A Mixed Convex/Nonconvex Distributed Localization Approach for the Deployment of Indoor Positioning Services

In this paper the indoor wireless localization problem is addressed both from the theoretical and application standpoints. The main result of the paper is on the theoretical side: the topological definition of regular and irregular nodes is introduced, and formal results are presented to support regularity as a desirable network property for the attainment of precise node localization. In force of this definition, a mixed convex/non-convex optimization approach has been derived for the solution of the positioning problem. The two procedures, suitably combined, allow the achievement of better convergence towards the best positioning of a multitude of blind wireless nodes. A completely decentralized, partially asynchronous algorithm is presented, which proceeds locally on each node based on the sole knowledge of the distances measured from, and of the estimated positions of the connected nodes only. Its repeated asynchronous application on each nodes guarantees the convergence of the algorithm to the positioning of the whole network, even in presence of a limited number of peripheral reference points. Indeed, no global information is required for the proper functioning of the algorithm. Simulations of relevant case studies have been performed to qualify the proposed scheme in realistic conditions, and the results are presented.