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Well it’s amazing what you find on You Tube these days.  It’s not all people falling off skateboards and cute pets.  This video https://www.youtube.com/watch?v=qWARLkZgNeI   by ‘nanolearning’ explains 3, 6, and 9 axis chips pretty well.  I’ll certainly be looking at more of their videos in future.  This nanotechnology is amazing. 
Returning to the question of deviating forces, the basic principle of such electronic compasses is to find a material which has magnetically affected properties and use clever signal processing to produce a fairly accurate indication of direction.  This means they’ll process whatever external magnetic fields they’re subjected to in all three axes very effectively, possibly with some sort of ‘firmware’ to screen out known internally generated magnetic interference.  Rapidly alternating external magnetic fields may or may not affect electronic compasses more than needle compasses; you’d need to know far more about the compass concerned.  Electronic compasses might well be more affected by changes to the vertical component of the steady external magnetic field, because they’re designed to be open to them so they can allow for tilt within the ‘firmware’, whereas the three design aims for a needle compass are Sensitivity, Aperiodicy, and Horizontality.  Also, don’t forget the HT pylon.  They’re usually galvanised mild steel.  DaveP