L2-stability of Discrete-time Kalman Filter with Random Coefficients under Incorrect Covariance

This paper studies the L2-stability of Kalman filter for discrete-time linear stochastic systems. Two main features, i.e., random coefficient matrices and incorrect covariances of process noise, measurement noise and initial value, are emphasized. Under suitable conditions, including boundedness of coefficient matrices, conditional observability and boundedness of initial error and noises, L2-stability of Kalman filter is achieved. The equivalence between Kalman filter and state-space least squares algorithm is established. Based on this equivalence, L2-stability of state estimation error by state-space least squares is also obtained. A numerical example is given to demonstrate the effectiveness of Kalman filtering algorithm.