Optimal structure and parameter adaptive estimators have been obtained for continuous a s well a s d i s c r e t e data gaussian process models with linear dynamlcs. Specifically, the essentially nonlinear adaptive estimators are shown to be decomposable (partition theorem) into two parts, a linear nonadaptive 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 ou-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.I.
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