An Exploratory Distributed Localization Algorithm Based on 3D Barycentric Coordinates

Abstract

This paper studies the exploratory distributed localization of networked mobile agents using only distance measurements in a GPS-Denied 3D environment. To deal with this challenging problem, an analytic solution is firstly provided to calculate the 3D barycentric coordinates for agents outside the convex hull formed by anchors. Then, a distributed Jacobi Under-Relaxation Iteration (JURI) algorithm is developed to address the static 3D localization problem in a noisy environment. Next, the proposed algorithm is extended for the localization of mobile targets, especially when the mobile agents cannot get enough neighbors' support. Since the proposed algorithms do not suffer from the constraint of the convex hull (exploratory localization); as a result, the proposed method can be scaled to the localization of large-scale networked agents. Finally, several simulation examples are given to validate the effectiveness of the proposed algorithm in different scenarios.