In this paper, a novel closed form solution is presented for solving the simultaneous localization and mapping (SLAM) problem. Unlike existing methods which rely on iterative feature matching, the proposed method utilises 3D phase correlation. This method provides high noise robustness, even in the presence of moving objects within the scene which are problematic for SLAM systems. Quantitative and qualitative experimental results are presented, evaluating the noise sensitivity, reconstruction quality and robustness in the context of moving objects.