Maximum-likelihood Kalman Filtering for Switching Discrete-time Linear Systems

State estimation is addressed for a class of discrete-time systems that may switch among different modes taken from a finite set. The system and measurement equations of each mode are assumed to be linear and perfectly known, but the current mode of the system is unknown. Moreover, we assume that independently normally distributed noises affect the dynamics and the measurements. First, relying on a well-established notion of mode observability developed "ad hoc" for switching systems, an approach to system mode estimation based on a maximum likelihood criterion is proposed. Second, such mode estimator is embedded in a Kalman filtering framework to estimate the continuous state. Under the assumption of mode observability, stability properties in terms of boundedness of the mean square estimation error are proved for the resulting filter. Simulation results that show the effectiveness of the proposed filter are reported.