本論文主要目的在於透過一個改良式的粒子濾波器進行目標物追蹤，並設計架構完
整的目標物追蹤融合系統。在現今許多估測的應用範疇中，為了建立更精確且更接近真
實情況的動態系統模型來描述物體狀態，非線性與非高斯的動態系統模型越來越被重
視。相較於部分傳統的估測器被用於線性且高斯雜訊的問題上，粒子濾波器(Particle
Filter) 被提出運用於非線性且非高斯雜訊的系統中。粒子濾波器擁有解決高度非線性與
非高斯估測問題的能力，這是傳統卡爾曼濾波器(Kalman Filter) 和擴展式卡爾曼濾波
器(Extended Kalamn Filter) 無法達到的，但相對於傳統濾波器成熟的技術，粒子濾
波器仍有許多特性可以被提出來討論。為了加強粒子濾波器的效能，本論文結合初始化
方法提供演算法初始狀態，使用最小平方估測方法建立出目標物的初始狀態分佈進行估
測。另外，也針對目標物速度的估測更新提出改善的架構於原主要的粒子濾波器中，加
入另一粒子濾波器演算法對目標物的速度進行更新。在提出的追蹤融合系統架構中，每
個感測器皆包含一個改良式的粒子濾波器對目標物進行追蹤，而感測網路中沒有融合中
心的存在也讓此架構更為強健。為了達到狀態資訊的有效表示、傳送及融合處理，我們
利用混合高斯模型(Gaussian Mixture Model; GMM) 去近似權重粒子集所表示的狀態
事後機率分佈，以得到更精簡的狀態表示且有效節省傳送的資料量。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運作模式與傳送機制，並利用混合高斯模型
的共變異交集演算法(Covariance Intersection Algorithm) 計算出感測節點間的融合結
果。模擬結果顯示出改良式粒子濾波器較傳統的粒子濾波器有更好的追蹤效能，此外，
利用改良式粒子濾波器所實現的解中心化資料融合系統亦能有效整合多感測點的估測結
果。

In this thesis, we investigate a decentralized data fusion system with improved
particle filters for target tracking. In many application areas, it becomes essential
to use nonlinear and non-Gaussian elements to accurately model the underlying
dynamics of a physical system. Particle filters have a great potential for solving
highly nonlinear and non-Gaussian estimation problems, in which the traditional
Kalman filter and extended Kalman filter may generally fail. To improve the tracking
performance of particle filters, initialization of the particles is studied. We
construct an initial state distribution by using least square estimation. In addition,
to enhance the tracking capability of particle filters, representation of target velocity
by another set of particles is considered. We include another layer of particle
filter inside the original particle filter for updating the velocity. In our proposed
architecture, we assume that each sensor node contain a particle filter and there
is no fusion center in the sensor network. Approximated a posteriori distribution
at the sensor is obtained by using the local particle filters with the Gaussian mixture
model (GMM), so that more compact representations of the distribution for
transmission can be obtained. To achieve information sharing and integration, the
GMM-covariance intersection algorithm is used in formulating the decentralized fusion
solutions. Simulation results are presented to illustrate that the performance
of the improved particle filter is better than standard particle filter. In addition,
simulation results of target tracking in the sensor system with three sensor nodes
are given to show the effectiveness and superiority 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 論文結構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 目標物追蹤系統之環境模型與粒子濾波器. . . . . . . . . . . . . . . . . . . 4
2.1 目標物追蹤系統之環境模型與問題. . . . . . . . . . . . . . . . . . . . 4
2.2 粒子濾波器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 重要性取樣. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 順序重要性取樣. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 重取樣. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 粒子濾波器演算法綜述. . . . . . . . . . . . . . . . . . . . . . 10
2.2.5 粒子濾波器的問題探討. . . . . . . . . . . . . . . . . . . . . . 12
3 改良式粒子濾波器應用於目標物追蹤之探討. . . . . . . . . . . . . . . . . . 16
3.1 粒子濾波器的初始化. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.1 最小平方近似法. . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.2 於粒子濾波器中使用最小平方近似法. . . . . . . . . . . . . . . 18
3.2 粒子濾波器目標物追蹤之速度估測. . . . . . . . . . . . . . . . . . . . 20
3.2.1 使用卡爾曼濾波器演算法加強粒子濾波器之追蹤效能. . . . . . 20
3.2.2 使用粒子濾波器演算法加強粒子濾波器之追蹤效能. . . . . . . 22
3.2.3 粒子濾波器於速度估測之綜述與優缺點. . . . . . . . . . . . . 23
4 使用改良式粒子濾波器之解中心化資料融合追蹤系統. . . . . . . . . . . . . 25
4.1 多感測器資料融合系統. . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 共變異交集演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.1 資料融合問題陳述與討論. . . . . . . . . . . . . . . . . . . . . 27
4.2.2 多變數共變異交集演算法. . . . . . . . . . . . . . . . . . . . . 30
4.2.3 共變異交集演算法綜述. . . . . . . . . . . . . . . . . . . . . . 33
4.3 使用改良式粒子濾波器於解中心化資料融合系統. . . . . . . . . . . . . 35
4.3.1 混合高斯模型與EM 演算法. . . . . . . . . . . . . . . . . . . 35
4.3.2 混合高斯模型之共變異交集演算法. . . . . . . . . . . . . . . . 38
5 電腦模擬與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.1 單一感測器局部估測結果之模擬與分析. . . . . . . . . . . . . . . . . 40
5.1.1 訊號模型與模擬環境設置. . . . . . . . . . . . . . . . . . . . . 40
5.1.2 粒子濾波器初始化之模擬與分析. . . . . . . . . . . . . . . . . 42
5.1.3 粒子濾波器加入目標物速度估測更新之模擬與分析. . . . . . . 49
5.1.4 粒子濾波器與擴展式卡爾曼濾波器之模擬與分析. . . . . . . . . 60
5.2 資料融合之模擬與分析. . . . . . . . . . . . . . . . . . . . . . . . . . 66
6 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
附錄A：蒙地卡羅取樣(Monte Carlo Sampling) . . . . . . . . . . . . . . . . . 75
附錄B：貝氏估測法(Bayesian Estimation) . . . . . . . . . . . . . . . . . . . . 76
附錄C：共變異交集演算法一致性之證明. . . . . . . . . . . . . . . . . . . . . 77

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