在解中心化資料融合的系統當中，若是基於雜訊環境為高斯雜訊且資訊更新量彼此不相關的假設前提下，可以利用資訊濾波器將多個感測器所提供的量測資訊進行融合。然而在真實狀況下，一般的系統或環境可能是非線性，且雜訊往往呈現非高斯分佈且存在相關性，因此就系統的強健性來考量，利用資訊濾波器去進行狀態估測與資料融合時並不能夠對所有類型的問題提供最佳的融合結果，而利用粒子濾波器搭配相關的融合演算法去取代資訊濾波器的資料融合便是一個可行的想法。不過就現有的相關研究來講，利用粒子濾波器來實現解中心化的資料融合的系統架構仍不常見，設計也多不完整，且粒子濾波器本身在實行狀態估測時亦存在若干影響其估測效能之問題，因此本論文主要目的在於透過一個改良式的粒子濾波器，並設計架構一個完整的目標物追蹤融合系統，設計的過程首先利用迭代擴展式卡爾曼濾波器(Iterated Extended Kalman Filter; IEKF) 來迭代產生粒子濾波器的重要性密度函數，融入最新的量測訊息，使產生的取樣粒子分佈更接近於真實的取樣分佈，而濾波後的結果也更符合真實的事後機率分佈。之後利用這改良式的粒子濾波器進行狀態估測與目標物追蹤，並利用混合高斯模型(Gaussian Mixture Models; GMMs) 去近似權重粒子集所表示的狀態事後機率分佈，求得更精簡的表示法以節省傳送的資料量。在資料融合方面，我們探討感測器在解中心化融合架構底下的操作行為與傳送機制，並利用混合高斯模型的共變異交集演算法(Covariance Intersection Algorithm) 計算解中心化的融合結果。由電腦模擬的結果可知，本論文所提出使用的改良式粒子濾波器在目標物追蹤上明顯較傳統式的粒子濾波器精準，而利用改良式粒子濾波器所實現的資料融合系統亦比一般資訊濾波器所提出之架構更加強健且是可行的。

In decentralized data fusion system, if the probability model of the noise is Gaussian and the innovation informations from the sensors are uncorrlated,the information filtering technique can be the best method to fuse the information from different sensors. However, in the realistic environments, information filter cannot provide the best solution of state estimation and data integration when the noises are non-Gaussian and correlated. Since particle filter are capable of dealing with non-linear and non-Gaussian problems, it is an intuitive approach to replace the information filter by particle filter with some suitable data fusion techniques.In this thesis, we investigate a decentralized data fusion system with improved particle filters for target tracking. In order to achieve better tracking performance, the Iterated Extended Kalman Filter framework is used to incorporate the newest observations into the proposal distribution of the particle filter. In our proposed architecture, each sensor consists of one particle filter, which is used in generating the local statistics of the system state. Gaussian mixture model (GMM) is adopted to approximate the posterior distribution of the weighted particles in the filters, thereby more compact representations of the distribution for transmmision can be obtained. To achieve information sharing and integration, the GMM-Covariance Intersection algorithm is used in formulating the decentralized fusion solutions. Simulation resluts of target tracking cases in a sensor system with two sensor nodes are given to show the effectiveness and superiorty of the proposed architecture.

誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 全文結構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 針對目標物追蹤系統之模型環境問題與可用之估測演算法. . . . . . . . . . . 4
2.1 目標物追蹤系統模型環境與問題. . . . . . . . . . . . . . . . . . . . . 4
2.2 粒子濾波器(Particle Filter) . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 重要性取樣(Importance Sampling) . . . . . . . . . . . . . . . 6
2.2.2 順序重要性取樣(Sequential Importance Sampling) . . . . . . 8
2.2.3 重取樣(Resampling) . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 粒子濾波器演算法綜述. . . . . . . . . . . . . . . . . . . . . . 10
2.2.5 粒子濾波器存在的主要問題. . . . . . . . . . . . . . . . . . . 11
2.3 迭代擴展式卡爾曼粒子濾波器(Iterated Extended Kalman Particle
Filter; IEKPF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 迭代擴展式卡爾曼濾波器與擴展式卡爾曼濾波器. . . . . . . . . 14
2.3.2 迭代擴展式卡爾曼粒子濾波器演算法綜述. . . . . . . . . . . . 17
2.3.3 迭代擴展式卡爾曼粒子濾波器演算法的優缺點. . . . . . . . . . 19
3 使用改良式粒子濾波器之解中心化資料融合與目標物追蹤系統. . . . . . . . . 20
3.1 多感測器資料融合系統分類與討論. . . . . . . . . . . . . . . . . . . . 20
3.2 共變異交集演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 一致性之說明. . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 資料融合問題陳述. . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.3 共變異交集演算法綜述. . . . . . . . . . . . . . . . . . . . . . 25
3.3 使用迭代擴展式卡爾曼粒子濾波器之解中心化資料融合系統. . . . . . . 28
3.3.1 混合高斯模型(Gaussian Mixtrue Models; GMMs)與EM 演算法29
3.3.2 混合高斯模型之共變異交集演算法. . . . . . . . . . . . . . . . 31
3.4 融合結果比較準則之討論. . . . . . . . . . . . . . . . . . . . . . . . . 32
4 電腦模擬分析與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1 單一感測器局部估測結果之模擬與分析. . . . . . . . . . . . . . . . . 33
4.1.1 訊號模型與模擬環境設置. . . . . . . . . . . . . . . . . . . . . 33
4.1.2 迭代擴展式卡爾曼粒子濾波器之模擬與討論. . . . . . . . . . . 35
4.2 資料融合之模擬與分析. . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.1 資料融合環境設置. . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.2 雙感測器解中心化資料融合. . . . . . . . . . . . . . . . . . . 56
5 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
附錄A：蒙地卡羅取樣(Monte Carlo Sampling) . . . . . . . . . . . . . . . . . 63
附錄B：貝氏估測法(Bayesian Estimation) . . . . . . . . . . . . . . . . . . . . 65
附錄C：迭代式卡爾曼濾波器之理論基礎(Iterated Extended Kalman Filter) . . 67
附錄D：共變異交集演算法一致性之證明. . . . . . . . . . . . . . . . . . . . . 69

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