Reduced-order Kalman recursive filter for non-square descriptor systems with correlated noise

Using singular value decomposition of matrix and the theory of generalized inverse matrix, the non-square descriptor discrete time stochastic system is decomposed into two subsystems. Based on the classical Kalman filtering theory, the state estimation problem is considered for non-square descriptor discrete time stochastic systems. A Reduced-order Kalman recursive filter for non-square descriptor systems with correlated noise is given. Some numerical examples illustrate the effectiveness of the proposed algorithm.