在探討定位及追蹤系統中，
目標物之行動定位與追蹤在無線通訊或是訊號處理中扮演著重要的腳色，
若以多感測器定位系統來定位目標物的位置，
可獲得精確的目標物估測位置與追蹤結果，
然而在多感測器的擺設位置與定位演算法之間的關係，
對整體的定位效能彼此間具有相互的影響。
本論文針對與時間資訊有關之訊號抵達時間差 (Time Difference of Arrival, TDOA) ，使用封閉型式最小平方定位方法，
包括球面內插法 (Spherical-Interpolation, SI) 及
球面交點法 (Spherical-Intersection, SX) ，
來計算目標物的估測位置座標。
然而此兩種定位方法不同於一般普遍使用求解非線性極小值之疊代演算法的過程，
受到目標物與配置感測器位置之間幾何關係影響，會有不同的定位效能，
此外；兩種演算法在數學式上的限制，也為本文所探討的議題。
若要達到目標物即時追蹤且精確定位的效果，
可以使用卡爾曼濾波器分別將球面內插法與球面交點法各自相結合，
一個定位與追蹤系統架構就此成型，
但是此兩種定位與追蹤系統模形本身還是存在著在多感測器陣列內或陣列外不同的特性，
考慮使用資料融合的方式進行估測結果之改善，
利用交互式多模估測器，
將內部平行運作之匹配濾波器進行改良為 SX-KF1 和 SI-KF2 這兩個定位與追蹤功能區塊，
其中卡爾曼濾波器量測雜訊的選擇，我們提出了時變量測雜訊變異數配置，
使整個定位估測系統架構，能隨著時間改變適應環境得到最佳的定位估測結果。
本文最後利用程式模擬，在假設的三維多感測器陣列中，
依據定位效能優劣判斷之均方根誤差值，
證實移動目標物不管在多感測器陣列內或陣列外，
皆能有效提升定位性能。

For target location and tracking in wireless communication systems, mobile target positioning and tracking play an important role.
Since multi-sensor system can be used as an efficient solution to target positioning process, more accurate target location estimation and tracking results can be obtained.
However, both the deployment of designed multi-sensor and location algorithm may affect the overall performance of position location.
In this thesis, based on the time difference of arrival (TDOA), two closed-form least-square location methods, spherical-interpolation (SI) method
and spherical-intersection (SX) method are used to estimate the target location. The two location methods are different from the usual process of
iterative and nonlinear minimization.
The locations of the target and the designed multiple sensors may yield geometric effects on location performance.
The constraints and performance of the two location methods will first be introduced.
To achieve real-time target tracking, the Kalman filtering structures are used to combine the SI and SX methods.
Because these two positioning and tracking systems have different and complementary performance inside and outside the multi-sensor array, we consider using data fusion to improve location estimation results by using interacting multiple model (IMM) based estimator, in which internal filters running in parallel are designed as the SX-KF1 and the SI-KF2. However, due to the time-varying characteristics of measurement noises, we propose an adjusting scheme for measurement noise variance assignment in the Kalman filters to obtain improved location estimation results. Simulation results are obtained by running Matlab program.
In three-dimensional multi-sensor array scenarios, the
results of moving target location estimation shows that the IMM-based estimators effectively improve the position performance.

目錄
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 序論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 相關研究. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 行動定位系統演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 與時間資訊有關行動定位技術. . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 訊號抵達時間(TOA) 定位方法. . . . . . . . . . . . . . . . . 5
2.1.2 訊號抵達時間差(TDOA) 定位方法. . . . . . . . . . . . . . . 8
2.2 具封閉型式最小平方TDOA 定位估測. . . . . . . . . . . . . . . . .11
2.2.1 球面內插法( Spherical-Interpolation, SI) . . . . . . . . . . . 14
2.2.2 球面交點法(Spherical-Intersection, SX) . . . . . . . . . . . 15
2.2.3 SI 和SX 定位演算法精準度比較. . . . . . . . . . . . . . . . 18
3 強健定位估測系統. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 定位估測器設計緣由. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 使用卡爾曼濾波器之資料平滑改善定位效能. . . . . . . . . . . . . . . 24
3.3 基於交互式多模演算法之改良架構. . . . . . . . . . . . . . . . . . . . 33
3.3.1 混合機率之計算(Calculation of the Mixing Probabilities) . . 36
3.3.2 估測訊號之權重結合與分配(Interaction/Mixing) . . . . . . . 37
3.3.3 匹配濾波器模組(Mode-Matched Filtering) . . . . . . . . . . 37
3.3.4 時變量測雜訊變異數配置(Time-Varying Measurement Noise
Variance Assignment) . . . . . . . . . . . . . . . . . . . . . 38
3.3.5 模型概似函數之計算(Calculation of the Mode Likelihood
Function) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.6 模型機率之更新(Mode Probability Update) . . . . . . . . . 40
3.3.7 估測訊號與共變數結合輸出(Estimation and Covariance Combination) . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 廣義強健定位估測系統架構. . . . . . . . . . . . . . . . . . . . . . . 40
4 多感測器環境之定位模擬及分析. . . . . . . . . . . . . . . . . . . . . . 42
4.1 定位效能優劣之判斷. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 移動目標在三維感測空間的定位. . . . . . . . . . . . . . . . . . . . .42
4.2.1 Case 1 : 目標物從多感測器陣列內移至陣列外. . . . . . .44
4.2.2 Case 2 : 目標物穿越多感測器陣列. . . . . . . . . . . . . . . 46
4.2.3 Case 3 : 目標物從多感測器陣列移出後再移入. . . . . . .52
4.2.4 Case 4 : 目標物從多感測器陣列之外極遠處移入再移出. . . . 58
5 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

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