In this study, we improved the matching efficiency of underwater terrain matching navigation. Firstly, a new geodesic-based method was developed by combining the law of the shortest arc in spherical geometry with the theory of the attitude control in space and maritime environments. Secondly, along a design track, the geodesic-based method helped reduce the radius of the search matching area, and improved the matching efficiency. Finally, for parameter setting, the search matching time of underwater terrain matching navigation was reduced from 9.84 s to 1.29 s (about 7.6 times), with the matching accuracy being invariable using the new geodesic-based method.
