Parameter estimation in linear static systems based on weighted least absolute value estimation
type: Item
instance of: scholarly article
title: Parameter estimation in linear static systems based on weighted least absolute value estimation
zbMATH Open document ID: 0644.93059
DOI: 10.1007/BF00962801
author: S. A. Soliman
author: G. S. Christensen
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: We present a new method for estimating a parameter vector of which measurements are carried out; however, these measurements are subjected to noise. First, we briefly consider least square estimation of such vector to obtain some well-known results. Then, we proceed to formulate the problem in the least absolute value (LAV) sense and show that we can obtain a set of overdetermined equations for the components of the unknown vector. These equations are solved using the least square approach to ascertain which points give the least residuals. Having gained that information, we set to zero a number of residuals equal to the rank of the matrix H. Let this rank be k; then, the number of points which satisfy the LAV solution identically is k; this is a requirement that the LAV solution must satisfy [see, \textit{W. W. Kotiuga} and \textit{M. Vidyasagar}, IEEE Trans. Power Apparatus Syst. PAS-101, No.4, 844-853 (1982); and \textit{I. Barrodale} and \textit{F. D. K. Roberts}, SIAM J. Numer. Anal. 15, 603-611 (1978; Zbl 0387.65027)]. Several examples are presented in the paper.
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93E12
zbMATH DE Number: 4051480
zbMATH Keywords: parameter vector
zbMATH Keywords: least square estimation
zbMATH Keywords: least absolute value
zbMATH Keywords: time-invariant
MaRDI profile type: Publication
cites work: An Efficient Algorithm for Discrete $l_1$ Linear Approximation with Linear Constraints
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cites work: Q3818224
cites work: Stochastic models, estimation, and control. Vol. 1
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full work available at URL: https://doi.org/10.1007/bf00962801
OpenAlex ID: W1971572606
description: scientific article; zbMATH DE number 4051480