A fully distributed weight design approach to consensus Kalman filtering for sensor networks

• Published in: Automatica (Oxford) Vol. 104; pp. 34 - 40
• Main Authors: Zhang, Ya, Tian, Yu-Ping
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2019
• Subjects: Consensus; Distributed Kalman filter; Packet dropouts; Switching networks; Weight design; Weight design; Distributed Kalman filter; Packet dropouts; Consensus; Switching networks
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2019.02.052

This paper proposes a consensus Kalman filtering algorithm based on the leader–follower structure and weighted average strategy for sensor networks. By introducing virtual estimation errors and confidence level functions, the weights are fully distributively and adaptively designed in a proportion form of the sensors’ confidence levels. It is proved that for time-invariant networks, the mean square estimation errors of all sensors are bounded if and only if the process node in the extended topology is globally reachable. For random networks with Bernoulli communication packet dropouts, the estimation errors are bounded in probability if and only if the process node in the union of all possible extended topologies is globally reachable. For arbitrarily switching communication networks, the mean square estimation errors are bounded as long as there exists an infinite sequence of uniformly bounded, non-overlapping time intervals such that the process node in the union of the extended topologies across each interval is globally reachable. For time-varying sensing networks with strongly connected communication topology, the estimation errors are bounded in mean square sense if the process node in the extended topology keeps globally reachable. Simulation examples are given to illustrate the theoretic results.