From a purely signal point of view, if you have a good characterization of the drone sound (your training set) and of the noise, then the appropriate filter would be something along the lines of a weiner type which statistically maximizes the SNR. Preventing your microphone from saturating when measuring the wind is very important as well, and a good use of a wind blocker or muffler.

If your microphone saturates its input that will distort the spectrum of the signal you are measuring.