Error analysis and enhancing of the ellipticity estimation of steel coils

Measuring the ellipticity of coils is an important topic for the quality assurance in the steel industry. The concentric ellipse fitting algorithm discussed in a previous paper, is an important step to estimate the ellipticity of steel coils, when only a few elliptic curve segments can be used as input data to be processed. In this paper the concentric ellipse fitting algorithm as given by Schleicher et al. is enhanced and adapted for various numerical calculation methods. The variance of the ellipticity estimation is analyzed for different estimators. At first for the simple ellipse fitting problem with only three parameters to be estimated and further for the concentric ellipse fitting problem. Based on these analyses a weighted concentric ellipse fitting algorithm is presented, which is shown to improve the estimation results especially for short data record lengths. Finally the improved algorithm is applied to an industrial application, where the ellipticity of steel coils has to be estimated.