On a new class of finite dimensional estimation algebras
type: Item
instance of: scholarly article
title: On a new class of finite dimensional estimation algebras
zbMATH Open document ID: 0628.93068
DOI: 10.1016/0167-6911(87)90012-0
author: Wing Shing Wong
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: It is now well-known that the so-called estimation algebra of a partially observed diffusion is infinite-dimensional except in some particular cases including the linear case; following Benesh' work [\textit{V. E. Benesh}, Stochastics 5, 65-92 (1981; Zbl 0458.60030)], several papers have dealt with the problem of finding new particular cases; the aim is indeed a better understanding of algebraic properties of the filtering problem. The system studied in this paper consists of a signal solution of \(dx(t)=f(x)dt+Gdw(t)\) where G is a non-singular matrix, and of an observed process of the form \(dy(t)=Hx(t)dt+dv(t)\). A sufficient condition for the estimation algebra to be finite-dimensional is given in terms of two matrix-valued functions; this condition contains both linear and Benesh' filters. Some examples are given.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93E10
zbMATH DE Number: 4023172
zbMATH Keywords: nonlinear filters
zbMATH Keywords: finite dimensional Lie algebras
zbMATH Keywords: estimation algebra
zbMATH Keywords: partially observed diffusion
reviewed by: Jean Picard
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90012-0
OpenAlex ID: W1997032888
cites work: New classes of finite-dimensional nonlinear filters
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cites work: Q3254327
description: scientific article; zbMATH DE number 4023172