Minimum-Energy Distributed Filtering

Abstract: The paper addresses the problem of distributed filtering with guaranteed convergence properties using minimum-energy filtering and $H_\infty$ filtering methodologies. A linear state space plant model is considered observed by a network of communicating sensors, in which individual sensor measurements may lead to an unobservable filtering problem. However, each filter locally shares estimates, that are subject to disturbances, with its respective neighboring filters to produce an estimate of the plant state. The minimum-energy strategy of the proposed local filter leads to a locally optimal time-varying filter gain facilitating the transient and the asymptotic convergence of the estimation error, with guaranteed $H_\infty$ performance. The filters are implementable using only the local measurements and information from the neighboring filters subject to disturbances. A key idea of the proposed algorithm is to locally approximate the neighboring estimates, that are not directly accessible, considering them as disturbance contaminated versions of the plant state. The proposed algorithm imposes minimal communication load on the network and is scalable to larger sensor networks.