Finite-Dimensional Filters with Nonlinear Drift IV: Classification of Finite-Dimensional Estimation Algebras of Maximal Rank with State–Space Dimension 3

Abstract

The idea of using estimation algebras to construct finite-dimensional nonlinear filters was first proposed by Brockett and Mitter independently. It turns out that the concept of estimation algebra plays a crucial role in the investigation of finite-dimensional nonlinear filters. In his talk at the International Congress of Mathematics in 1983, Brockett proposed a classification of all finite dimensional estimation algebras. Chiou and Yau classify all finite-dimensional estimation algebras of maximal rank with dimension of the state space less than or equal to two. In this paper we succeed in classifying all finite-dimensional estimation algebras of maximal rank with state–space dimension equal to three. Thus from the Lie algebraic point of view, we have now understood generically all finite dimensional filters with state–space dimension less than four.