Estimation algebras with state dimension 2
Xi Wu, Stephen S.‐T. Yau · Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) · 2003
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.