Estimating the parameters of a circle by heteroscedastic regression models

Abstract

For fitting a circle to a set of noisy data, a statistical treatment is given using a linear model with heteroscedastic variances when angular differences 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.