A generalisation of the Delogne-Kasa method for fitting hyperspheres

Zelniker, Emanuel E. and Clarkson, I. Vaughan L. (2004). A generalisation of the Delogne-Kasa method for fitting hyperspheres. In: K. Teague and S. Acton, Proceedings of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computing. The Thirty-Eighth Asilomar Conference on Signals, Systems and Computing, Pacific Grove, California, (2069-2073). 7-10 November, 2004. doi:10.1109/ACSSC.2004.1399530

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Author Zelniker, Emanuel E.
Clarkson, I. Vaughan L.
Title of paper A generalisation of the Delogne-Kasa method for fitting hyperspheres
Formatted title
A generalisation of the Delogne-KÅsa method for fitting hyperspheres
Conference name The Thirty-Eighth Asilomar Conference on Signals, Systems and Computing
Conference location Pacific Grove, California
Conference dates 7-10 November, 2004
Proceedings title Proceedings of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computing   Check publisher's open access policy
Journal name Conference Record - Asilomar Conference on Signals, Systems and Computers   Check publisher's open access policy
Place of Publication The United States of America
Publisher IEEE
Publication Year 2004
Sub-type Fully published paper
DOI 10.1109/ACSSC.2004.1399530
ISBN 0-7803-8623-X
ISSN 1058-6393
Editor K. Teague
S. Acton
Volume 2
Start page 2069
End page 2073
Total pages 5
Collection year 2004
Language eng
Abstract/Summary In this paper, we examine the problem of fitting a hypersphere to a set of noisy measurements of points on its surface. Our work generalises an estimator of Delogne (Proc. IMEKO-Symp. Microwave Measurements 1972,117-123) which he proposed for circles and which has been shown by Kasa (IEEE Trans. Instrum. Meas. 25, 1976, 8-14) to be convenient for its ease of analysis and computation. We also generalise Chan's 'circular functional relationship' to describe the distribution of points. We derive the Cramer-Rao lower bound (CRLB) under this model and we derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We perform a statistical analysis of the estimate of the hypersphere's centre. 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 M + 1, where M is the dimension of the hypersphere. The variance exists when the number of sample points is greater than M + 2. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the CRLB. We provide simulation results to support our findings.
Subjects E1
230202 Stochastic Analysis and Modelling
780101 Mathematical sciences
Q-Index Code E1

 
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Created: Thu, 23 Aug 2007, 19:27:33 EST