Circle fitting by iterative inversion

This paper recalls a relatively unknown method of circle fitting (J. A. Brandon and A. Cowley, “A weighted least squares method for circle fitting to frequency response data,” Journal of Sound and Vibration, vol. 83, no. 3, pp. 419-424, 1983) which has been derived using a classical geometric result. We propose a modification of this technique by re-weighting the data, iterating the procedure and choosing at every step as the new inversion point the one diametrically opposite to the previous.