Abstract
The most important, natural and practical approach to variable-structure multiple-model estimation is the recursive adaptive model-set (RAMS) approach. It consists of two functional components: model-set adaptation and model- set sequence conditioned estimation. This paper makes contribution to the second component. Specifically, a general, optimal single-step and highly efficient recursion for model-set sequence conditioned estimation based on an arbitrary time-varying model-set sequence is obtained by an extension of the well-known interacting multiple-model (IMM) algorithm. This recursion provides a natural and systematic algorithm, which is optimal within the RAMS approach, for assigning the probabilities to newly activated models and initializing the filters based on these models. In addition, an optimal and highly efficient fusion method is presented for obtaining the overall estimate from these based on two arbitrary model sets, not necessarily disjoint. The optimal recursion and fusion provide a solution to the problem of model-set sequence conditioned estimation that is fairly satisfactory for most practical situations. The results presented here have been employed in the recent development of two variable-structure MM estimators, the likely-mode set and the model-group switching algorithms, that are generally applicable, easily implementable, and significantly superior the best fixed-structure MM estimators available.
