Distributed Estimation in Networks of Linear Time-invariant Systems

This paper is concerned with the problem of distributed Kalman filtering in a network of several interconnected subsystems. We consider networks, which can be either homogeneous or heterogeneous, of linear time-invariant subsystems, given in state-space form. We propose a distributed Kalman filtering scheme for this setup. The proposed scheme provides estimates based only on locally available measurements. We compare its outcomes with those of a centralized Kalman filter, which offers the best minimum error variance estimate, using all measurements available all over the network. We show that the estimate produced by the proposed method asymptotically approaches to that of the centralized Kalman filter, i.e., the optimal one with global knowledge of all network parameters, and we are able to bound the convergence rate. Moreover, if the initial states of all subsystems are mutually uncorrelated, the estimates of these two schemes are identical at each time step.