This paper presents a novel navigation system based on the integration of a combined Long Baseline / Ultra Short Baseline (LBL/USBL) acoustic positioning system. First, an Attitude and Heading Reference System is proposed that relies solely on the LBL/USBL and a triad of rate gyros, avoiding the use of magnetometers, with globally exponentially stable (GES) error dynamics. A position and ocean current estimation solution is then introduced, which is fed by the position fixes obtained from the LBL/USBL and relative linear velocity measurements, provided by a Doppler velocity log (DVL). The resulting overall navigation system consists in a cascade system with GES error dynamics. Finally, simulation results are presented and discussed in order to evaluate the performance of the proposed solution.