轉動目標物常常出現在影像系統中，且有時候同時為一個移動式目標，我們稱之為移動式轉動目標物。在追蹤議題中，對目標物上的一點做追蹤會比對整個目標物做追蹤來的容易，所以我們利用目標物上的特徵點來對整個目標物的狀態進行估測，如：角速度、虛擬轉動中心和移動速度。在這些參數中，虛擬轉動中心由於不包含轉動的量，因此可以利用其來代表目標物的位置。傳統上擴展式卡爾曼濾波器(extended Kalman filter)、非察覺型卡爾曼濾波器(unscented Kalman filter) 和粒子濾波器(particle filter) 能用來處理這樣的非線性問題，但其中也存在了線性化誤差或高計算量的問題。線性化誤差使擴展式卡爾曼濾波器不能精準的估測角速度，而其他兩種則有很高的計算複雜度。本論文在處理移動式轉動目標物的追蹤時，先給定一個初始角速度，將非線性的模型轉換成線性模型，並在新的演算法架構中，將角速度分開估測，再利用回授的概念，來修正角速度的初始值。對於角速度的估測，在嘗試了利用快速傅立葉轉換來估測角速度的方法後，發現此方法的收斂時間會受到角速度快慢的影響，以及角速度方向估測的問題。因此另外提出了利用卡爾曼濾波器和虛擬觀測值來估測角速度的方法，其能精準地估測角速度，並且擁有較低的計算複雜度與收斂時間。當獲得準確的角速度資訊，利用角速度、轉動半徑和角速度的幾何關係，可以很容易的預測出虛擬中心的位置。另外，在影像系統中，量測值在表示為位置座標時會被量化，且目標物可能會被遮蔽。針對量化的誤差，本論文修改了原有的量測方程式，並利用卡爾曼濾波器來降低量化誤差的影響。而目標物被遮蔽的情況，我們則利用前一個狀態來預測現在的狀態。最後利用電腦模擬，驗證了本論文提出的方法能適應各種不同的環境與追蹤不同運動模式的移動式轉動目標物。

Spinning targets are usually observed in videos. The targets may sometimes appear as mobile targets at the same time. The targets become mobile spinning targets. Tracking a single point on a target is easier than tracking the whole target. We use a characteristic point on the target to estimate the interested parameters, such as angular velocity, virtual rotation center and moving velocity. Among these parameters, virtual rotation center does not spin, therefore it can be used to represent the position of the target. Traditionally, extended Kalman filter (EKF), unscented Kalman filter (UKF) and particle filter (PF) are choices for solving the nonlinear problems, but some problems exist. Linearization errors cause that EKF cannot accurately estimate the angular velocity. UKF and PF have high computational complexity. In the thesis, we give angular velocity an initial value. So we can establish a linear dynamic system model to displace the nonlinear model. Then, a new structure is proposed to avoid errors caused by initial value of angular velocity. In the structure, angular velocity is estimated individually and used to correct the initial value by feedback. We try to use fast Fourier transform to estimate angular velocity. But the convergence time of this method is affected by the value of angular velocity, and the direction of angular velocity can not be estimated directly. Therefore, Kalman filter (KF) with pseudo measurement is proposed to estimate the value of angular velocity. The estimator is accurate and has low computational complexity. Once angular velocity is estimated, we can easily predict the virtual rotation center from geometric relationship. In video system, measurements may be quantized and targets may sometimes be obstacled. We fix the measurement equation and use KF to mitigate quantization error. When measurements for the target is missing, the previous state is used to predict the current state. Finally, computer simulations are conducted to verify the effectiveless of the proposed method. The method can work in environments where measurement noise or quantization error exists. The methods can also be applied to different kinds of mobile spinning targets.

致謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 動態系統模型與演算法架構. . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 動態系統模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 演算法架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 卡爾曼濾波器. . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 利用頻譜密度估測角速度. . . . . . . . . . . . . . . . . . . . . 10
2.2.3 利用虛擬量測值和卡爾曼濾波器估測角速度. . . . . . . . . . . 13
2.2.4 轉動物體的虛擬轉動中心估測. . . . . . . . . . . . . . . . . . 15
2.2.5 針對車輪目標對演算法進行修正. . . . . . . . . . . . . . . . . 16
2.3 角速度估測對追蹤效能的提升. . . . . . . . . . . . . . . . . . . . . . 18
3 應用於影像系統與其遭遇的問題. . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 追蹤演算法應用於影像系統. . . . . . . . . . . . . . . . . . . . . . . 24
3.2 於影像系統上所遭遇的量化問題. . . . . . . . . . . . . . . . . . . . . 25
3.3 量化誤差對演算法效能的影響. . . . . . . . . . . . . . . . . . . . . . 27
4 電腦模擬與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1 CASE I：轉動的車輪. . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 CASE II：移動中的轉動風車. . . . . . . . . . . . . . . . . . . . . . 34
4.3 CASE III：迴力鏢. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
附錄A：結合卡式速度之增強式協調轉彎模型的狀態轉換矩陣推導. . . . . . . . 54
附錄B：利用擴展式卡爾曼濾波器追蹤移動式轉動目標物. . . . . . . . . . . . . 56

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