Kalman filtering for descriptor systems with current and delayed measurements

A class of discrete-time Kalman filtering problem for the descriptor time-varying systems with current and delayed measurements is considered. Using the known maximum likelihood (ML) estimation results and the method of measurements reorganization, the optimal Kalman filter and corresponding Riccati equations for descriptor systems involving current and delayed measurements are derived. Our solution does not require system augmentation or system transformation, and the estimator is given in terms of two Riccati equations of the same order as that of the system state. A simple algorithm is presented for the problem.