  This paper studies the distributed state estimation problem for a class of
discrete time-varying systems over sensor networks. Firstly, it is shown that a
networked Kalman filter with optimal gain parameter is actually a centralized
filter, since it requires each sensor to have global information which is
usually forbidden in large networks. Then, a sub-optimal distributed Kalman
filter (DKF) is proposed by employing the covariance intersection (CI) fusion
strategy. It is proven that the proposed DKF is of consistency, that is, the
upper bound of error covariance matrix can be provided by the filter in real
time. The consistency also enables the design of adaptive CI weights for better
filter precision. Furthermore, the boundedness of covariance matrix and the
convergence of the proposed filter are proven based on the strong connectivity
of directed network topology and the global observability which permits the
sub-system with local sensor's measurements to be unobservable. Meanwhile, to
keep the covariance of the estimation error bounded, the proposed DKF does not
require the system matrix to be nonsingular at each moment, which seems to be a
necessary condition in the main DKF designs under global observability.
Finally, simulation results of two examples show the effectiveness of the
algorithm in the considered scenarios.
