I have been doing a little investigating of the Teensy Audio Library for a FFT so that I could just extract the phase and bin magnitude (bin size 43 Hz) with the 1024 bin library.  Sadly magnitude but no phase.  I could roll my own with a Goertzel algorithm but that would involve work.  

I am finding that getting a very narrow filter is easy with the 16 Biquad cascaded filters by just dialing up the "Q" parameter.  There is a warning to use caution above 0.707 so that signals don't exceed 1.0.  Going up to 10 didn't seem to cause distortion problems though it did ring like a bell.  I wonder if that could be a good long as long as I can distinguish the Doppler from just ringing.  

There must be a million ways of doing this.  Any other ideas?