Finite dimensional estimation algebras with state dimension 3 and rank 2, Mitter conjecture

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.

KEYWORDS:

• Estimation theory
• algebraic methods
• nonlinear models
• finite dimensional filter

AMS CLASSIFICATIONS:

• 17B30
• 35K15
• 60G35
• 93E11

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author would like to thank China Scholarship Council for their support [grant number 201606210725]. This work was supported by the National Natural Science Foundation of China [grant number 11471184] and the start-up fund from Tsinghua university.