Efficient procedures for fitting circles and ellipses with application to sliding termination measurements

A problem which occurs regularly in various disciplines, including microwave engineering, is that of fitting a circle or an ellipse to a set of noisy points. This problem occurs, for instance, in some methods of Q-factor measurement and in precision reflectometry. A statistical treatment of this problem, which assumes known angular differences between data points, is given. The effect of the data-point distribution about the circle or ellipse on the variances of the estimators for the coordinates of its center is also examined.