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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.

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

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

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Date deposited: 06 Jan 2007
Last modified: 19 Jul 2019 22:29

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