In image processing phase correlation has been shown to outperform feature matching in several contexts. In this paper, a novel volume registration technique is proposed 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. Furthermore, a novel projection method is proposed which performs Fourier based volume registration 3 times faster. Quantitative and qualitative experimental results are presented, evaluating the proposed method’s the noise sensitivity, performance, reconstruction quality and robustness in the context of moving objects.