Exact Convex Relaxation-Based Sensor Network Localization Using Noisy Distance Measurements

This article studies the problem of distributed localization for a sensor network consisting of target nodes and anchor nodes using only noisy distance measurements, which is challenging when the target nodes are outside the convex hull of the anchor nodes. The concerned localization problem is formulated as a squared-range-based least-squares estimation problem, and a coordinate descent scheme-based distributed localization method is developed where each subproblem can be exactly resolved using the Lagrangian convex relaxation technique and the convergence of the proposed distributed algorithm can be guaranteed. Simulation examples show that the proposed localization method has a high chance to reach the globally optimal solution in the absence of measurement noise and yields reliable localization results in the presence of measurement noise.