Model-Set Design, Choice, and Comparison for Multiple-Model Approach to Hybrid Estimation

The most important problem in the application of the multiple-model approach is the design of the model set used. This paper deals with this challenging topic in a general setting, along with model-set choice and comparison. General and representative problems of model-set design, choice, and comparison are considered. Modeling of models as well as true mode as random variables is proposed. Several general methods for design of model sets are presented by minimizing distribution mismatch, minimizing modal distance, and moment matching. The concept of relative efficacy of each model in a set and its two quantitative descriptions are introduced. Optimality criteria and performance measures for model-set design, choice, and comparison based on base-state estimation, mode estimation, mode identification, hybrid-state estimation, information metrics, and hypothesis testing are presented. Several computationally efficient and easily implementable solutions of the model-set choice problems based on sequential hypothesis testing are presented, some of which are optimal. Examples that demonstrate how some of these theoretical results can be used as well as their effectiveness are given. Many of the general results presented in this paper are also useful for performance evaluation of MM algorithms.