Optimal adaptive estimation: Structure and parameter adaption

TLDR

The estimators decompose into a linear Kalman‑Bucy filter bank and a nonlinear adaptive component, enabling application to state estimation with non‑Gaussian initial states, measurement uncertainty, and system identification. The adaptive estimators achieve optimal structure and parameter adaptation for continuous and discrete Gaussian process models, with closed‑form conditional‑error‑covariance for online evaluation and demonstrated applicability to engineering problems.

Abstract

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 nonadaptive part consisting of a bank of Kalman-Bucy filters and a nonlinear part that incorporates the 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 non-Gaussian initial state, to estimation under measurement uncertainty (joint detection-estimation) as well as to system identification. Examples are given of the application of the adaptive estimators to structure and parameter adaptation indicating their applicability to engineering problems.