Magnetometer math

Hello all,
I am trying to use a magnetometer as a reference vector for yaw drift cancellation in the direction cosine matrix. 

Ok, so here's the nuts and bolts.  If I measure a three axis magnetic vector in the aircraft frame of reference, the direction cosine matrix allows me to translate that vector back to the earth frame of reference. 

Once it is rotated back, what exactly am I looking at?  Do I compare the rotated vector to an Earth fixed magnetic field vector (i.e. from the NOAA tables)?  If so, I have myself convinced that the rotated vector from the aircraft should exactly match the Earth fixed vector assuming a perfect matrix and compass.  Assuming that is the case then any discrepancy between the Earth fixed vector and the rotated vector would be due to yaw drift or compass error. 




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