Optimal adaptive estimation: Structure and parameter adaptation

Optimal structure and parameter adaptive estimators have been obtained for continuous as well as discrete data gaussian process models with linear dynamics. Specifically, the essentially nonlinear adaptive estimators are shown to be decomposable (partition theorem) into two parts, a linear non-adaptive part consisting of a bank of Kalman-Bucy filters, and a nonlinear part that incorporates the learning or adaptive nature of the estimator. The conditional-error-covariance matrix of the estimator is also obtained in a form suitable for on-line performance evaluation. The adaptive estimators are applied to the problem of state-estimation with nongaussian initial state and also to estimation under measurement uncertainty (joint detection-estimation). Examples are given of the application of the proposed adaptive estimators to structure and parameter adaptation indicating their applicability to practical engineering problems.