Estimation algebras with state dimension 2

Author

Wu, Xi ; Yau, Stephen S T

Author_Institution

Dept. of Math. Stat. & Comput. Sci., Illinois Univ., Chicago, IL, USA

Volume

3

fYear

2001

fDate

2001

Firstpage

2556

Abstract

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

Keywords

nonlinear filters; partial differential equations; state estimation; Euler operator; estimation algebras; finite dimensional estimation algebra; general finite dimensional estimation algebras; nonlinear filtering systems; partial differential equation; state dimension; state dimension 2; Algebra; Computer science; Ear; Filtering theory; Mathematics; Nonlinear equations; Nonlinear filters; Partial differential equations; State estimation; Statistics;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.980649

Filename

980649