L2-stability of discrete-time Kalman filter with incorrect covariances

In this paper, we consider the L2-stability of Kalman filter for discrete-time linear system with random coefficient matrices, where incorrect covariances of process noise, measurement noise and initial value are emphasized. We prove, under some suitable conditions, such as boundedness of coefficient matrices, conditional observability and boundedness of initial error and noises, the L2-stability of state estimation error by Kalman filter is achieved. The equivalence between Kalman filter and state-space least squares algorithm is also contained. Based on this equivalence, the L2-stability of state estimation error by state-space least squares is obtained, too. A numerical example is given to demonstrate the efficiency of the estimation algorithm.