Monte Carlo Methods for Node Self-Localization and Nonlinear Target Tracking in Wireless Sensor Networks

Abstract

Most applications of wireless sensor networks (WSN) rely on the accurate localization of the network nodes [Patwari et al., 2005]. In particular, for network-based navigation and tracking applications it is usually assumed that the sensors, and possibly any data fusion centers (DFCs) in charge of processing the data collected by the network, are placed at a priori known locations. Alternatively, when the number of nodes is too large, WSNs are usually equipped with beacons that can be used as a reference to locate the remaining nodes [Sun et al., 2005]. In both scenarios, the accuracy of node localization depends on some external system that must provide the position of either the whole set of nodes or, at least, the beacons [Patwari et al., 2005]. Although beacon-free network designs are feasible [Sun et al., 2005, Ihler et al., 2005, Fang et al., 2005, Vemula et al., 2006], they usually involve complicated and energy-consuming local communications among nodes which should, ideally, be very simple. In this paper, we address the problem of tracking a maneuvering target that moves along a region monitored by a WSN whose nodes, including both the sensors and the DFCs, are located at unknown positions. Therefore, the target trajectory, its velocity and all node locations must be estimated jointly, without assuming the availability of beacons. We advocate an approach that consists of three stages: initialization of the WSN, target and node tracking, and data fusion. At initialization, the network collects a set of data related to the distances among nodes. These data can be obtained in a number of ways, but here we assume that each sensor node is able to detect, with a certain probability of error, other nodes located nearby and transmit this information to the DFCs. These data are then used by the DFCs to acquire initial estimates of the node positions. An effective tool to perform this computation is the accelerated random search (ARS) method of [Appel et al., 2003], possibly complemented with an iterated importances sampling procedure [Cappe et al., 2004] to produce a random population of node positions approximately distributed according to their postrior probability distribution given the available data. This approach is appealing because it couples naturally with the algorithms in the tracking phase. We propose to carry out target tracking by means of sequential Monte Carlo (SMC) methods, also known as particle filters (PFs) [Doucet et al., 2000, 2001, Crisan & Doucet, O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg