探討目標物追蹤的問題中，卡爾曼濾波器(Kalman Filter, KF) 是廣泛運用的估測器之一，但是能否適應目標物運動狀態之變化，往往取決於狀態變化的模型假設。而交互式多模(Interacting Multiple Model, IMM) 估測器藉著一組平行的卡爾曼濾波器之間交互作用(interaction)，能夠解決追蹤機動性目標物的模型假設問題而達到良好的估測效果。交互式多模演算法可視為提供適應目標物運動狀態變化的一種軟性處理程序(soft switching)，機率權重的使用與更新能使具有不同狀態模型之多個卡爾曼濾波器以交互式估測模式呈現較佳的狀態估測結果。然而，當使用交互式多模估測器對目標物進行追蹤，若受到環境因素限制而影響感測器資訊來源的可信度，或系統中使用不同類型的感測接收器，為了提高追蹤目標物的精準度與量測資料的正確性，我們可利用多感測器資料融合(Multi-Sensor Data Fusion) 的概念，將多個交互式多模估測器應用於此估測架構之中，藉以獲得更多目標物的量測資訊。在本論文中，透過兩個交互式多模估測器權重更新的資料融合，我們提出雙交互式多模(Dual-IMM) 估測器。假設兩個感測器對於移動目標的量測訊號受到不同程度的雜訊影響，這些量測資訊可分別透過兩個交互式多模估測器處理，之後再將估測器內部的估測值、模型機率(model probability) 和模型轉移機率矩陣(model transition probability) 進行資訊的交換傳送並依據演算法統整及合併資料，因此可避免單一交互式多模估測器因訊號資料量不足或週遭環境等干擾因素影響，而未能達到所預期之追蹤精準度。透過電腦模擬結果可驗證，當兩個交互式多模估測器的量測雜訊有明顯差異時，雙交互式多模估測器能藉由具備量測雜訊較小
的估測器對量測雜訊較大的進行輔助而提升追蹤效能；在兩個交互式多模估測器所接受到的量測雜訊相同的情況，兩個交互式多模估測器皆可獲得較佳的估測結果。我們提出的雙交互式多模估測器能夠進一步延伸為多交互式多模估測器進行估測與資料融合。

In solving target tracking problems, the Kalman filter (KF) is one of the most widely used estimators. Whether the state of target movement 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 Kalman filters to solve the hypothetical model of tracking maneuvering target. Based on the function
of soft switching, the IMM algorithm, with parallel Kalman filters of different dimensions, can perform well by adjusting the model weights. Nonetheless, the uncertainty in measured data and the types of sensing systems used for target tracking may still hinder the signal processing in the IMM. In order to improve the performance of target tracking and signal estimation, the concept of data fusion can be adapted in the IMM-based structures. Multiple IMM based estimators can be used in the structure of multi-sensor data fusion. In this thesis, we propose a dual-IMM estimator structure, in which data fusion of the two IMM estimators is achieved by updating associated model probabilities. Suppose that two sensors for measuring the moving target is affected by the different degrees of noise, the measured data
can be processed first through two separate IMM estimators. Then, the IMM-based estimators exchange with each other the estimates, model probabilities and model transition probabilities. The dual-IMM estimator will integrate the shared data
based on the proposed dual-IMM algorithm. The dual-IMM estimator can be used to avoid degraded performance of single IMM with insufficient data or undesirable environmental effects. The simulation results show that a single IMM estimator with smaller measurement noise level can be used to compensate the other IMM, which is affected by larger measurement noise. Improved overall performance from the dual-IMM estimator is obtained. Generally speaking, the two IMM estimators in the proposed structure achieve better performance when same level of measurement noise is assumed. The proposed dual-IMM estimator structure can be easily
extended to multiple-IMM structure for estimation and data fusion.

誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景與動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 論文結構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 目標物估測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 資料融合. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 訊號模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 卡爾曼濾波器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 交互式多模估測器. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 雙交互式多模估測器. . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1 估測器設計緣由. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 雙交互式多模估測器架構. . . . . . . . . . . . . . . . . . . . . . 14
3.2.1 更新權重. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.2 對估測值作權重分配. . . . . . . . . . . . . . . . . . . . . . . 18
3.2.3 卡爾曼濾波器. . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.4 計算模型的概似函數. . . . . . . . . . . . . . . . . . . . . . . 20
3.2.5 更新模型機率. . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.6 結合估測值與共變數. . . . . . . . . . . . . . . . . . . . . . . 21
3.3 雙交互式多模估測器優缺點. . . . . . . . . . . . . . . . . . . . 21
3.4 雙交互式多模延伸. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 雙交互式多模模擬與分析. . . . . . . . . . . . . . . . . . . . . . . 25
4.1 模擬環境參數設置. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 模擬結果與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.1 Case1(兩估測器具備相等量測雜訊σ2u1 = 0.1 與 σ2u2 = 0.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.2 Case2(兩估測器具備相異量測雜訊σ2u1= 10 與 σ2u2}= 0.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 38
5 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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