I would say, before you dive into multi-fractal stochastic calculus, maybe take a step back and work on some fundamentals that have been used to solved this problem before. Look up Kalman filtering, Doppler filters, correlations, and microphone directivity.

The problem you are trying to solve here can be classically expressed as X'=Ax+Bu; Y = Cx + Du + Ev. Where Ax models the noise generating dynamics of the the drone, Bu models the control of the drone (typically random from your perspective), C,D,E model how the noise reaches and is processed by your microphone, and v is a random source simulating the wind.