  This paper is concerned with the problem of distributed Kalman filtering in a
network of interconnected subsystems with distributed control protocols. We
consider networks, which can be either homogeneous or heterogeneous, of linear
time-invariant subsystems, given in the state-space form. We propose a
distributed Kalman filtering scheme for this setup. The proposed method
provides, at each node, an estimation of the state parameter, only based on
locally available measurements and those from the neighbor nodes. The special
feature of this method is that it exploits the particular structure of the
considered network to obtain an estimate using only one prediction/update step
at each time step. We show that the estimate produced by the proposed method
asymptotically approaches 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.
