Recent results on classification of finite dimensional maximal rank estimation algebras with state space dimension up to 5

The idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed independently by Brockett (1981) and Mitter (1979). Brockett proposed to classify all finite dimensional estimation algebras. An affirmative solution to Brockett´s problem will allow one to construct all possible finite dimensional recursive filters from the Lie algebraic point of view. In this paper we classify all maximal rank finite dimensional estimation algebras with state space dimension five