An Exploratory Distributed Localization Algorithm Based on 3D Barycentric Coordinates

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. 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.

I. Introduction

The fast development of the Internet of Things (IOT) enables the interconnection of mobile devices, sensors, agents, users, machines and vehicles in a large scale, and the location awareness enables the networked agents to be operated and managed efficiently and accurately [1], [2], [3]. The localization of networked agents is a hot research topic due to its wide range of applications. For the cooperative planning and control of multi-agents [4], [5], [6] operating in a network, each agent should obtain its own location information so that the formation control or cooperative task can be fulfilled. Moreover, the localization technology of sensor networks is also applied in many other fields, such as enterprise attendance [7], worker location acquisition in mines [8], monitoring of expensive equipment in factories [9], etc.