Sensors_**2010**, _10_, 5171 - 5192; doi:10.3390/s100505171  
_Review_  
**Location Estimation in Wireless Sensor Networks Using Spring-Relaxation Technique**  
**[PERSON] \({}^{1,\star}\), [PERSON] \({}^{1}\), [PERSON] \({}^{2}\) and [PERSON] \({}^{3}\)**  
\({}^{1}\) School of Computer Engineering, Nanyang Technological University, \(639798\), Singapore;  
E-Mail: [EMAIL_ADDRESS]  
\({}^{2}\) Department of Electrical Electronic Engineering, Auckland University of Technology, New Zealand;  
E-Mail: [EMAIL_ADDRESS]  
\({}^{3}\) School of Computing and Mathematical Sciences, Auckland University of Technology, New Zealand;  
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\({}^{\star}\) Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS];  
Tel. : +65-6790-6579; Fax: +65-6792-6559 (CEMNET). _Received: 25 March 2010; in revised form: 15 April 2010 / Accepted: 10 May 2010 / Published: 25 May 2010_  
**Abstract:** Accurate and low-cost autonomous self-localization is a critical requirement of various applications of a large-scale distributed wireless sensor network (WSN). Due to its massive deployment of sensors, explicit measurements based on specialized localization hardware such as the Global Positioning System (GPS) is not practical. In this paper, we propose a low-cost WSN localization solution. Our design uses received signal strength indicators for ranging, light weight distributed algorithms based on the spring-relaxation technique for location computation, and the cooperative approach to achieve certain location estimation accuracy with a low number of nodes with known locations. We provide analysis to show the suitability of the spring-relaxation technique for WSN localization with cooperative approach, and perform simulation experiments to illustrate its accuracy in localization. **Keywords:** wireless sensor networks; localization; cooperative; spring-relaxation technique Introduction  
Supported by the great development in RF and MEMS IC design, large-scale distributed wireless sensor networks (WSNs) are widely applied to many areas involving monitoring, tracking, and controlling. Specific applications of wireless sensor networks include vehicle surveillance, environment monitoring, health care applications, and home automation [1; 2; 3; 4; 5]. Accurate and low-cost autonomous self-localization of the sensors is a critical requirement in these WSNs. The main reason is that the locations of sensors are necessary in a variety of applications, such as environment monitoring, object detection, target tracking, and security surveillance. In these applications, sensor locations must be known to make sense of the reported data. Additionally, sensor location information can be very useful for geographic routing protocols [6], clustering algorithms [7], and geographic data fusion algorithms [8]. Sensor localization is a challenging issue in the design and development of WSNs in various applications [9]. Sensors will need to last for years without battery replacement, so that power consumption and energy efficiency is of great concern. The localization algorithm should be designed in an easily implemented and energy efficient way, so that it will not limit the main operation of the sensors. Moreover, movement of sensors is also a common setup in various applications of WSNs. In these applications, the localization algorithm should be designed to cope with sensor mobility and changing connectivity. In addition, the localization algorithm should be autonomous and self-configuration without significant human attendance. In general, a localization algorithm is often based on computation using obtained measurements with respect to devices with known absolute locations where the measurements may include ranges or angles in an absolute or a relative description, such as time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), received signal strength (RSS), and others. The Global Positioning System (GPS) [10] is an example of a localization system that uses TDOA as the measurements for localization.