Distributed optimization techniques for range localization in networked systems

This work investigates the problem of distributed estimation of the position of agents in a networked system, from pairwise distance measurements between them. Although the underlying geometrical problem has been studied quite extensively, most of the state-of-the-art algorithms for network localization presuppose a central unit, capable of collecting agents´ measurements and retrieving the configuration of the whole network. Here, we explore decentralized, or distributed, approaches for range localization, and we develop two algorithms in which distributed optimization techniques are applied for localization, namely a distributed gradient method with Barzilai-Borwein stepsizes and a distributed Gauss-Newton approach. The advantage of these approaches is that each agent may autonomously compute its position estimate, exchanging information only with its neighbors, without need of communicating with a central station and without needing complete knowledge of the network structure. The proposed algorithms are proved to converge, under an hypothesis of network connectivity, to the same solution of their centralized counterparts.