A circle fitting procedure and its error analysis

Abstract

An efficient least squares circle fitting procedure and its general random-error analysis are described. The first-order random errors of the center coordinates and the radius of the fitted circle are discussed in detail. The effect of data point distribution along the circle is investigated, and for an important microwave application (sliding termination measurements) the frequency dependence is also evaluated. The effects of the second-order error terms are also discussed and general formulas are given. Finally an estimation of data point error is provided.