The betatron tune in the Large Hadron Collider (LHC) is measured using a Base-Band Tune (BBQ) system. The processing of these BBQ signals is often perturbed by 50 Hz noise harmonics present in the beam. This causes the tune measurement algorithm, currently based on peak detection, to provide incorrect tune estimates during the acceleration cycle with values that oscillate between neighbouring harmonics. The LHC tune feedback (QFB) cannot be used to its full extent in these conditions as it relies on stable and reliable tune estimates. In this work we propose new tune estimation algorithms, designed to mitigate this problem through different techniques. As ground-truth of the real tune measurement does not exist, we developed a surrogate model, which allowed us to perform a comparative analysis of a simple weighted moving average, Gaussian Processes and different deep learning techniques. The simulated dataset used to train the deep models was also improved using a variant of Generative Adversarial Networks (GANs) called SimGAN. In addition we demonstrate how these methods perform with respect to the present tune estimation algorithm.