On the stability of the recursive Kalman filter with Markov jump parameters

This paper addresses stability of the discrete-time, standard recursive Kalman Filter when the parameters of the filter are driven by a Markov chain. In this context, the error covariance matrices calculated via a Riccati difference equation form a stochastic process, making difficult to derive bounds for the estimation error. We show that the actual error covariance matrix is mean bounded from above, even in presence of incorrect noise model for the initial condition of the system, under the assumptions that the system is weakly controllable and stochastically detectable. Illustrative examples are included.