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Underwater docking is critical to enable the persistent operation of Autonomous Underwater Vehicles (AUVs). For this, the AUV must be capable of detecting and localizing the docking station, which is complex due to the highly dynamic undersea environment. Image-based solutions offer a high acquisition rate and versatile alternative to adapt to this environment; however, the underwater environment presents challenges such as low visibility, high turbidity, and distortion. In addition to this, field experiments to validate underwater docking capabilities can be costly and dangerous due to the specialized equipment and safety considerations required to conduct the experiments. This work compares different deep-learning architectures to perform underwater docking detection and classification. The architecture with the best performance is then compressed using knowledge distillation under the teacher-student paradigm to reduce the network's memory footprint, allowing real-time implementation. To reduce the simulation-to-reality gap, a Generative Adversarial Network (GAN) is used to do image-to-image translation, converting the Gazebo simulation image into a realistic underwater-looking image. The obtained image is then processed using an underwater image formation model to simulate image attenuation over distance under different water types. The proposed method is finally evaluated according to the AUV docking success rate and compared with classical vision methods. The simulation results show an improvement of 20% in the high turbidity scenarios regardless of the underwater currents. Furthermore, we show the performance of the proposed approach by showing experimental results on the off-the-shelf AUV Iver3.