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.) .

The variation is 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 IRS. The aircraft must now know where it was. The "Thought Process" of the equipment is as follows: because a variation has modified some of the navigational information which the aircraft acquired, it is not sure where it is. However, it is sure where it isn't and knows where it was. It now subtracts where it should be from where it wasn't ( or vice-versa ) and by differentiating this from the algebraic difference between where it shouldn't be and where it was, it is able to obtain the difference between its deviation and its variation; this difference being called error.