在室內環境中, 以多感測器定位系統來定位目標物的位置, 由於使用的是低功率、輕巧、便宜、且具低複雜度運算能力的感測器, 因此可於目標物位置之估測上降低成本,
然而在定位演算法與多感測器的架設位置上, 對整體室內空間之定位效能卻有很大的影響。本文針對訊號之抵達時間差TDOA(Time Difference of Arrival), 使用線性矯正球面內插定位法(Linear-Correction Spherical-Interpolation, LCSI) 來估測目標物的位置。此演算法主要是由線性矯正最小平方法(Linear-Correction Least-Squares, LCLS) 及具封閉解之球面內插法(Spherical-Interpolation, SI) 結合而成。SI演算法有別於一般疊代式之非線性極小值的求解過程, 然而在受到誤差及目標物與感測器位置幾何關係影響之情況下, 會具有不同的定位效能, 因此將SI 演算法取代LCLS 演算法中LS(Least-Squares) 部分而成為線性矯正球面內插定位法(LCSI), 即對SI 演算法進行線性矯正進而產生一個較好的估測效能, 如此不僅在實現步驟上較為簡便, 也可將SI 演算法在定位效能上做改善。此外,LCSI 演算法自身的限制亦為本文所探討的議題。TDOA定位系統中, 三維立體空間的幾何精度稀釋(Geometric Dilution of Precision, GDOP) 效應, 顯示誤差對於感測器陣列內外區域之定位效能的影響。本文最後利用程式模擬, 在假設的三維室內空間中, 設計可行的感測器陣列組合與目標物的移動高度, 依據電腦模擬出來之各種不同演算法的GDOP 值, 來證明LCSI
演算法不同於其他方法之優點。

In indoor environment, the multi-sensor system can be used as an efficient solution for target location process, in terms of lower estimation cost, due to the factor that sensors have the advantages of low power, simple, cheap, and low operation complexity. However, the location methods and the placements of designed multisensor have great impact on the location performance. Based on the time difference of arrival (TDOA), the present research utilizes linear-correction spherical-interpolation (LCSI) method to estimate the location of its targets. The method is a combination of the linear-correction least-squares
method and the spherical-interpolation method. Apart from the usual process of iterative, nonlinear minimization, and consequently, under the influence of noise interference and target-sensor geometry, the spherical-interpolation method will produce better results; therefore, SI method is used in place of the LS part of the LCLS method and named as the LCSI method. The objective is to correct the SI method to generate a better estimate performance. In addition to the performance issues, the limitation of the methods will also be examined. The geometric dilution of precision (GDOP) of the TDOA location method in the
3-D scenario is demonstrated with the effects on location performance of both inside and outside of the multi-sensor formation. Programmed 3-D scenario are used in the simulations, where cases with three
different multiple sensor formations and two different target heights are investigated. From the simulation results of various location methods, it can be seen
that LCSI has has its advantages over other methods in the wireless TDOA location.

目錄
1 緒論. . . . . . . . . . . . . . . . . . . . . . . . .1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 相關研究與研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 無線定位法則與定位誤差來源. . . . . . . . . . . . . . . . . . . . . . . . .4
2.1 無線定位系統. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 訊號抵達時間定位法. . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 訊號抵達時間差定位法. . . . . . . . . . . . . . . . . . . . . 6
2.2 無線通道特性. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 抵達時間的量測誤差. . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 多重路徑傳播. . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 非視線傳播. . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 線性矯正球面內插定位法(Linear-Correction Spherical-Interpolation, LCSI) . . . . . . . . . . . . . . . . . . . . . . . . .11
3.1 TDOA系統中之定位演算法. . . . . . . . . . . . . . . . . . . . . . 11
3.1.1 球面內插法. . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.2 線性矯正最小平方法. . . . . . . . . . . . . . . . . . . . . . 14
3.1.3 球面交點法. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 誤差標準. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 線性矯正球面內插法. . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 TDOA系統中的GDOP 理論值分佈. . . . . . . . . . . . . . . . . 27
3.4.1 二維平面空間定位分佈. . . . . . . . . . . . . . . . . . . . . 27
3.4.2 三維立體空間定位分佈. . . . . . . . . . . . . . . . . . . . . 28
4 室內定位模擬及分析. . . . . . . . . . . . . . . . . . . . . . . . .32
4.1 定位效能優劣的判斷依據. . . . . . . . . . . . . . . . . . . . . . . 32
4.2 三維立體空間的定位模擬. . . . . . . . . . . . . . . . . . . . . . . 32
4.2.1 定位模擬環境. . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.2 定位模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . 37
5 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . 49
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . 50

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