© The Author 2010. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org doi:10.1093/comjnl/bxq001 Localization Algorithms for Wireless Sensor Retrieval Yuan Zhang 1,2,∗ , Lichun Bao 2 , Shih-Hsien Yang 2 , Max Welling 2 and Di Wu 2 1 Computer Science and Technology Department, Jilin University, Changchun, China. 2 Computer Science Department, University of California, Irvine, CA, USA. ∗ Corresponding author: zhangyuan2u@gmail.com In wireless sensor networks (WSNs), localization has many important applications, among which wireless sensor retrieval bears special importance for cost saving, data analysis and security purposes. Localization for sensor retrieval is especially challenging due to the fact that the number and locations of these sensors are both unknown. In this paper, we propose two probabilistic localization algorithms that iteratively identify the locations of multiple wireless sensors in WSNs, one of which calculates location information offline, and the other online. In both algorithms, we implement a two-step localization process — the first step is called Grid-LEGMM (grid location estimation based on the Gaussian mixture model), a coarse-grain location search using grids by choosing the proper number and locations of the wireless sensors that maximize a likelihood estimation, and the second step is called EM-LEGMM (expectation maximization based on the Gaussian mixture model), which uses the EM-method to refine the results of Grid-LEGMM. An additional step in the online localization algorithm is a credit-based filtering mechanism that removes spurious sensor locations. The performance of both offline and online localization algorithms are analyzed using the Cramer–Rao lower bound (CRLB), and evaluated using simulations and real testbed experiments. Keywords: localization; expectation maximization; Gaussian mixture model; path loss model Received 15 August 2009; revised 25 November 2009 Handling editor: Yu-Chee Tseng 1. INTRODUCTION Large-scale wireless sensor networks (WSNs) are widely deployed for environmental monitoring, control and interaction applications. However, before mass production of wireless sensor nodes, it is cost effective and energy efficient to retrieve the decommissioned sensors after sensory tasks. In addition, some sensor information analysis might only be feasible after collecting them due to the storage and computational complexities of data analysis. In wireless sensor retrieval applications, localization is the key challenge [23]. The simplest solution for network localization is to equip every wireless node with a GPS (global positioning system) device. Caballeroa et al. [10] used a mobile robot equipped with a GPS device to exchange its location information with the wireless sensors in outdoor environments. However, a GPS device is unavailable to the most wireless node due to considerations on either cost or the GPS satellite signal reception limitations. Therefore, in-network localization becomes the only choice for practical reasons. A variety of in-network localization solutions have been explored, which can be categorized into two classes: range-free and range-based [2, 3, 23]. Both approaches require a certain number of reference nodes with known location coordinate information, called anchors. Range-free approaches use the topological information to infer nodal locations, therefore saving any special hardware costs, and trading off the accuracy and scalability of the location estimations [4, 9]. He et al. [2] proposed the APIT range-free localization scheme, which divides the network area into triangular regions to gradually narrow down the locations of the node. In [23, 24], a localization algorithm based on the hop count, called DV-HOP, was presented. To localize the nodes, the anchors flood their location information along with incremental hop-distance information to the corresponding anchors. Other nodes calibrate their relative locations based on the received anchor locations, the hop count and the average distance per hop. In [20], a centroid-based approach is proposed. Anchors beacon their The Computer Journal, 2010 The Computer Journal Advance Access published February 9, 2010 at National Chiao Tung University Library on July 11, 2010 http://comjnl.oxfordjournals.org Downloaded from