Improved Algorithms to determine the Non-Linear Optics Model of the SPS from Non-Linear Chromaticity

In recent years several measurements of the SPS nonlinear chromaticity have been performed in order to determine the non-linear optics model of the SPS machine at injection energy for different cycles. In 2006 additional measurements have been performed at injection and during the ramp for the cycle used to accelerate the LHC beam. New and more robust matching algorithms have been developed in 2006 to fit the model to the measurements up to arbitrary chromatic order. In this paper we describe the algorithms used in the analysis of the data and we summarize and compare the results from all experiments.