Mode-set adaptation in multiple-model estimators for hybrid systems

In view of the numerous recent applications of multiple-model estimation algorithms, the choice of the set of models is a major issue. Often, for practical problems an algorithm using a fixed set of small number of models can not yield accurate results. Apart from the increase in computation, use of more models does not guarantee better performance - actually, it may yield even poorer results. To solve this problem, this paper introduces the concept of variable structure, i.e., adaptation of model set, and proposes several variable structure algorithms, as contrasted to the existing efforts of developing better implementable versions of the optimal estimator which uses a fixed set of models. The optimal variable structure estimator is derived and it is shown that the estimator usually considered to be the optimal is only the best within the fixed structure class. Three recursive algorithms are presented in a new framework based on graph theory. The superiority of the new approach is illustrated in numerical examples of a nonstationary noise identification problem.