General model-set design methods for multiple-model approach

Multiple-model approach provides the state-of-the-art solutions to many problems involving estimation, filtering, control, and/or modeling. One of the most important problems in the application of the multiple-model approach is the design of the model set used in a multiple-model algorithm. To our knowledge, however, it has never been addressed systematically in the literature. This paper deals with this challenging topic in a general setting. General problems of model-set design are considered. A concept of a random model is introduced. In other words, modeling of models used in a multiple model (MM) algorithm as well as the true model as random variables is proposed. Three classes of general methods for optimal design of model sets-by minimizing distribution mismatch, minimizing modal distance, and moment matching, respectively-are proposed. Theoretical results that address many of the associated issues are presented. 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.