This paper presents the implementation of a measurement system that uses a four microphone array and a data-driven algorithm to estimate depth of cut during end milling operations. The audible range acoustic emission signals captured with the microphones are combined using a spectral subtraction and a blind source separation algorithm to reduce the impact of noise and reverberation. Afterwards, a set of features are extracted from these signals which are finally fed into a nonlinear regression algorithm assisted by machine learning techniques for the contactless monitoring of the milling process. The main advantages of this algorithm lie in relatively simple implementation and good accuracy in its results, which reduce the variance of the current noncontact monitoring systems. To validate this method, the results have been compared with the values obtained with a precision dynamometer and a geometric model algorithm obtaining a mean error of 1% while maintaining an STD below 0.2 mm.