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dc.contributor.authorZelniker, Emanuel Emilen
dc.contributor.authorClarkson, Vaughan L.en
dc.identifier.citationConference 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.2069-2073en
dc.descriptionCopyright © 2004 IEEEen
dc.description.abstractIn 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.en
dc.description.statementofresponsibilityZelniker, E.E.; Clarkson, I.V.L.en
dc.publisherIEEE: Institute of Electrical and Electronics Engineersen
dc.titleA generalisation of the Delogne-Kasa method for fitting hyperspheresen
dc.typeConference paperen
dc.contributor.schoolSchool of Computer Scienceen
dc.contributor.conferenceAsilomar Conference on Signals, Systems & Computers (38th : 2004 : Pacific Grove, California)en
Appears in Collections:Computer Science publications

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