Filtering for bimodal systems: the case of unknown switching statistics

This paper considers the problem of state estimation for discrete-time systems whose dynamics randomly switches between two linear stochastic behaviors (bimodal systems). The novelty of this paper is that no statistical information on the switching process is assumed available for the filter design. Two different approaches are here proposed to solve the estimation problem in these conditions. One method is based on a combined use of stochastic singular systems and of the minimax filtering theory, while the other relies on the maximum entropy principle. Based on these approaches two filtering algorithms are derived, whose features are theoretically and numerically compared. Some attention has been devoted to the study of the asymptotic properties of both the filters