3-D RSS-AOA Based Target Localization Method in Wireless Sensor Networks Using Convex Relaxation

Abstract

This paper addresses a target localization problem in 3-D wireless sensor networks using a hybrid system that fuses received signal strength and angle of arrival measurements. First, we formulate the received signal strength and angle of arrival measurement models as the pseudo-linear equations. Then, the bias is derived from the 3-D angle of arrival measurements that take the measurement noise into account to improve the localization performance. Furthermore, a non-convex estimator is derived based on the Least Squares criterion. Finally, semi-definite relaxation and second-order cone relaxation are applied to transform the derived non-convex estimator into a convex one. We propose a semi-definite relaxation and second-order cone relaxation-based estimator which yields the best performance under a large measurement noise or a small measurement noise. The generalization of the proposed method for known transmit power can also be applied to the case when transmit power is not know. Theoretical analysis and computer simulations corroborate the superior performance of the proposed localization methods over the existing ones. INDEX TERMS Target localization, received signal strength, angle of arrival, convex relaxation.

Multi-Target Localization Based on Unidentified Multiple RSS/AOA Measurements in Wireless Sensor Networks

“…Let be the known position of the i -th sensor (anchor) node for and be the unknown position of the m -th sensor (target) for . We assume that all anchor nodes have array antenna or directional antenna to measure AOA (azimuth and elevation angle) [ 37 ] via the line-of-sight (LoS) path from the target [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. In the presence of multiple targets, we assume that each anchor node receives signals from the targets, and the RSS, azimuth angle, and elevation angle are measured from these signals.…”

“…Most existing studies regarding multi-target detection in WSNs assume that the targets are sparsely located over networks and, therefore, each anchor node contains a single set of RSS/AOA measurements from a single target. Various multi-target localization methods that exploit the network topology [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] or apply compressive sensing [ 25 , 26 , 27 ] have been proposed. Some existing studies assume that each anchor node can identify the origin of the RSS/AOA measurements using, for example, code division multiplexing access codes [ 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 ], therefore solving multiple single-target localization problems.…”

An SOCP Estimator for Hybrid RSS and AOA Target Localization in Sensor Networks

“…Many advances related to RSS-AOA-based localization have been made recently, in both non-cooperative [ 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ] (where targets are allowed to communicate with anchors exclusively) and cooperative networks [ 22 , 29 ] (where targets can communicate with any sensor within their communication range). In [ 21 ], the authors employed an unbiased constant which takes advantage of the link quality through the path loss and angle noise variance to solve the non-cooperative problem by means of weighted linear least squares.…”

“…Although the proposed SDP estimators work well even in noisy environments, their computation complexity is very high, and for the case of unknown transmit power, the authors actually solve two SDP problems, which results in an increased execution time of the algorithms. In [ 28 ], the authors started by deriving pseudo-linear equations for the RSS and AOA measurement models. Based on a least squares (LS) criterion, a novel objective function was derived, which gave rise to a non-convex problem.…”

“…The works in [ 12 , 15 , 21 , 22 , 23 , 24 , 26 , 27 , 28 , 30 ] considered angle measurement noise to be a Gaussian random variable. However, the von Mises distribution is a more appropriate distribution to model angular noise [ 31 ].…”