Hi everyone! I just finished this post, please enjoy it and let me know if you have questions or suggestions (especially regarding the math portions, of which I have a hard time understanding anything beyond year 2 calculus!).
Thinking about noise reduction I come up with low pass or band pass filters and using multiple microphones to correlate the signal. However I have no experience, at all.
In the most simple case, simply adding two slightly separated signals should not increase the noise. The problem is, the helicopter sound itself is very noisy, so I'm not sure this would work well. A lot of microphones might be needed, increasing the cost many times.
For low pass filtering, there are mufflers for microphones, did you have those?
Edit: and of course that's not really getting any points in the computer science department.
Summing multiple measurements will grow the noise at the rate of the sum of the squares (also called the 2 norm) because noise is hopefully uncorrelated. The signal, because it is correlated, will sum simply so that with enough measurements your SNR will increase. These measurements can be done in space or time.
We did think of mufflers, but we didn't have them as we were using a dataset collected by another researcher, who used the same system in a quiet environment, then in a windy 'real world' environment. We used this data for training, testing and validation, but didn't have the equipment or time to make a new dataset :(
But this is probably the most practical solution, the data we have doesn't allow for it however. This could be used in the real world and the system could be more accurate, however in a crowded environment there will be other sounds the microphone will pick up, so some type of noise filter would be needed anyway.
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.
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.
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For low pass filtering, there are mufflers for microphones, did you have those?
Edit: and of course that's not really getting any points in the computer science department.
But this is probably the most practical solution, the data we have doesn't allow for it however. This could be used in the real world and the system could be more accurate, however in a crowded environment there will be other sounds the microphone will pick up, so some type of noise filter would be needed anyway.
If your microphone saturates its input that will distort the spectrum of the signal you are measuring.
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.