A distributed gradient method for localization of formations using relative range measurements

Several applications of networked systems require nodes to have precise knowledge of their geometric position. A common setup is the case in which each node is capable of measuring distances with respect to a subset of mates and has to estimate its position in a given reference frame. 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. In this paper, we explore a decentralized approach to localization based on a distributed implementation of a gradient method with Barzilai-Borwein stepsizes. The advantage of this approach 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. This decentralized scheme is proved to converge, under an hypothesis of network connectivity, to the same solution as its centralized counterpart. Computational performance and scalability of the described approach are also illustrated through numerical experiments.