探討目標物的追蹤問題中，卡爾曼濾波器 (Kalman filter,KF) 是現有估測系統中經常使用的演算法，但能否因應目標物狀態之變化，往往取決於狀態變化模型的假設。交互多模(interacting multiple model, IMM) 估測器可藉著多個平行卡爾曼濾波器之間的交互作用，利用模型機率的更新，使每個平行卡爾曼濾波器具備動態的模型機率分配。當此類估測器用於追蹤一般移動目標物之線性動態運動，使用兩個卡爾曼濾波器通常能獲得良好的追蹤效能，可針對目標物的不同運動狀態進行良好的追蹤，而模型機率也會隨著模型之估測精準度進行疊代與更新。在本論文中，我們採用「合作式交互多模演算法 (cooperative IMM-based algorithm)」，利用多感測器資料融合的技術，將多個同類型的交互多模估測器所分別產生的資訊進行資料共享，以避免交互多模估測器因訊號資料量不足或週遭環境干擾等因素影響所預期之追蹤精準度。藉由估測器內部的估測值、模型機率和模型轉移機率矩陣將各個交互多模估測器處理之後的資訊進行資料融合。這種由交互多模估測器延伸成的融合架構，和一般使用分散式交互多模估測器的融合架構不同，不需要額外的融合中心 (fusion center) 進行資料融合，可直接在資訊處理平台執行演算法時，同步進行資訊交換和權重分配，避免誤差持續累加。使用多感測器資料融合的技術，可能會因為許多不同的環境因素，導致未能達到所預期之追蹤精準度，例如不同類型的感測器對於移動目標物的量測訊號會被不同程度的量測雜訊所影響。由電腦模擬結果可得知，合作式交互多模演算法可藉由受到量測雜訊影響較小的估測器對受到量測雜訊影響較大的估測器進行輔助以提升追蹤效能；同時若各感測器受到量測雜訊影響相同的情形之下，合作式交互多模演算法相較於交互多模演算法可獲得較佳的估測效能。除此之外，若有部分感測器無法順利感測資訊，導致對應之估測器內部演算法中的模型機率無法更新，且卡爾曼濾波器只能進行預測而不能進行更正的步驟，以上的種種問題會使得對應之估測器無法正常追蹤目標物。此時可對原本的合作式交互多模演算法略作改良，經由調整權重分配和模型機率，使得對估測值作權重分配時採信其他估測器所傳送過來的資訊，透過電腦模擬結果可得知，可在部分感測器無法順利感測資訊時能夠持續追蹤目標物，且相較於改良前的合作式交互多模演算法能獲得較佳的估測效能。

In solving target tracking problems, the Kalman filter (KF) is a systematic estimation algorithm. Whether the state of a moving target adapts to the changes in the observations depends on the model assumptions. The interacting multiple model (IMM) algorithm uses interaction of a bank of parallel KFs by updating associated model probabilities. Every parallel KF has its model probability adjusted by the dynamic system. For moving targets of different dynamic linear models, an IMM with two KFs generally performs well. In this thesis, in order to improve the performance of target tracking and state estimation, multi-sensor data fusion technique will be used. Same types of IMMs can be incorporated in the cooperative IMM-based algorithm. The IMM-based estimators exchange with each other the estimates, model robabilities and model transition probabilities. A distributed algorithm for multi-sensor tracking usually needs a fusion center that integrates decisions or estimates, but the proposed cooperative IMM-based algorithm does not use the architecture. Cooperative IMM estimator structures exchange weights and estimates on the platforms to avoid accumulation of errors. Performance of data fusion may degrade due to different kinds of undesirable environmental effects. The simulations show that an IMM estimator with smaller measurement noise level can be used to compensate the other IMM, which is affected by larger measurement noise. In addition, failure of a sensor will cause the problem that model probabilities can not be updated in the corresponding estimator. Kalman filters will not be able to perform state correction for the moving target. To tackle the problem, we can use the estimates from other IMM estimators by adjusting the corresponding weights and model probabilities. The simulations show that the proposed cooperative IMM structure effectively improve the tracking performance.

論文審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
圖次. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 目標物追蹤與估測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 資料融合. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 線性等速度模型. . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 線性等加速度模型. . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 卡爾曼濾波器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 交互多模估測器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 合作式交互多模估測器設計緣由. . . . . . . . . . . . . . . . . . . . . 17
2.5.1 感測器與交互多模估測器的結合. . . . . . . . . . . . . . . . . 17
2.5.2 合作式交互多模估測器與分散式交互多模估測器的比較. . . . . 18
2.6 合作式交互多模估測器架構. . . . . . . . . . . . . . . . . . . . . . . 19
2.7 合作式交互多模演算法流程. . . . . . . . . . . . . . . . . . . . . . . 21
2.7.1 更新權重. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7.2 對估測值作權重分配. . . . . . . . . . . . . . . . . . . . . . . 25
2.7.3 卡爾曼濾波器. . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7.4 計算模型的概似函數. . . . . . . . . . . . . . . . . . . . . . . 27
2.7.5 更新模型機率. . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7.6 結合估測值與共變數矩陣. . . . . . . . . . . . . . . . . . . . . 27
3 合作式交互多模演算法所遭遇之困境及其改良架構. . . . . . . . . . . . . . . 29
3.1 合作式交互多模演算法的優點以及會遭遇到的困境. . . . . . . . . . . 29
3.2 基於量測雜訊變化的合作式交互多模演算法之改良架構. . . . . . . . . 30
3.2.1 量測雜訊的標準差假設檢定法結合滑動視窗之資料共享鑑別. . . 31
3.2.2 基於資料共享鑑別的合作式交互多模演算法之改良架構. . . . . 33
3.3 量測訊號發生異常時的合作式交互多模演算法之改良架構. . . . . . . . 37
3.3.1 更新和調整權重. . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 調整權重後對估測值重新作權重分配. . . . . . . . . . . . . . . 42
3.3.3 使用卡爾曼濾波器作預測步驟. . . . . . . . . . . . . . . . . . 43
3.3.4 維持模型機率. . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.5 結合卡爾曼濾波器之預測步驟的預測值與共變數矩陣. . . . . . 45
4 合作式交互多模演算法模擬與分析. . . . . . . . . . . . . . . . . . . . . . . 46
4.1 模擬環境參數設置. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 交互多模演算法與合作式交互多模演算法模擬分析(兩個估測器為例) . . 48
4.2.1 Scenario 1 (估測器受到量測雜訊的影響相同) . . . . . . . . . 51
4.2.2 Scenario 2 (估測器受到量測雜訊的影響相異) . . . . . . . . . 54
4.3 交互多模演算法與合作式交互多模演算法模擬分析(三個估測器為例) . . 59
4.3.1 Scenario 3 (估測器受到量測雜訊的影響相同) . . . . . . . . . 59
4.3.2 Scenario 4 (估測器受到量測雜訊的影響相異) . . . . . . . . . 59
4.4 基於量測雜訊變化的合作式交互多模演算法之改良架構模擬分析與比較. 66
4.5 量測訊號發生異常時的合作式交互多模演算法模擬分析與比較. . . . . . 71
5 總結與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

[1] D. Hall and J. Llinas, “An introduction to multisensor data fusion,” Proceedings of the IEEE, vol. 85, no. 1, pp. 6–23, 1997.
[2] X.-R. Li and V. P. Jilkov, “Survey of maneuvering target tracking. Part I. Dynamic models,” IEEE Transactions on Aerospace and Electronic Systems, vol. 39, no. 4, pp. 1333–1364, Oct. 2003.
[3] ——, “A survey of maneuvering target tracking–Part III: Measurement models,” in Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, July 2001, pp. 423–426.
[4] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. New Jersey: Prentice Hall, 1993, vol. 1.
[5] H. A. P. Blom, “An efficient filter for abruptly changing systems,” in Proceedings of the IEEE Conference on Decision and Control, vol. 23, 1984, pp. 656–658.
[6] H. A. P. Blom and Y. Bar-Shalom, “The interacting multiple model algorithm for systems with Markovian switching coefficients,” IEEE Transactions on Automatic Control, vol. 33, no. 8, pp. 780–783, Aug. 1988.
[7] Y. Bar-Shalom, K.-C. Chang, and H. A. P. Blom, “Tracking a maneuvering target using input estimation versus the interacting multiple model algorithm,” IEEE Transactions on Aerospace and Electronic Systems, vol. 25, no. 2, pp. 296–300, Mar. 1989.
[8] T. Kirubarajan and Y. Bar-Shalom, “Kalman filter versus IMM estimator: when do we need the latter?” IEEE Transactions on Aerospace and Electronic Systems, vol. 39, no. 4, pp. 1452–1457, Oct. 2003.
[9] E. Mazor, A. Averbuch, Y. Bar-Shalom, and J. Dayan, “Interacting multiple model methods in target tracking: a survey,” IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no. 1, pp. 103–123, Jan. 1998.
[10] L. Bloomer and J. E. Gray, “Are more models better?: the effect of the model transition matrix on the IMM filter,” in Proceedings of the 34th Southeastern Symposium on System Theory, 2002, pp. 20–25.
[11] J.-Y. Shiu, “Dual-IMM system for target tracking and data fusion,” Master’s thesis, Department of Electrical Engineering of National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China, 2009.
[12] Y.-W. Hong, W.-J. Huang, and C.-C. Kuo, Cooperative Communications and Networking: Technologies and System Design, 1st ed. Springer, 2010.
[13] Y. Ouyang, P.-C. Lan, T.-W. Lo, Y.-C. Tien, S.-Y. Ho, and P.-C. Yeh, Probabilistic cooperative location estimation in wireless networks,” in Proceedings of IEEE Wireless Communications and Networking Conference, 2010, pp. 1–6.
[14] Y. Ouyang, P.-C. Lan, S.-Y. Ho, Y.-C. Tien, T.-W. Lo, and P.-C. Yeh, Distributed cooperative location estimation (D-COOLEST) in wireless environments,” in Proceedings of the IEEE 17th International Conference on Telecommunications (ICT), 2010, pp. 872–878.
[15] D. Sworder, J. Boyd, R. Eliott, and R. Hutchins, “Data fusion using multiple models,” in Proceedings of the 34th Asilomar Conference on Signals, Systems and Computers, vol. 2, 2000, pp. 1749–1753.
[15] D. Sworder, J. Boyd, R. Eliott, and R. Hutchins, “Data fusion using multiple models,” in Proceedings of the 34th Asilomar Conference on Signals, Systems and Computers, vol. 2, 2000, pp. 1749–1753.
[16] X. R. Li and Y. Bar-Shalom, “Multiple-model estimation with variable structure,” IEEE Transactions on Automatic Control, vol. 41, no. 4, pp. 478–493, Apr. 1996.
[17] J. Hartikainnen and S. Sarkka, Optimal filtering with Kalman filters and smoothers - A Manual for Matlab toolbox EKF/UKF, version 1.2 ed., Department
of Biomedical Engineering and Computational Science, Helsinki University
of Technology, Feb. 2008.
[18] Y. Bar-Shalom, X.-R. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software. New York: Wiley, 2001.
[19] Z. Din and L. Hong, “Development of a distributed IMM algorithm for multiplatform multi-sensor tracking,” in Proceedings of the IEEE/SICE/RSJ International Conference on Multisensor Fusion and Integration for Intelligent Systems, 1996, pp. 455–461.
[20] J. Xu and F. Xue, “Distributed interacting multiple model joint probabilistic data association algorithm based on fuzzy weighted method,” in Proceedings of Computer Application and System Modeling International Conference, vol. 9, 2010, pp. 12–16. [21] Q.-H. Quan and S.-H. Li, “The model set multiple hypotheses IMM algorithm for maneuvering target tracking,” in Proceedings of the 9th International Conference on Signal Processing, 2008, pp. 2302–2305.
[22] C.-D. Wann and W.-T. Liu, “Positioning and tracking with NLOS mitigation using extended Kalman filter in UWB systems,” in Proceedings of the Interational Conference on Pervasive Systems and Computing, Las Vegas, Nevada, USA, Jun., 2005.
[23] C.-D. Wann and C.-S. Hsueh, “NLOS mitigation with biased Kalman filters for range estimation in UWB systems,” in Proceedings of IEEE Region 10 Conference, 2007, pp. 1–4.
[24] S. M. Kay, Fundamentals of statistical signal processing: Detection Theory. New Jersey: Prentice Hall, 1993, vol. 2.
[25] A. B. Marcovitz, Introduction to logic design, 2nd ed. New York: Mcgraw-Hill, 2005.
[26] M. Cen, X. Liu, and D. Luo, “Multi-sensor IMM estimator for uncertain measurement,” in Proceedings of the 5th International Conference on Wireless Communications, Networking and Mobile Computing, 2009, pp. 1–4.
[27] S. Mohamed and S. Nahavandi, “Optimal multisensor data fusion for linear systems with missing measurements,” in Proceedings of SoSE'08. IEEE International Conference on System of Systems Engineering, 2008, pp. 1–4.
[28] A. Farina, S. I. M. Meloni, L. Timmoneri, and D. Vigilante, “Comparison of two IMM tracking and classifier architectures based on extended and unscented Kalman filter with CRLB,” in Proceedings of IEEE 13th Workshop on Statistical Signal Processing, 2005, pp. 485–490.
[29] D.-J. Jwo and C.-H. Tseng, “GPS navigation processing using the IMM-based EKF,” in Proceedings of the 3rd International Conference on Sensing Technology, 2008, pp. 589–594.