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Type: Conference paper
Title: A generalisation of the Delogne-Kasa method for fitting hyperspheres
Author: Zelniker, Emanuel Emil
Clarkson, Vaughan L.
Citation: Conference record of the Thirty-Eighth Asilomar Conference on Signals, Systems & Computers : November 7-10, 2004, Pacific Grove, California / Michael B. Matthews (ed.), vol. 2, pp.2069-2073
Publisher: IEEE: Institute of Electrical and Electronics Engineers
Issue Date: 2004
ISBN: 0780386221
ISSN: 1058-6393
Conference Name: Asilomar Conference on Signals, Systems & Computers (38th : 2004 : Pacific Grove, California)
School/Discipline: School of Computer Science
Statement of
Zelniker, E.E.; Clarkson, I.V.L.
Abstract: 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.
Description: Copyright © 2004 IEEE
RMID: 0020064271
DOI: 10.1109/ACSSC.2004.1399530
Appears in Collections:Computer Science publications

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