本論文主旨在研究無線感測網路(Wireless Sensor Network) 中利用已知座標位置之地標與目標物到地標之間的距離資訊建立目標函數,並使用無約束條件直接搜尋法進行目標函數最優化以求得目標物之座標位置。地標是由網路中所有節點經由地標選取演算法選取而來,由於地標選取演算法耗費時間過久,勢必需要簡化架構,以距離資訊重複方法加速選取效率。因為節點之涵蓋範圍有限,必須結合多重跳躍(Multi-Hop)方式和最短路徑概念估測非鄰近之目標物到地標間的距離,因此利用最短路徑距離估測模型可以快速求得,不過由於距離估測誤差過大,必須結合步長誤差判斷進行距離估測修正,將使的目標物之定位誤差上有明顯的降低。

本論文利用無約束條件直接搜尋法中的單純形調優法(Simplex Evolutionary Method, SEM)、座標轉換法(Cyclic Coordinate Method, CCM)和波威爾法(Powell Method, PM)進行目標函數最優化。由於CCM和PM 定位演算法在應用上面臨求解搜尋方向前進長度之問題,因此我們提出結合CCM-SEM 和結合PM-SEM定位演算法不僅保留原本架構,利用單變數之SEM 求解搜尋方向前進長度問題將顯的快
速且有效率。

本論文最後利用程式模擬,在一個單位面積之二維空間中隨機產生節點並做地標選取。令目標物佈置於整個環境中進行定位演算法效能分析,其中也將針對結合步長誤差判斷後所造成定位效能之影響進行探討,並討論節點個數、地標個數、節點涵蓋範圍對於定位演算法效能上之影響。由模擬結果可以得知,以地標個數為四個或者節點個數為100個為例,其定位誤差有明顯降低;而結合步長誤差將使的定位更精確。

The main purpose of this thesis is to utilize landmarks with known coordinates and the distance between a target and landmarks to establish an objective function, and to optimize the objective function by using unconstrained direct search method to estimate the coordinate of target. A number of nodes in the sensor network serve as the landmarks according to landmark selection algorithm. Since the landmark selection algorithm is time-consuming, a simplified scheme that would improve the algorithm is to reuse the distance information that had been computed. Due to the limit of transmission range between nodes, utilizing the shortest-path distance estimation model can quickly estimate the distance between the target and non-adjacent landmarks. The main conception of the model is combining the manner of multi-hop with the shortest-path model. Due to the possible errors in distance estimation, the error per hop is considered for reducing the estimation errors. It will obviously reduce the localization errors of the target.

The thesis utilizes unconstrained direct search method to optimize the objective functions such as the simplex evolutionary method (SEM), the cyclic coordinate method(CCM) and the Powell method (PM). CCM and PM will tackle the problem of finding the forward length along search direction. Hence, two schemes that combine CCM or PM with SEM are proposed to resolve the problem.

Finally, simulations are conducted to generate random some nodes in an known area and to select landmarks from the nodes. Let the target be assigned in the area and do performance analysis of positioning algorithm. We discuss the performance of the positioning algorithm by considering the error per hop approach. We also discuss the effects on positioning by changing some variables such as the number of nodes, the number of landmarks and the transmission range of nodes. It is seen that the positioning errors will be reduced in examples where the number of landmark are four or the number of node are four hundred. The performance of positioning becomes accurate by reducing the distance estimation error.

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 無線感測網路估測最短路徑距離近似模型4
2.1 無線感測器測距原理. . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 無線測距原理. . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 最短路徑測距概念. . . . . . . . . . . . . . . . . . . . . . . 6
2.2 估測最短路徑距離近似模型. . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 測距數學模型. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 測距模型演算法流程. . . . . . . . . . . . . . . . . . . . . . 10
2.3 無線感測網路之地標選取法. . . . . . . . . . . . . . . . . . . . . . 11
2.3.1 地標選取原理及演算法流程. . . . . . . . . . . . . . . . . . 11
2.3.2 快速地標選取演算法. . . . . . . . . . . . . . . . . . . . . . 14
2.4 非線性目標函數之建立. . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 一般節點之目標函數建立. . . . . . . . . . . . . . . . . . . 16
2.4.2 結合步長誤差判斷之目標函數. . . . . . . . . . . . . . . . . 17
3 針對目標物之定位演算法19
3.1 最優化與定位觀念概述. . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 無約束非線性函數最優化直接搜尋法. . . . . . . . . . . . . . . . . 20
3.2.1 座標轉換法(Cyclic Coordinate Method) . . . . . . . . . . 20
3.2.2 波威爾法(Powell Method) . . . . . . . . . . . . . . . . . . 22
3.2.3 單純形調優法(Simplex Evolutionary Method) . . . . . . . 25
3.3 結合CCM-SEM 與結合PM-SEM 定位演算法. . . . . . . . . . . . 32
3.4 定位演算法之比較. . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 電腦模擬分析與討論36
4.1 最短路徑距離估測模型特性分析. . . . . . . . . . . . . . . . . . . . 36
4.2 定位演算法之效能分析. . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.1 定位之距離誤差討論. . . . . . . . . . . . . . . . . . . . . . 41
4.2.2 結合步長誤差判斷之定位影響. . . . . . . . . . . . . . . . . 44
4.3 影響定位效能之參數設定. . . . . . . . . . . . . . . . . . . . . . . 48
4.3.1 地標個數之定位影響. . . . . . . . . . . . . . . . . . . . . . 48
4.3.2 CCM-SEM和PM-SEM 定位演算法初始點設定之影響. . . . 51
5 結論與建議54
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2 建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
參考文獻56

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