Distributed Set-Theoretic Parameter Estimation in Networks with Ambiguous Measurements

Dimitris Ampeliotis, Christos Mavrokefalidis, Kostas Berberidis, Sergios Theodoridis

Abstract: Distributed estimation of a parameter vector in a network of sensor nodes with ambiguous measurements is considered. These ambiguities may be due to interference, poor calibration, high noise levels or any other cause. Cooperation among the nodes is required to resolve them. In such a setting, non-convex constraint sets may be required at the nodes, in order to accurately model the local ambiguities. We propose to handle the resulting non-convexity by expressing the involved non-convex sets as unions of convex sets, such that, for each node, only one such convex set is actually relevant to the estimation task. A procedure is employed in which the nodes properly select one of their convex sets with the aim to reach network-wide agreement. In this formulation, agreement can be reached when the nodes select sets with non-empty intersection. To this end, a learning algorithm is proposed and then a sketch of a proof for its convergence under some mild conditions is carried out. Finally, proper numerical results that support the theoretical findings are shown.