Optimal Hybrid Estimation in 3D Wireless Sensor Networks: A Combined TOA and AOA Approach Using Generalized Trust Region and Second-Order Cone Relaxation Methods

Abstract

This paper addresses a target location problem utilizing hybrid measurements of time-of-arrival (TOA) and angle-of-arrival (AOA) in a three-dimensional wireless sensor network (WSN). It introduces a novel non-convex estimator based on the least squares (LS) criterion, which is transformed into a generalized trust region subproblem (GTRS) framework that closely approximates the maximum likelihood (ML) estimation. The optimal solution can then be achieved using the simple bisection method. Additionally, a second-order cone relaxation method is proposed to convert the original non-convex problem into a convex optimization problem, facilitating an easy acquisition of a suboptimal solution. The paper also derives the Cramer-Rao lower bound for the estimator based on hybrid TOA and AOA measurements in a three-dimensional WSN. Both theoretical analysis and computer simulation results demonstrate that the proposed methods offer strong performance.