When I flew the CRJ200 there was usually a problem with the heading reference. The heading for the cm1 was obtained from the right flux valve located near the end of the right wing. The cm2 was the opposite flux valve. There was always a small difference between both hdgs. A very curious fact was, every day, when taxiing near the same building, one of the hdgs deviated more than 8 degrees to the other, with the correspondent caution msg. It was corrected by itself as the plane were far away from the building, and by the TO time the difference was good enough to continuation of the flight. The wind shown on each display after the TO was very different, becoming the same as the difference on the hdg disappeared. If you want to see that very clear on the CRJ, try to vary during the fly, the hdg of the PNF with the small lever at the center pedestal for the gyro correction,. You will see that a pair degrees variation in hdg produces a huge variation in the calculated wind. Moving the gyrocompass further away, you can obtain amazing winds on the ND.
As far as I know, airplanes not having ADIRUs obtains wind from a continuous computation HDG vs TRK and TAS vs GS.
I believe the ADIRUs calculates the wind from track, drift and GS obtained with 3D gyros and accelerometers and the TAS obtained by the ADC, but this could not be exact.
Both systems are very accurate, except during ground operations. In that cases drift is forced to be 0, so the only real data is the head/tail wind component which is the same as the TAS/GS difference.
Tailwinds