Convergence of linear coupled Riccati equations with applications to distributed filtering in sensor networks

Abstract

This paper studies the convergence property of a class of linear coupled Riccati equations and applies it to convergence analysis of distributed filtering algorithms. Firstly a necessary and sufficient condition for convergence of linear distributed algebraic Riccati equations is proposed. Then based on Kalman filtering algorithm and weighted average strategy, optimal filtering algorithms are designed for two special random networks, and their statistical convergence conditions are further given. Specially, for homogeneous sensor networks, convergence conditions on the sensing/communicaton link loss probability of the network are also explicitly given.