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Estimating the parameters of a circle by heteroscedastic regression models

✍ Scribed by Su-Ju Yin; Song-Gui Wang

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
236 KB
Volume
124
Category
Article
ISSN
0378-3758

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✦ Synopsis

For ΓΏtting a circle to a set of noisy data, a statistical treatment is given using a linear model with heteroscedastic variances when angular di erences between successive data points are known. A two-stage estimate of circle parameters is proposed, and its statistical properties are also established. In particular, we show that the two-stage estimate is uniformly better than the ordinary least-squares estimate under the criterion of mean squares error. Our simulation results also show that at least for small sample sizes the two-stage estimate has smaller mean squares error than the maximum likelihood estimates.

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