多感測器資料融合目標物追蹤系統中, 在量測雜訊假設成不相關的前提下, 利用資訊濾波器運作過程, 可順利實現分佈式定位, 然而不同的感測器的量測雜訊經常會呈現
相關性。在量測雜訊相關性的情況下, 量測雜訊共變數矩陣將不是對角矩陣, 將不能再使用一般的資訊濾波器過程實現分佈式定位。利用矩陣分解法, 可將量測雜訊共變數
矩陣分解成對角矩陣, 藉著量測模型的轉換, 相關的量測雜訊成分能夠被轉換成等效不相關的假性量測雜訊, 再利用等效的觀察模型所推導的資訊濾波器過程, 可以使得
多感測器順利進行分佈式處理。本篇論文我們將利用Cholesky 分解法進行矩陣分解,主要是因為Cholesky 分解法是高斯消去法的應用, 在計算過程上有許多可以利用的優點, 但是利用Cholesky 分解法而實行分佈式定位必須將系統中各感測器量測資料重新作線性組合, 所以所有的感測器必須均能互相溝通。在實際狀況下, 感測器網路每個感測器皆能互相直接溝通並不常見, 因此藉由研究Cholesky 分解在數學上所觀察到的特性, 我們提出在各種感測器連結情形下之分佈式運作架構, 並更進一步討論在各種連結情形下資訊的傳輸模式, 以最少的傳輸次數達到整個系統以分佈式架構運作的效果。在分佈式無線定位的問題上, 以混合型TDOA/AOA 定位為運作模式, 其中
包括NLOS 的鑑別與抑制過程, 將原本利用卡爾曼濾波器作中心化的處理方式, 在量測雜訊不相關的情況下, 使用分組方式再利用擴展式資訊濾波器實現分佈式定位; 而
在量測雜訊呈現相關性的情況下, 利用Cholesky 分解法以及所推導之擴展式資訊濾波器變化型實行分佈式定位。我們利用電腦模擬來驗證所提出之分佈式運作架構, 由結果可知, 所提出之架構是有效的, 幾種感測器連結模式皆能利用所提出之架構進行分佈式多感測器資料融合目標物追蹤運作, 並且能有良好的定位及追蹤效能。

In multi-sensor data fusion target tracking system, using information filtering can implement distributed location with uncorrelated measurement noises, but
the measurement noises of different sensors are often correlated. If measurement noises are correlated, the covariance matrix of measurement noises is not a diagonal matrix. We can not use information filtering to implement distributed
location with correlated measurement noises. By using the matrix theory, the covariance matrix of measurement noises can be transformed to a diagonal matrix. The observation models are transformed to new observation models, and
the multi-sensor measurements with correlated measurement noises are transformed to equivalent pseudo ones with uncorrelated measurement noises. There are many methods in the matrix theory, we use Cholesky fatorization in this thesis. Cholesky fatorization is from Gaussian elimination, and there are many advantages in the computation process.However, the observation models need
to be transformed to new observation models, and the measurement datas for the approach need to be separated and recombined. For measurement datas being separated and recombined, every sensor must communicate with each other. In practice, one sensor does not directly communicate with other sensors except its direct neighbors. By formulating the Cholesky factorization process, we present
architectures which are applied in wireless distributed location. Distributed architectures with clustered nodes are proposed to achieve measurement exchange and information sharing for wireless location and target tracking. With limited times
of data exchanges between clustered nodes, the correlated noise components in the measurements are transformed into uncorrelated ones through the Cholesky process, and the resultant information can be directly shared and processed by the derived extended information filters at the nodes in the distributed system. Hybrid TDOA/AOA wireless location systems with the NLOS error effects are
used as examples in investigating the distributed information architecture. Simulation results show that the proposed distributed information processing and data fusion architecture effectively achieve improved location and tracking accuracy.

目錄
1 緒論1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文結構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 無線定位法與非視線誤差鑑別抑制3
2.1 無線定位原理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 訊號抵達角度定位法. . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 訊號抵達時間定位法. . . . . . . . . . . . . . . . . . . . . . 4
2.1.3 訊號抵達的時間差定位法. . . . . . . . . . . . . . . . . . . 5
2.1.4 混合式定位法. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 TDOA/AOA定位. . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 TDOA/AOA定位法概述. . . . . . . . . . . . . . . . . . . 7
2.2.2 TDOA/AOA定位系統架構. . . . . . . . . . . . . . . . . . 9
2.3 參數模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 時間之參數模型. . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 角度之參數模型. . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 非視線誤差之鑑別與抑制. . . . . . . . . . . . . . . . . . . . . . . 13
2.4.1 卡爾曼濾波器. . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.2 時間非視線誤差之鑑別. . . . . . . . . . . . . . . . . . . . . 15
2.4.3 時間非視線誤差之抑制. . . . . . . . . . . . . . . . . . . . . 15
2.4.4 角度非視線誤差之抑制. . . . . . . . . . . . . . . . . . . . . 16
2.5 基於卡爾曼濾波器的多感測器融合追蹤方法介紹. . . . . . . . . . . 16
2.5.1 狀態向量融合法與量測值融合法. . . . . . . . . . . . . . . . 16
2.5.2 中心化與解中心化的架構. . . . . . . . . . . . . . . . . . . 17
3 分佈式TDOA/AOA 定位法20
3.1 分佈式TDOA/AOA 之概念介紹. . . . . . . . . . . . . . . . . . . 20
3.2 擴展式卡爾曼濾波器. . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 多感測器的資料融合. . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 資訊濾波器(Information Filter,IF) . . . . . . . . . . . . . 23
3.3.2 解中心化之運算. . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 使用擴展式資訊濾波器之TDOA/AOA 定位. . . . . . . . . . . . . 26
3.4.1 擴展式資訊濾波器. . . . . . . . . . . . . . . . . . . . . . . 26
3.4.2 用擴展式資訊濾波器作解中心化運算. . . . . . . . . . . . . 28
3.4.3 使用擴展式資訊濾波器之分佈式定位. . . . . . . . . . . . . 29
3.5 當量測雜訊存在相關性時所遇到的問題. . . . . . . . . . . . . . . . 31
4 量測雜訊存在相關性之探討33
4.1 對於相關量測雜訊的追蹤系統中心化融合方法. . . . . . . . . . . . . 33
4.1.1 針對相關性量測雜訊之中心化演算法系統模型. . . . . . . . 34
4.1.2 針對相關性量測雜訊的多感測器中心化融合追蹤方法. . . . . 35
4.1.3 量測雜訊的分解. . . . . . . . . . . . . . . . . . . . . . . . 36
4.1.4 Cholesky分解所形成的中心化演算法深入思考. . . . . . . . 39
4.2 利用Cholesky 方法進行雜訊相關性之分解與實現分佈式運算. . . . 41
4.2.1 兩個感測群組中存在量測雜訊相關性之探討. . . . . . . . . . 42
4.2.2 三個感測群組中存在量測雜訊相關性之探討. . . . . . . . . . 53
4.3 多感測器在量測雜訊相關下解中心化處理. . . . . . . . . . . . . . . 61
4.3.1 一維鏈狀架構之探討. . . . . . . . . . . . . . . . . . . . . . 61
4.3.2 Cholesky分解法在幾種架構之運用. . . . . . . . . . . . . . 68
4.3.3 感測器群組與群組之運作方式. . . . . . . . . . . . . . . . . 71
5 分佈式無線定位電腦模擬與效能分析74
5.1 兩個定位群組之效能分析(含有NLOS) . . . . . . . . . . . . . . . . 74
5.1.1 根據相關係數不同所作的效能分析. . . . . . . . . . . . . . 76
5.1.2 非視線感測器數量對融合定位效能之影響. . . . . . . . . . . 79
5.2 三個定位群組及五個定位群組之分佈式效能分析(含有NLOS) . . . . 90
5.2.1 三個群組之效能分析. . . . . . . . . . . . . . . . . . . . . . 90
5.2.2 五個群組之效能分析. . . . . . . . . . . . . . . . . . . . . . 99
6 結論與建議123
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