Improved algebraic methods for circle fitting

Abstract

Inspired by the circle fitting algorithm “Hyper” of Al-Sharadqah and Chernov [1], which eliminates the second order “essential bias” that excludes terms of O(σ²/N²), we extend their analysis and show that by a small modification the second order bias can be eliminated completely. By numerical experiments, we show that this results in better performance when the number N of points is small and the noise is large.