A distributed Kalman filtering algorithm with fast finite-time convergence for sensor networks

This paper proposes a new distributed algorithm for Kalman filtering. It is assumed that a linear discrete-time dynamic system is monitored by a network of sensors with some being active and some idle. The goal of distributed state estimation is to devise a distributed algorithm such that each node can independently compute the optimal state estimate by using its local measurements and information exchange with its neighbours. The proposed algorithm applies to acyclic network graphs (i.e., tree graphs) with fast finite-time convergence, but is also applicable to cyclic graphs by combining it with a distributed loop removal algorithm. The proposed algorithm enjoys low complexities, robustness against transmission adversaries and asynchronous implementability. The proposed distributed algorithm also applies to maximum likelihood estimation and weighted least-squares estimation, as special cases. With simple modifications, the proposed algorithm also applies to an important problem in signal processing called distributed field estimation.