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This paper introduces robust globally optimal hand-eye self-calibration of camera orientation for the automotive domain. The main contribution are new feasibility problems to integrate this problem into a branch-and-bound parameter space search. The algorithm constitutes the first guaranteed globally optimal maximizer for the support of all three orientation parameters with respect to an a priori defined threshold of reprojection errors. The algorithm operates directly on interest point correspondences and does not depend on any structure and motion preprocessing to estimate camera poses. The complete system is implemented and validated on both synthetic and real automotive datasets.