A simple explanation of inertial navigation systems
The equipment, and hence 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 where it isn't from where it is, depending on which is greater ), it obtains a difference or deviation. The inertial reference system uses deviations to generate corrective commands to fly 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 as the position where it originally wasn't, the system will acquire a variation. (Variations are caused by external factors, and discussion of these factors is beyond the scope of this simple explanation.)
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Happy flying.