Optimal adaptive estimation: Structure and parameter adaptation-Part I: Linear models and continuous data

A Bayesian approach to optimal adaptive estimation with continuous data is presented. Both structure and parameter adaptation are considered and specific recursive adaptation algorithms are derived for gaussian process models and linear dynamics. Specifically, for the class of adaptive estimation problems with linear dynamic models and gaussian excitations, a form of the "partition" theorem will be given that is applicable both for structure and parameter adaptation. The "partition" or "decomposition" theorem effects the partition of the essentially nonlinear estimation problem into two parts, a linear non-adaptive part consisting of ordinary Kalman estimators and a nonlinear part that incorporates the adaptive or learning nature of the adaptive estimator. In addition, a simple performance measure is introduced for the on-line performance evaluation of the adaptive estimator. The on-line performance measure utilizes quantities available from the adaptive estimator and hence a minimum of additional computational effort is required for evaluation.