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

被引：8

作者：

Shi, Ji ^{[1
]}

Yau, Stephen S. T. ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing, Peoples R China

来源：

INTERNATIONAL JOURNAL OF CONTROL | 2020年 / 93卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Estimation theory; algebraic methods; nonlinear models; finite dimensional filter; CLASSIFICATION;

D O I：

10.1080/00207179.2018.1550268

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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 omega-matrix must be a constant matrix. Moreover, all functions in the estimation algebra must be linear functions.

引用

页码：2177 / 2186

页数：10

共 20 条

[1]

Benes V. E., 1981, Stochastics, V5, P65, DOI 10.1080/17442508108833174

[2]

Brockett, 1981, NONLINEAR SYSTEMS NO

[3]

Brockett R. W., 1980, GEOMETRY CONDITIONAL

[4]

Brockett R.W., 1983, P INT C MATHMATICIAN, P1357