Designing a high-performance controller for an Autonomous Underwater Vehicle (AUV) is a challenging task. There are often numerous requirements, sometimes contradicting, such as speed, precision, robustness, and energy-efficiency. In this paper, we propose a theoretical concept for improving the performance of AUV controllers based on the ability to learn periodic signals. The proposed learning approach is based on adaptive oscillators that are able to learn online the frequency, amplitude and phase of zero-mean periodic signals. Such signals occur naturally in open water due to waves, currents, and gravity, but can also be caused by the dynamics and hydrodynamics of the AUV itself. We formulate the theoretical basis of the approach, and demonstrate its abilities on synthetic input signals. Further evaluation is conducted in simulation with a dynamic model of the Girona 500 AUV on a hovering task.