Bayesian Model Class Selection and Self-Calibratable Model Classes for Real-Time System Identification

Abstract

This chapter introduces the Bayesian model class selection for real-time system identification and an adaptive reconfiguring strategy for the model classes. In addition to parametric estimation, another critical problem in system identification is to determine a suitable model class for describing the underlying dynamical system. By utilizing the Bayes’ theorem to obtain the plausibilities of a set of model classes, model class selection can be performed accordingly. The proposed method provides simultaneous model class selection and parametric identification in a real-time manner. On the other hand, although Bayesian model class selection allows for determination of the most suitable model class among a set of prescribed model class candidates, it does not guarantee a good model class to be selected. It is possible that all the prescribed model class candidates are inadequate. Thus, a new third level of system identification is presented to resolve this problem by using self-calibratable model classes. This self-calibrating strategy can correct the deficiencies of the model classes and achieve reliable real-time identification results for time-varying dynamical systems. On the other hand, the large number of prescribed model class candidates will hamper the performance of real-time system identification. In order to resolve this problem, a hierarchical strategy is proposed. It only requires a small number of model classes but a large solution space can be explored. Although the algorithms presented in this chapter are based on the EKF, the real-time model class selection component and the adaptive reconfiguring strategy for model class selection can be easily embedded into other filtering tools.