Parametrizations in control, estimation and filtering problems: accuracy aspects
type: Item
instance of: scholarly article
title: Parametrizations in control, estimation and filtering problems: accuracy aspects
zbMATH Open document ID: 0929.93002
author: Michel Gevers
author: Gang Li
published in: Communications and Control Engineering
publication date: 1993-09-05T00:00:00Z
review text: The book is devoted to the effects of finite arithmetic computations on the performance of digital filters, controllers and estimators. In contrast to the history and achievements of standard numerical analysis, this area is relatively new with first results obtained in the mid seventies. The basic approach adopted in the book is the formulation of optimal realization (or parametrization) problems in which the aim is to minimize a measure of the performance degradation due to numerical (roundoff in particular) errors. Indeed, although different realizations are equivalent in exact arithmetic (without roundoff errors), they have at the same time different sensitivities to parameter errors which leads to different propagation of errors. The book has several objectives: to collect the existing results and present them in a coherent way, to present a number of new optimal filter realization results, to produce optimal and suboptimal realizations in the context of numerical errors, to investigate the optimal parametrization of controllers in terms of reducing the finite precision effects on the closed loop system, to compare the robustness to numerical errors of optimal shift operator state space realizations vs. optimal \(\delta\)-operator realizations and finally to investigate the role of pre-filtering the data in estimation, identification and filtering problems. The book is divided into 12 chapters, includes 60 figures and 127 references. A number of numerical examples is also included. A motivation and a general statement of objectives are given in the Introduction. Chapter 2 (Finite Word Length Errors and Computations) is devoted to the fundamentals of finite arithmetic computations (fixed-point computations in particular) in signal processing. We note that there are significant differences between floating- and fixed-point computations. Usually the first are considered in standard numerical analysis while the last are typical for the performance of digital filter…
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93C62
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 409054
zbMATH Keywords: numerical errors
zbMATH Keywords: shift operator realizations
zbMATH Keywords: finite arithmetic computations
zbMATH Keywords: performance
zbMATH Keywords: digital filters
zbMATH Keywords: optimal filter realization
zbMATH Keywords: robustness
zbMATH Keywords: \(\delta\)-operator realizations
zbMATH Keywords: pre-filtering
zbMATH Keywords: estimation
zbMATH Keywords: identification
zbMATH Keywords: design
zbMATH Keywords: sensitivity measure
zbMATH Keywords: roundoff noise
zbMATH Keywords: Schur canonical form
zbMATH Keywords: sparse forms
zbMATH Keywords: linear-quadratic optimization
zbMATH Keywords: pole assignment problem
zbMATH Keywords: generalized polynomial parametrizations
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 409054