I discovered a sound that leaks your exact location (and it's everywhere) [video]
youtube.com
youtube.com
The example with two prop planes seems a bit contrived (not that it wouldn't work with jets, they are usually just much higher up and have less distinct fundamental frequencies). Having two planes within audible range (stated at ~10 km slant range in the video) is a pretty rare event for a lot of places, even in the US with widespread general aviation.
I need a better spectrograph to be sure.
One thing I think is still true, is that you can't completely algorithmically automate this and will have to extract the doppler curves manually from more noisy spectrograms, using your own judgement on what counts as a proper signal or not.
Would be curious to hear from someone who does similar audio analysis.