Sensors_**2011**, _11_, 9989-10009; doi:10.3390/s111009989  
Sensors  
ISSN 1424-8220  
www.mdpi.com/journal/sensors  
Article  
**Collaborative Localization Algorithms for Wireless Sensor Networks with Reduced Localization Error**  
**[PERSON] \({}^{1,\star}\) and [PERSON] \({}^{2,3}\)**  
\({}^{1}\) Department of Computer Science and Information Engineering, Chang Gung University,  
Kwei-Shan, 33302, Taiwan  
\({}^{2}\) Department of Information Communication, Yuan-Ze University, Chungli, 32003, Taiwan;  
E-Mail: [EMAIL_ADDRESS]  
\({}^{3}\) Department of Computer Science and Engineering, Yuan-Ze University, Chungli, 32003, Taiwan  
\({}^{\star}\) Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS]. Received: 23 August 2011; in revised form: 12 October 2011 / Accepted: 18 October 2011 /  
_Published: 21 October 2011_  
**Abstract:** Localization is an important research issue in Wireless Sensor Networks (WSNs). Though Global Positioning System (GPS) can be used to locate the position of the sensors, unfortunately it is limited to outdoor applications and is costly and power consuming. In order to find location of sensor nodes without help of GPS, collaboration among nodes is highly essential so that localization can be accomplished efficiently. In this paper, novel localization algorithms are proposed to find out possible location information of the normal nodes in a collaborative manner for an outdoor environment with help of few beacons and anchor nodes. In our localization scheme, at most three beacon nodes should be collaborated to find out the accurate location information of any normal node. Besides, analytical methods are designed to calculate and reduce the localization error using probability distribution function. Performance evaluation of our algorithm shows that there is a tradeoff between deployed number of beacon nodes and localization error, and average localization time of the network can be increased with increase in the number of normal nodes deployed over a region. **Keywords:** wireless sensor networks; localization; error estimation Introduction  
In recent years, with rapid advances in Micro Electro Mechanical Systems (MEMS) technology, research on Wireless Sensor Networks (WSNs) has received extensive interest. It is getting popular due to its low cost and small size and its applications in military and civilian surveillance. However, wireless sensor networks have a few inherent limitations. e.g., limited hardware, limited transmission range, and large scale network system and the traditional protocols or mechanisms cannot use in WSNs. Hence, several issues are needed to consider in WSNs to construct an efficient and robust network. For example, sensor nodes have limited computation capability and limited power supply, and therefore low complexity algorithms and power saving schemes should be designed. In wireless sensor networks, localization of nodes plays an important role in most of the applications. When sensors are deployed over a network, normally they have only connectivity information with their neighbors, without knowing their own location information. In some situations, the problem can have easy solution if location information of the nodes is available. For example, routing path can be constructed easily, and coverage hole can easily be detected, if nodes have location information. Knowing relative location of sensors allows the location-based addressing and routing protocols, which can improve network robustness and energy-efficiency effectively. Recent research results show that nodes with location information lead to increased performance of applications and reduced power consumption. In addition, more accurate location information leads to the more accurate result that application needs. In summary, localization is an essential part of WSNs. Sensors are intended to be low-cost disposable devices, and currently developed solutions such as global position system (GPS) [1] are inadequate for the hardware and power-limited sensors.