Abstract: For long gap tunable undulator systems in free-electron laser (FEL), phase shifters with high control accuracy are required to ensure that the phases of the radiation field between two adjacent undulators matched with each other.We have studied the impact of control accuracy of phase shifter and analyzed its error sources.This study aims to improve the control accuracy of phase shifters and tries to overcome the shortcomings of the traditional calibration methods, such as complicated calibration procedure and low accuracy manual operations.Based on the improved Gaussian-Newton parameter estimation, this paper proposes an automatic error calibration system for phase shifters, including the preliminary concept and the algorithm.This method has been applied to installing and calibrating all the phase shifters of the European X-ray Free Electron (Euro-XFEL).The control accuracy of each phase shifter reaches micrometer-level in the environment of high magnetic forces, which satisfies the specified engineering design requirements.