A General Systematic Method for Model-Set Design

Model-set design is one of the most important topics of the multiple-model (MM) approach, which is the state of the art for many estimation, control, and modeling problems. The work presented here proposes a general systematic model-set design method in the parameter space of a system based on number theoretic (NT) methods for design of statistical experiments. The system is characterized by uncertain parameters that describe the mode space, and the models used in the model set are designed to approximate the mode by minimizing distribution mismatch. Two types of F-uniform model sets that perform well are proposed: one by the NT methods, the other according to an F-centered discrepancy. In order to improve the performance of the F-uniform model sets further, two types of expected mode augmentation (EMA) are applied. Simulation examples are given and compared with results from the Monte-Carlo method to demonstrate the designs and their performance.