近年來，隨著位置感知應用與服務需求的快速增加，無線感測網路(WSNs, wireless sensor networks)之室內定位技術受到極大的重視。一般而言，WSNs定位可分為集中式方法或分散式方法，然而在大規模和/或密集的網路中，分散式方法在能量效率上的表現會優於集中式方法。因此，在WSNs中開發具有高準確度和追蹤效能的分散式定位技術是有價值的。
在本論文中，我們根據遞迴式最佳化處理，提出數種新式WSNs定位演算法，包括遞迴式最小平方法、改良式凸集投影法(POCS, projection onto convex sets)以及遞迴式加權最小絕對值法。這些定位演算法是被證明經由最小化一與時間相關的遞迴式成本函數，然後以分散式之疊代的方法來實現。更具體來說，參與定位的感測節點利用其局部估計值的加權平均以及可靠度資訊去疊代計算目標物的位置，其中目標物的最新位置估計值是經由目前感測節點的觀測值和先前感測節點的目標物位置估計值所計算獲得。所提出的演算法可視為帶有一個適當步階的遞迴式子梯度演算法或是POCS演算法，在每次的疊代會採取一個有效規則去更新可變步階，且最後能保證收斂到一個駐點。電腦模擬結果顯示，相較於之前相關的演算法，我們提出的演算法可達到更好的定位準確度。
為了能在WSNs中追蹤目標物，我們進一步提出一分散式加權擴展型卡爾曼濾波(WEKF, weighted extended Kalman filtering)定位與追蹤演算法，其中一訊息傳遞演算法是被使用於感測節點之間的通訊以及選擇目標物移動區域附近的感測節點來參與定位。在目前的疊代中，感測節點會計算一個目標物位置估計值，然後將此估計值傳送到下一個感測節點去執行下一次的疊代計算。更新的程序是循環傳遞在目標物附近的參與感測節點之間。我們亦提供了收斂性分析和電腦模擬結果，去驗證所提出之WEKF演算法的收斂和效力。

With a growing demand for location-aware applications and services, indoor positioning techniques based on wireless sensor networks (WSNs) have received great attention in recent years. Positioning in WSNs can be realized in a centralized or decentralized way, where the decentralized approach generally has a better energy efficiency than the centralized approach in large-scale and/or dense networks. It is therefore worth exploiting decentralized positioning schemes that can provide good location accuracy and tracking performance for WSNs.
In this dissertation, we propose some new decentralized positioning algorithms based on recursive optimization procedures for WSNs, including the recursive least-squares, the improved projection onto convex sets (POCS), and the recursive weighted least absolute value method. Each of these algorithms is derived from the minimization of a recursive-in-time cost function and then realized in an iterative decentralized manner. Specifically, the target location can be calculated iteratively by taking a weighted average of the local estimates based on the participating sensor nodes’ reliability information, where a participating sensor node computes the newest location estimate according to its own observation and the most recent local estimate passed from the previous participating sensor node. All the proposed schemes adopt an effective rule for updating the step size at each iteration and guarantee convergence to a stationary point, where every one of them is equivalent to the incremental subgradient method or the POCS method with an appropriate variable step size. Computer simulation results show that the proposed schemes have better location accuracy than previous related methods.
To track a target in WSNs, we further propose a decentralized weighted extended Kalman filtering (WEKF) scheme for positioning and tracking, where a message-passing algorithm is adopted for inter-sensor-node communications and for adaptively selecting the participating sensor nodes as the target moves within the area of interest. During each iteration, the current participating sensor node computes a local estimate and passes it on to the next participating sensor node for further processing. The update process is circulated only among the selected participating sensor nodes that surround the target. A convergence analysis is given to show that the proposed WEKF-based method converges. Computer simulation results are also given to demonstrate the effectiveness of the proposed approach.

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