Finite dimensional estimation algebras with state dimension 3 and rank 2, Mitter conjecture. Issue 9 (1st September 2020)

• Record Type: Journal Article
• Authors: Shi, Ji; Yau, Stephen S. T.
• Is Part Of: International journal of control. Volume 93:Issue 9(2020)
• Page Start: 2177
• Page End: 2186
• Publication Date: 2020-09-01
• Subjects: Estimation theory -- algebraic methods -- nonlinear models -- finite dimensional filter; 17B30 -- 35K15 -- 60G35 -- 93E11; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1550268
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: In this paper, we study the structure of finite dimensional estimation algebras with state dimension 3 and rank 2 arising from a nonlinear filtering system by using the theories of the Euler operator and under-determined partial differential equations. It is proved that if the estimation algebra contains a degree two polynomial, then the Wong Ω-matrix must be a constant matrix. Moreover, all functions in the estimation algebra must be linear functions.