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In this paper, we propose a novel navigation method for underwater vehicles based on a single seafloor station (SS), with which the vehicles can estimate their positions and orientations with respect to the SS without the need of expensive inertial navigation system or time-consuming calibration. This method is suitable for near-seafloor applications requiring real-time and accurate positioning, such as seafloor imaging and sampling. The method is also suitable for autonomous underwater vehicles (AUVs) since no other external aid is necessary other than SS. The key idea is to utilize mutual acoustical measurements between the vehicle and the SS. Simply explained: 1) the vehicle starts by interrogating the SS acoustically and measures the range between the two units as well as the bearing of the SS with respect to the vehicle in the vehicle reference frame; and then, 2) the SS computes the bearing of the vehicle with respect to the SS and transmits this information back to the vehicle using a similar acoustical device. By combining this information and inputting it into a nonlinear filter structure that includes measurements of the vehicle's ground velocity and yaw angular velocity, the vehicle computes its position and heading estimates. A pair of acoustical devices named acoustical localization and communication (ALOC) devices that can communicate and calculate their relative positions have been built. Sea trials were carried out in October 2011 using the AUV Tri-Dog1 (TD) and a trial SS at Kagoshima Bay in Japan. The AUV successfully navigated around the SS based on the measurements of the ALOC device mounted on both the AUV and the SS. The performance of the method was verified through simulations based on the experimental results.