Optimal filtering in systems with degenerate noises in observations
type: Item
instance of: scholarly article
title: Optimal filtering in systems with degenerate noises in observations
zbMATH Open document ID: 1058.93054
author: Yanyan Li
published in: Automation and Remote Control
publication date: 2004-10-19T00:00:00Z
review text: The paper is devoted to the filtering problem for linear stochastic differential systems with degenerate noises in the observations. The implicit value for the filtering estimate can be obtained as a limit in the mean-square sense of a sequence of certain regularized estimates of the Kalman filter. The aim of the author is to construct optimal filtering estimates for the class of observation systems with piecewise constant coefficients. He proposes a special differential transformation for the initial observations. The initial and transformed observations are equivalent in the sense that the respective \(\sigma\)-algebras coincide and the transformation order is not greater than the order of the initial system. The optimal filtering estimate is expressed as the solution of some stochastic differential equation with measure.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93B17
zbMATH DE Number: 2108714
zbMATH Keywords: optimal filtering
zbMATH Keywords: degenerate noises
zbMATH Keywords: linear stochastic differential systems
zbMATH Keywords: regularized estimates
zbMATH Keywords: Kalman filter
zbMATH Keywords: piecewise constant coefficients
zbMATH Keywords: differential transformation
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2108714