The second plot shows the transfer function between the UPS signal and h. Green points are those with coherence larger than 0.03 (!). The transfer function shows a smooth 1/f^4 shape (see the superimposed red line).
As a first noise subtraction trial, I filtered the UPS signal with a two complex poles at 1 Hz (Q=3) to recover the 1/f^4 shape. I also tentatively notched the 50 Hz line. Then I subtracted this from hrec, with a coefficient empirically optimized by hand.
The noise reduction obtained in hrec is shown in the third plot. The coherence between the subtracted channel and the UPS sniffer is significantly reduced, see plot 4. Of course the performances of this very simple subtraction are bad below 10 Hz (no hrec there!) and around 50 Hz harmonics (which are independently canceled in hrec I believe).
In conclusion, this is a proof of principle that magnetic noise can be subtracted from dark fringe even with very simple techniques which could in principle be applied online in the reconstruction stream. More efficient subtractions could be obtained implementing adaptive schemes, if needed, and using all the magnetic probes.
