A circle fitting procedure using semi-parametric modelling: Toward an improved sliding load calibration procedure

Circle fitting problems often occur in microwave engineering when dealing with variable delays (e.g. calibration using a sliding load). In this paper an efficient semi-parametric circle fitting procedure is proposed which takes into account the phase relationships over the frequencies. It produces more accurate results by the parsimonious principle, requires less measurements and is more robust to the settings of the positions of the sliding load than the nonparametric model [1]. Using the variance of the estimates, optimal position settings are proposed together with a statistically based validation technique to detect systematic errors with respect to the circle model. The performance of the proposed method is illustrated on sliding load measurements up to 50 GHz, illustrating that the accuracy of the semi-parametric method using 3 positions is comparable to the nonparametric method with 6 positions.