Mode estimation techniques for switching discrete-time linear systems

Discrete-time systems are considered 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. The focus here is on the estimation of the mode of the system in the presence of disturbances. Different techniques are proposed and compared, each one well suited for a specific situation. In particular, when disturbances belong to known compact sets, "exact" conditions for the determination of modes consistent with the measures are given. If noises are zero-mean random variables with unknown distributions, a minimum-distance criterion is proposed. Finally, in the case of Gaussian noises, a method based on the maximum likelihood is adopted.