State Estimation for Discrete Systems with Switching Parameters

The problem of state estimation for discrete systems with parameters which may be switching within a finite set of values is considered. In the general case it is shown that the optimal estimator requires a bank of elemental estimators with its number growing exponentially with time. For the Markov parameter case, it is found that the optimal estimator requires only N2 elemental estimators where N is the number of possible parameter values.