That's awesome! One very simple thing you can do with that is pass the signal through a bandpass filter (say 2kHz-10kHz) before evaluating power levels to minimize false positives from wind and other environmental noises.

Another method that can be effective with the identification itself is to convert the signal to a spectrograph and classify the resulting images with a neural net.

Vote for the second, but you won't need a neural net, a sum-of-squared differences on a set of reference spectra would probably get you 99% there.