Usability assessment of selected methods of optimization for some measurement task in coordinate measurement technique

This paper presents the comparison of selected methods of optimization on the example of some measurement task in coordinate measurement technique. The task consists in the computation of coordinates of the center and radius of a circle which approximates some set of measured points using least squares. The application of the least squares method follows an approach used in conventional analysis of an associated element in coordinate measurement technique. The coordinates of points are measured on a CNC machine tool equipped with a measuring probe.

► We examine fitting the sets of points, simulated and measured on CMM, to a circle.
► We develop the application of 5 optimization methods and compare obtained results.
► Polak–Ribiére–Polyak method requires least iterations than other conjugate gradients.
► The optimum number of measurement points to get limited dispersion of results is 20.
► Computations using more than 20 measurement points are considerably more expensive.