A new approach to decentralized constrained nonlinear estimation over noisy communication links

Abstract

This paper investigates constrained nonlinear estimation over noisy communication links. The estimation is solved by a set of nodes in a fully distributed fashion. The unknown parameter of interest is assumed to be belonging to a closed convex set. The measurement of each node is nonlinearly related to the unknown parameter. The communication among adjacent nodes is corrupted by the additive communication noises. We propose a decentralized projection consensus+innovation algorithm with communication noises to solve the nonlinear estimation problem and develop a novel approach to analyze its convergence. For the case of fixed graph, by introducing an auxiliary matrix and combination of the graph Laplacian and the auxiliary matrix, we prove that the algorithm converges in mean square and almost surely if the combined persistence of excitation (CPE) condition holds and the measurement function satisfies the Lipschitz continuity and monotonicity conditions. Furthermore, for the case of the time-varying graphs, we establish the jointly combined persistence of excitation (JCPE) condition guaranteeing convergence in mean square. Both the CPE and JCPE conditions are proposed for the first time and do not require that the graph is balanced. The JCPE condition holds even when the graph is disconnected at infinitely many time instants. A simulation example is presented to demonstrate our theoretical results.