A necessary and sufficient condition for semi-stability of the recursive Kalman filter

This paper studies semi-stability for Kalman filters in the context of linear time-varying systems with incorrect noise information. Semi- stability is a key property, as it ensures that the actual estimation error does not diverge exponentially. As the main result of the paper we present a necessary and sufficient condition for the recursive Kalman filter to be semi-stable, relying on the relevant data of the system and noise. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist.