Mixed Convex/Non-Convex Distributed Localization Algorithm for the Deployment of Indoor Positioning Services

In this paper a fully decentralized algorithm for indoor wireless localization is presented. The algorithm combines the use of convex and non-convex optimization procedures, nested to achieve better converge towards the best positioning of a multitude of blind wireless nodes. The algorithm proceeds locally on each node, based on the sole knowledge of the measured distances from, and estimated positions of, the connected nodes only. Repeated asynchronous application on each node of the local procedure guarantees hierarchical convergence of the algorithm to the positioning of the whole network, even in presence of a limited number of peripheral anchors. No global information is required for the proper functioning of the algorithm. From the theoretical standpoint, the paper introduces the geometrical definition of regular and irregular nodes, which is shown to be a useful concept, given a network topology, for the characterization of the convergence properties of the localization problem.