Aircraft Inertial Navigation System
The aircraft knows where it is at all times. It knows this because it knows where it isn’t. By subtracting where it is from where it isn’t, or from where it isn’t from where it is (depending on which is greater), it obtains a difference or deviation.
The inertial guidance system uses deviations to generate corrective commands to drive the aircraft from a position where it is to a position where it isn’t. The aircraft arrives at the position where it wasn’t; consequently the position where it was is now the position where it isn’t.
In the event that the position where it is now is not the same position where it originally wasn’t, the system acquires a variation, this variation being the difference between where the aircraft is and where the aircraft wasn’t. If the variation is considered to be a significant factor, it too may be corrected by the inertial guidance system. However, the aircraft must now know, also, where it was.
The “thought process” of the aircraft is as follows: because a variation has modified some of the information the aircraft obtained, the aircraft is not sure where it was. It now subtracts where it should be from where it wasn’t, and by differentiating this from the algebraic difference between its deviation and it’s variation, it obtains the difference called error, usually attributed to the pilot. 