
5.1.2 單目標物追蹤之模擬. . . . . . . . . . . . . . . . . . . . . . 40
5.2 多機動目標追蹤環境之模擬. . . . . . . . . . . . . . . . . . . . . . 51
5.2.1 訊號模型與模擬環境設置. . . . . . . . . . . . . . . . . . . 51
5.2.2 兩個目標物之追蹤模擬. . . . . . . . . . . . . . . . . . . . . 51
5.2.3 多於兩個目標物之追蹤模擬. . . . . . . . . . . . . . . . . . 55
6 結論與建議59
參考文獻61

[1] S. M. Kay, Fundamentals of statistical signal processing : estimation theory. Prentice Hall PTR, 1993.
[2] R. A. Singer and R. G. Sea, “New results in optimizing surveillance system tracking and data correlation performance in dense multitarget environments,” IEEE Transactions on Automatic Control, vol. 18, pp. 571 – 582, December 1973.
[3] Y. Bar-Shalom and E. Tse, “Tracking in a cluttered environment with probabilistic data association,” Automatica, vol. 11, 1975.
[4] D. Reid, “An algorithm for tracking multiple targets,” IEEE Transactions on Automatic Control, vol. AC-24, pp. 843–845, December 1979.
[5] T. E. Fortmann, Y. Bar-shahom, and M. Scheffe, “Sonar tracking of multiple targets using joint probabilistic data association,” IEEE Journal of Oceanic Engineering, vol. OE-8, pp. 173–184, JULY 1983.
[6] J. M. Hammersley and K. W. Morton, “Poor man’s Monte Carlo,” Journal of the Royal Statistical Society B, vol. 16, pp. 23–38, 1954.
[7] J. E. Handschin and D. Q. Mayne, “Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering,” International Journal of Control, vol. 9, no. 5, pp. 547–559, 1969.
[8] H. Akashi and H. Kumamoto, “Random sampling approach to state estimation in switching environments,” Automatica, vol. 13, pp. 429–434, 1977.
[9] N. J. Gordon, D. J. Salmond, and A. F. M. Smith, “Novel approach to nonlinear/non-Gaussian Bayesian state estimation,” IEEE Proceedings on Radar and Signal Processing, vol. 140, no. 2, pp. 107–113, 1993.
[10] B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman filter : particle filter for tracking applications. Artech House Publishers, 2004.
[11] J. Miguez, M. F. Bugallo, and P. M. Djuric, “A new class of particle filters for random dynamic systems with unknown statistics,” EURASIP Journal on Applied Signal Processing, pp. 2278–2294, January 2004.
[12] X. R. Li and V. P. Jilkov, “A survey of maneuvering target tracking : dynamic models,” Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, April 2000.
[13] P. Smith and G. Buechler, “A branching algorithm for discriminating and tracking multiple objects,” IEEE Transactions on Automatic Control, vol. AC-20, pp. 101–104, February 1975.
[14] C. Morefield, “Application of 0-1 integer programming to multitarget tracking problems,” IEEE Transactions on Automatic Control, vol. 22, pp. 302–312, 1977.
[15] N. Ikoma, N. Ichimura, T. Higuchi, and H. Maeda, “Particle filter based method for maneuvering target tracking,” IEEE International Workshop on Intelligent Signal Processing, pp. 1–6, May 2001.
[16] Y. Yu and Q. Cheng, “Particle filters for maneuvering target tracking problem,”Signal Processing, vol. 86, pp. 195–203, January 2006.
[17] C. Hue, J.-P. L. Cadre, and P. Perez, “Sequential Monte Carlo methods for multiple target tracking and data fusion,” IEEE Transactions on signal processing, vol. 50, pp. 309–325, February 2002.
[18] O. Frank, J. Nieto, J. Gujvant, and S. Scheding, “Multiple target tracking using sequential Monte Carlo methods and statistical data association,”Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), vol. 3, pp. 2718–2723, October 2003.
[19] R. Karlsson and F. Gustafsson, “Monte Carlo data association for multiple target tracking,” Target Tracking: Algorithms and Applications ,IEE, vol. 1, pp. 13/1–13/5, October 2001.
[20] R. Douc, O. Cappe, and E. Moulines, “Comparison of resampling schemes for particle filtering,” Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, pp. 64–69, 2005.
[21] M. Bolic, P. M. Djuric, and S. Hong, “New resampling algorithms for particle filters,” Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal. Processing (ICASSP 03), Hong Kong, vol. 2, pp. II 589–592, April 2003.
[22] J. Carpenter, P. Clifford, and P. Fearnhead, “Improved particle filter for nonlinear problems,” IEE Proceedings of the Radar,Sonar Navig., vol. 146, February 1999.
[23] J. Miguez, “Analysis of selection methods for cost-reference particle filtering with applications to maneuvering target tracking and dynamic optimization,”Digital Signal Processing,ELSEVIER, vol. 17, pp. 787–807, July 2007.
[24] M. F. Bugallo, M. Vemula, and P. M. Djuric, “On proposal functions for cost-reference particle filtering,” Fourth IEEE Workshop on Sensor Array and Multichannel Processing, pp. 486–490, July 2006.
[25] J. Miguez, S. Xu, M. F. Bugallo, and P. M. Djuric, “Joint estimation of states and transition functions of dynamic systems using cost-reference particle filtering,” Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 05), pp. IV – 361–364, 2005.
[26] M. F. Bugallo, S. Xu, J. Miguez, and P. M. Djuric, “Maneuvering target tracking using cost reference particle filtering,” Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP04), vol. 3, pp. iii–968–971, May 2004.
[27] S. Xu, M. F. Bugallo, and P. M. Djuric, “Maneuvering target tracking with simplified cost reference particle filters,” Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 06), pp. IV – 937–940, 2006.
[28] M. F. Bugallo, S. Xu, and P. M. Djuric, “Performance comparison of EKF and particle filtering methods for maneuvering targets,” Elsevier Digital Signal Processing Journal, vol. 17, pp. 774–786, July 2007.