Optimal linear filtering under parameter uncertainty
type: Item
instance of: scholarly article
title: Optimal linear filtering under parameter uncertainty
zbMATH Open document ID: 0988.93082
DOI: 10.1109/78.738249
author: José C. Geromel
published in: IEEE Transactions on Signal Processing
publication date: 2002-07-05T00:00:00Z
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 1632201
zbMATH Keywords: linear stochastic system
zbMATH Keywords: minimum error variance
zbMATH Keywords: robust linear filter
zbMATH Keywords: convex bounded parameter uncertainty
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1109/78.738249
OpenAlex ID: W2111812602
review text: The author considers the linear time-invariant matrix system of the form NEWLINE\[NEWLINE\dot{x}=Ax+Bw,\quad y=Cx+Dw, \quad z=LxNEWLINE\]NEWLINE with white noise \(w\). It is supposed that the total matrix consisting of \(A\), \(B\), \(C\), \(D\) is unknown, but it belongs to a given convex bounded polyhedral domain. The problem of designing a guaranteed minimum error variance robust filter is solved, and a complete design methodology of robust filters is proposed. The results generalize the previous ones in several directions. Namely, all system matrices can be corrupted by parameter uncertainty, and also the admissible uncertainty may be structured. A comparison with previous results [\textit{I. R. Petersen} and \textit{D. C. MacFarlane}, ``Robust estimation for uncertain system'' in Proc. 30th IEEE Conf. Decision Contr., Brighton, U.K. (1991)] demonstrates that the author's method provides a robust filter with better or at least equal performance. Moreover, it applies to more general models of parametric uncertainties, and no unidimensional search (with respect to the parameter \(\varepsilon\)) is needed. Some numerical results are presented.
reviewed by: Yuliya S. Mishura
description: scientific article; zbMATH DE number 1632201