Distributed Localization of Networked Agents in GPS-Denied 3D Environments

This paper studies the distributed localization of networked agents using only distance measurements in a GPS-Denied 3D environment, which extends the existing results to the 3D localization in the presence of measurement noise and greatly improves its applications in internet of things. To deal with the distributed 3D localization, the barycentric coordinates of an agent in a tetrahedron are introduced by employing the Cayley-Menger determinants, which enables the localization problem of networked agents to be equivalently transformed into a linear estimation problem. Then, a recursive estimation algorithm is developed under the Jacobi Over-Relaxation (JOR) framework which recursively solves the linear estimation problem in a distributed manner; as a result, the proposed method can be scaled to the localization of large-scale networked agents. Finally, a simulation example is given to show the effectiveness of the proposed algorithm.