Optimal distributed state estimations for a networked dynamical system

A new recursive state estimation procedure is derived for a networked system. This estimation utilizes only local system output, can be easily realized in a distributed way, and can be simply scaled to systems with a large amount of subsystems. It is proved that when estimation error variances are adopted in performance comparisons, the optimal gain matrix is usually unique. Recursive and explicit expressions are derived for both this optimal gain matrix and the covariance matrix of the corresponding estimation errors. Some numerical simulation results are included to illustrate the effectiveness of the suggested procedure.