NavList:

Frank wrote:  A systematic error should never be assumed or calculated unless there is direct, positive reason to believe that such an error exists.

which is true.  For an example of when systematic errors could be assumed, such errors were realised and indeed corrected for when it came to aircraft sextants relying on a bubble or pendulous reference and an averaging mechanism, particularly in high flying jets in the 50s, 60s, and 70s, possibly flying in permanent twilight close to the pole, where radio aids were in short supply.  

There was Coriolis acceleration, and possibly rhumb line steering to allow for.  When each single observation might last up to two minutes, you might travel 16nm, so the effect of change of variation on heading might need to be allowed for.  Changes in heading due to Dutch roll and speed due to the phugoid, whose periods might not coincide with the length of the observation were recorded and corrected for (using the Mears Slide in the RAF).  In permanent near twilight close to the Pole, the Sun might just be visible from the troposphere, but deep study of the refraction formulae was necessary, because the correction was large and changed rapidly below Hs =0.  With RAF sextants, which were stepped, there was often a different index error to apply for each 10 degree step.  On the other hand, they didn’t have to worry about dip. DaveP