A statistical analysis of the Delogne-Kasa method for fitting circles

Zelniker, Emanuel E. and Clarkson, I. Vaughan, L. (2006) A statistical analysis of the Delogne-Kasa method for fitting circles. Digital Signal Processing, 16 5: 498-522.

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Author Zelniker, Emanuel E.
Clarkson, I. Vaughan, L.
Title A statistical analysis of the Delogne-Kasa method for fitting circles
Journal name Digital Signal Processing   Check publisher's open access policy
ISSN 1051-2004
Publication date 2006-09
Sub-type Article (original research)
DOI 10.1016/j.dsp.2005.04.001
Volume 16
Issue 5
Start page 498
End page 522
Total pages 25
Place of publication San Diego
Publisher Elsevier Inc.
Collection year 2006
Language eng
Subject 280404 Numerical Analysis
230202 Stochastic Analysis and Modelling
230118 Optimisation
230203 Statistical Theory
230201 Probability Theory
230204 Applied Statistics
Abstract In this paper, we examine the problem of fitting a circle to a set of noisy measurements of points on the circle's circumference. Delogne (Proc. IMEKO-Symp. Microwave Measurements 1972, 117-123) has proposed an estimator which has been shown by Kasa (IEEE Trans. Instrum. Meas. 25, 1976, 8-14) to be convenient for its ease of analysis and computation. Using Chan's circular functional model to describe the distribution of points, we perform a statistical analysis of the estimate of the circle's centre, assuming independent, identically distributed Gaussian measurement errors. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than 3 and the variance exists when this number is greater than 4. We also derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the Cramer-Rao lower bound.
Keyword circle fitting
least squares
maximum-likelihood estimation
Moore-Penrose inverse
Cramer-Rao lower bound
random matrices
Wishart distribution
Q-Index Code C1

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Created: Fri, 05 May 2006, 10:00:00 EST by Emanuel Emil Zelniker on behalf of School of Information Technol and Elec Engineering