Recent results on classification of low dimensional estimation algebras

The idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed by Brockelt and Clark, and Mitter independently. In his famous talk at the International Congress of Mathematics in 1983, Brockelt proposed to classify all finite dimensional estimation algebras. An affirmative solution to Brockett´s problem allows us to construct all possible finite dimensional recursive filters from the Lie algebraic point of view. In this paper, we report the development of classification of all estimation algebras with dimension at most 5 with arbitrary state space dimension.