A deterministic approach for general discrete-time Kalman filter for singular systems

In this paper, the Kalman filter and the corresponding Riccati equation for discrete-time, time-variant descriptor systems are addressed in their most general formulation. A new "9-block" form for the optimal filter is derived using deterministic approach. This new expression, besides including one step delayed state, presents an interesting simple and symmetric structure. Stability results for this filter are also presented.