Subtended angle-based network localization via distributed bearing vector estimation

Abstract

This paper considers the problem of localizing ordinary nodes in a planar network using only subtended angle measurements and the known positions of beacon nodes. Unlike distance-or bearing-based formulations, the available measurements here consist solely of subtended angles between neighboring nodes. We first formulate the subtended angle-based network localization problem in the plane. We then propose a constructive algorithm that generates a topology for which the resulting network is localizable. Based on reconstructed inter-node bearing vectors, we develop a distributed position estimation law over a sparse interaction graph. We show that the proposed estimator globally asymptotically converges to the true node positions, while reducing the per-node communication and computation burden compared to using the full communication graph. Numerical simulations are provided to validate the theoretical results.