無線感測網路之線性最小平方差定位研究

Abstract

在室內及室外環境之下，估測出目標物(人或物)的位置有許多重要的應用。而GPS系統在被遮蔽的環境之下精準度不良，所以我們需要一個無線感測的定位系統。靠著許多感測器對於目標的距離(或角度)量測，透過定位之演算法，我們可以估算出待測物的位置。而感測器測距的準度越好，定位的準確度當然越好，所以我們修正傳統的相關測距法，利用訊號飛行時間和其能量的聯合關係，將可以提升精準度。另外，在測距時，感測器與待測物的直接路徑若不存在時，將會使得測到的距離過長，使位置估測產生很大的偏差。我們根據最大概似法，提出了減少誤差的方法。由於一般定位演算法是利用最小平方差方法來達成，其方程式為非線性方程式。為了降低運算複雜度，我們將探討三種典型的線性化方法，並分析其中兩種較常見線性化最小平方差方法之準確度。當感測器增加時，我們推導出準確度與感測器個數的關係。另外，當待測物移動時，其運動軌跡的估測也是定位技術中重要的議題。但過去利用Kalman filter來估測軌跡的運算複雜度過高，我們將其化簡，在準確度相差不大的結果下，進一步降低運算複雜度。

Sensor network localization relies on the range (or angle) measurement from the mobile (object) and the sensors with known positions. The location of the mobile can be estimated via these measurements. Accuracy of the localization algorithms highly depends on the accuracy of measured ranges. By considering both time-of-arrival (TOA) and received signal power, a range estimation method is proposed to improve ranging accuracy. Besides, the range measurement often suffers from non-line-of-sight (NLOS) effect and the range estimation might be much longer than the true range. As a result, the localization performance can degrade severely. We propose a NLOS mitigation algorithm based on simplified maximum-likelihood (ML). To alleviate the nonlinearity issue encountered in a least-squares localization model, three linearization techniques will be studied. Theoretical derivation shows that the asymptotic error is inversely proportional to the number of sensors. Besides, a simplified Kalman filter with lower complexity is proposed to track a moving mobile. Computer simulations will be performed to validate the theoretical analysis and compare performance of different algorithms.