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.
