This seems equivalent to http://www.mathworks.com/matlabcentral/fileexchange/5557-circle-fit. Also, other algorithms are often more accurate when fitting data along only an arc (e.g., http://www.mathworks.com/matlabcentral/fileexchange/22643 ).

A good reference for fitting data to circles: "Least Squares Fitting of Circles" by N. Chernov and C. Lesort, Journal of Mathematical Imaging and Vision, Vol 23, 239-252 (2005). Nikolai Chernov has several good functions in the FEX for fitting to circles and ellipses.