Estimation algebras with state dimension 2

This paper considers general finite dimensional estimation algebras associated with nonlinear filtering systems. Some structural results axe obtained. The properties of Euler operator and the solutions to an under-determined partial differential equation, which inevitably arise in an estimation algebra, are studied. These tools and techniques are applied to the study of finite dimensional estimation algebras with state dimension 2 to obtain a complete classification result. It is shown that a finite dimensional estimation algebra with state dimension 2 can only have dimension less than or equal to 6. Moreover, Mitter conjecture and Levine conjecture hold for finite dimensional estimation algebras with state dimension 2