A Localization Error Estimation Method Based on Maximum Likelihood for Wireless Sensor Networks

A composed localization error estimation method is presented for the application in wireless sensor networks (WSNs) which employs maximum likelihood (ML) to locate. Two statistic indexes are given in this method to characterize the whole localization performance of WSN in error aspect. The number of WSN nodes can be determined before deploying to achieve the necessary localization accuracy. Through mathematic analysis, the expressions of mathematical expectation and standard deviation of a WSN are acquired. Besides, based on the expressions, the two indexes are calculated through Monte Carlo simulation. An application applying this method demonstrates the procedure of determining the optimum numbers of unknown nodes (who doesn't know their positions) and anchor nodes (who know their positions).

I. Introduction

With the quick development of radio frequency (RF) devices and micro electromechanical systems (MEMS), WSN used for information acquisition are becoming more popular in many different fields [1]. For example, placing sensors in battle field to collect field information such as enemy location, the ingredients of biochemical weapons, etc. Besides, in civilian applications field, WSNs are widely used for environmental monitoring, health monitoring, structural health monitoring, industrial monitoring, smart building monitoring, high-precision agriculture and seismic activity detection [2]–[10]. For most applications, the localization information of nodes are required to determine where an event happens especially for those application in which WSNs are used for target localization [11], [12]. First and foremost, nodes should be deployed in a specific field. There are three alternative deployment approaches: application-specific deterministic deployment, random deployment, and grid-based deployment [13], [14], [15], [16]. Non-deterministic deployment is scalable to large-scale applications.