NEW CLASSES OF FINITE DIMENSIONAL FILTERS WITH NONMAXIMAL RANK ESTIMATION ALGEBRA ON STATE DIMENSION n AND LINEAR RANK n-2

被引：6

作者：

Jiao, Xiao-pei ^{[1
]}

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

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2020年 / 58卷 / 06期

基金：

中国国家自然科学基金;

关键词：

finite dimensional filters; estimation algebra; Wong's Omega-matrix; nonmaximal rank; NONLINEAR DRIFT; CLASSIFICATION;

D O I：

10.1137/20M1350467

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Ever since the Kalman filter technique was popularized, there has been an abundance of interest in finding new classes of finite dimensional recursive filters. In this paper, by applying Wong's theorem [W. S. Wong, Systems Control Lett, 9 (1987), pp. 79-83], we construct a new class of finite dimensional filters with arbitrary state space dimension n and linear rank n - 2. Importantly, we show that in the new class of nonlinear filtering systems, the entries of Wong's Omega-matrix need not be constants or polynomials and can be C-infinity functions.

引用

页码：3413 / 3427

页数：15

共 24 条

[1]

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

[2]

Bensoussan A., 1992, STOCHASTIC CONTROL P

[3]

Brockett R., 1980, Analysis and Optimization of Stochastic Systems, P299

[4]

Brockett RogerW., 1981, STOCHASTIC SYSTEMS M, P441, DOI [10.1007/978-94-009-8546-923, DOI 10.1007/978-94-009-8546-923]

[5]

Chaleyat-Maurel M., 1984, STOCHASTICS, V13, P83, DOI [10.1080/17442508408833312, DOI 10.1080/17442508408833312]

[6] Finite-dimensional filters with nonlinear drift .6. Linear structure of Omega [J].

Chen, J ;

Yau, SST .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 1996, 9 (04) :370-385

[7] Real-Time Solution of Time-Varying Yau Filtering Problems via Direct Method and Gaussian Approximation [J].

Chen, Xiuqiong ;

Shi, Ji ;

Yau, Stephen S-T .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2019, 64 (04) :1648-1654

[8] FINITE-DIMENSIONAL FILTERS WITH NONLINEAR DRIFT .2. BROCKETTS PROBLEM ON CLASSIFICATION OF FINITE-DIMENSIONAL ESTIMATION ALGEBRAS [J].

CHIOU, WL ;

YAU, SST .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1994, 32 (01) :297-310

[9]

Dong W., 2019, INT J CONTROL, V92, P1

[10] NONEXISTENCE OF FINITE-DIMENSIONAL FILTERS FOR CONDITIONAL STATISTICS OF THE CUBIC SENSOR PROBLEM [J].

HAZEWINKEL, M ;

MARCUS, SI ;

SUSSMANN, HJ .

SYSTEMS & CONTROL LETTERS, 1983, 3 (06) :331-340

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