Mathematical Problems in Engineering

Volume 2016, Article ID 1892893, 9 pages

http://dx.doi.org/10.1155/2016/1892893

## A Least Square-Based Self-Adaptive Localization Method for Wireless Sensor Networks

^{1}State Key Laboratory of Satellite Navigation System and Equipment Technology, Shijiazhuang, China^{2}The 54th Research Institute of China Electronic Technology Corporation, Shijiazhuang, China^{3}School of Information and Electrical Engineering, Harbin Institute of Technology at Weihai, Weihai, China

Received 9 March 2016; Revised 14 June 2016; Accepted 25 October 2016

Academic Editor: Tamas Kalmar-Nagy

Copyright © 2016 Baoguo Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In the wireless sensor network (WSN) localization methods based on Received Signal Strength Indicator (RSSI), it is usually required to determine the parameters of the radio signal propagation model before estimating the distance between the anchor node and an unknown node with reference to their communication RSSI value. And finally we use a localization algorithm to estimate the location of the unknown node. However, this localization method, though high in localization accuracy, has weaknesses such as complex working procedure and poor system versatility. Concerning these defects, a self-adaptive WSN localization method based on least square is proposed, which uses the least square criterion to estimate the parameters of radio signal propagation model, which positively reduces the computation amount in the estimation process. The experimental results show that the proposed self-adaptive localization method outputs a high processing efficiency while satisfying the high localization accuracy requirement. Conclusively, the proposed method is of definite practical value.

#### 1. Introduction

Generally, two steps are needed for the wireless sensor networks (WSN) localization algorithm to estimate the location of an unknown node based on the Received Signal Strength Indicator (RSSI) [1]. Step is to try to determine the propagation parameters of the radio signal communication model with a fitting technique by measuring the mapping relation between RSSI and the distance . Step is to estimate the distance between the unknown node and each anchor node with reference to the communication RSSI value between them and obtain the estimated position value of the unknown node with reference to the coordinates of those anchor nodes. Therefore, this localization method requires a preliminary test for the environment [2] so as to determine the propagation parameters of the model. The lighted localization method Bounding-box (B-box for simplicity) [3] and its improved version [4–7], such as weighted B-box, 3-point centroid B-box, and 3-point weighted 3-point centroid B-box, were proposed to conduct localization of the unknown node.

However, the preliminary environmental test is a very complicated process that requires large amounts of experimental works. Besides, the preliminary test must be taken in a fixed localization environment. In case of any changes in the communication environment, the parameters in the radio signal propagation model would change along location information which plays an important role in location-based service application system, leading to error increment to the distance estimated upon RSSI value or the original model becoming not applicable any more. The factors affecting the environment usually include temperature, humidity, interference, and non-line-of-sight (NLOS) [8–10], which are subject to change along with the environment and time. Thus, the localization system that can keep high accuracy in a dynamic environment will be more promising. To satisfy this requirement, a maximum likelihood-based self-adaptive localization algorithm is proposed, which does not require a preliminary test for the environment in a dynamic environment but needs considerable computation amount. A distributed self-adaptive localization algorithm is proposed in the reference document [4], which, however, only investigates the localization issue when the communications range is fixed and poor in versatility. Hu and Evans proposed a Monte Carlo localization (MCL) method for mobile sensor node, and its computational time complexity is , where is the number of Monte Carlo sample points, is the number of localization points, and is the number of anchor nodes [11]. Min et al. proposed an improved version of MCL, which is called Monte Carlo localization algorithm based on anchor node selection (MCLAS) [12], and the computational time complexity is also . To locate the mobile node, Shan et al. proposed self-adaptive localization algorithm based on Monte Carlo and gray prediction model (GPLA); however, the complexity is high [13]. For the pose-tracking problem in a dynamic and highly occluded environment, literature [14] proposed a self-adaptive tracking algorithm for mobile robots. And maximum likelihood-based self-adaptive localization algorithm is proposed for dynamic localization, of which complexity is , where is the number of anchor nodes,* n* is the number of iterations, and* m* is the number of localization points.

In consideration of this, an analysis was given to the working process of self-adaptive localization algorithm. It was found that the propagation parameters in the radio signal propagation model became linear after the model was taken from the logarithm, and the computational amount could be reduced significantly using the least square method. Hence, this paper proposes the least square-based self-adaptive WSN localization method.

#### 2. A Least Square-Based Self-Adaptive Localization Method

In this section, the system flow of the least square-based self-adaptive localization method is presented before every part is elaborated.

##### 2.1. System Flow of Least Square-Based Self-Adaptive Localization Method

In the proposed self-adaptive localization algorithm, initialization is given firstly, including parameter initialization and representation of RSSI in probability density, before self-adaptive localization is performed iteratively. It is divided into two steps. The first step is to estimate the location of the unknown node and the second step is to estimate the parameter in the propagation model. Graphically, the workflow of the proposed least square-based self-adaptive localization method is illustrated in Figure 1.