In global Structure-from-Motion(SfM) methods, many works have explored synchronization based on pairwise measurements. However, few have investigated the possibility of incorporating higher order measurements into the SfM pipeline, even though higher order measurements contain more complex geometric information. In this talk, we introduce a higher-order synchronization framework that leverages triplet and quadruplet view geometries. We establish new theoretical constraints on a set of trifocal and quadrifocal tensors, expressed as low multilinear rank tensors. We then present two practical frameworks—TrifocalSync and QuadSync for trifocal and quadrifocal tensor synchronization. Our methods show the potential of higher-order synchronization by improving location estimation quality on benchmark SfM datasets.