A hyperbolic acoustic system for underwater robot self-localization is presented. Anchored transducers send acoustic signals which are observed by a receiver. The system is passive with one-way signal transmission. Time differences of arrival (TDOAs) between the emitted signals are estimated by the receiver via cross-correlation. These TDOAs are fed to an Extended Kalman Filter to estimate the global position of the receiver. We describe the complete signal processing chain as well as challenges in hardware and software design. Experimental results in air and water show the feasibility of the system. This paper demonstrates that acoustic one-way localization is possible with off-the-shelf hardware in experimental test tanks.