The University of Southampton
University of Southampton Institutional Repository

Consistent least squares fitting of ellipsoids

Consistent least squares fitting of ellipsoids
Consistent least squares fitting of ellipsoids
A parameter estimation problem for ellipsoid fitting in the presence of measurement errors is considered. The ordinary least squares estimator is inconsistent, and due to the nonlinearity of the model, the orthogonal regression estimator is inconsistent as well, \ie, these estimators do not converge to the true value of the parameters, as the sample size tends to infinity. A consistent estimator is proposed, based on a proper correction of the ordinary least squares estimator. The correction is explicitly given in terms of the true value of the noise variance.
adjusted least squares, consistent estimator, ellipsoid fitting, orthogonal regression, quadratic measurement error model, total least squares
177-194
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Kukush, A.
9cf76e13-c463-47c3-9467-0ae6b04df4ef
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Kukush, A.
9cf76e13-c463-47c3-9467-0ae6b04df4ef
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678

Markovsky, I., Kukush, A. and Van Huffel, S. (2004) Consistent least squares fitting of ellipsoids. Numerische Mathematik, 98 (1), 177-194.

Record type: Article

Abstract

A parameter estimation problem for ellipsoid fitting in the presence of measurement errors is considered. The ordinary least squares estimator is inconsistent, and due to the nonlinearity of the model, the orthogonal regression estimator is inconsistent as well, \ie, these estimators do not converge to the true value of the parameters, as the sample size tends to infinity. A consistent estimator is proposed, based on a proper correction of the ordinary least squares estimator. The correction is explicitly given in terms of the true value of the noise variance.

Text
ellest_comp_published.pdf - Other
Download (193kB)

More information

Published date: 2004
Keywords: adjusted least squares, consistent estimator, ellipsoid fitting, orthogonal regression, quadratic measurement error model, total least squares
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 263295
URI: http://eprints.soton.ac.uk/id/eprint/263295
PURE UUID: 3a644fe6-dbd3-4c7e-ab2e-c47466d37beb

Catalogue record

Date deposited: 06 Jan 2007
Last modified: 14 Mar 2024 07:28

Export record

Contributors

Author: I. Markovsky
Author: A. Kukush
Author: S. Van Huffel

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×