Consensus-based linear distributed filtering

• Published in: Automatica (Oxford) Vol. 48; no. 8; pp. 1776 - 1782
• Main Authors: Matei, Ion, Baras, John S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-08-2012; Elsevier
• Subjects: Applied sciences; Asymptotic properties; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Consensus; Control theory. Systems; Convergence; Cost engineering; Distributed filtering; Error detection; Exact sciences and technology; Filtering; Filtration; Gain; Modelling and identification; Sensor networks; Software; Stochastic processes; Sensor networks; Distributed filtering; Consensus; Estimation error; Probabilistic approach; Error estimation; Discrete time processes; Distributed system; Stochastic process; Stationary condition; Asymptotic stability; Upper bound; Optimal filtering; Linear filtering; Quadratic cost; System identification; Riccati equation; Sensor array
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2012.05.042

We address the consensus-based distributed linear filtering problem, where a discrete time, linear stochastic process is observed by a network of sensors. We assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable, i.e. for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors (without noise) is asymptotically stable. Next, we develop a distributed, sub-optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost. In the stationary case, we provide sufficient conditions under which this scheme converges; conditions expressed in terms of the convergence properties of a set of coupled Riccati equations.