This explanation of GPS appeared on the Malibu Mirage Owners and Pilots
Association (MMOPA) List and clears up a number of misconceptions about
how this all works. A fellow Pilot friend of mine posted this to a forum......
Aircraft GPS Systems:
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 (whichever is the greater), it
obtains a difference, or deviation.
The GPS uses deviations to generate error signal commands which instruct
the aircraft to move from a position where it is to a position where it
isn't, arriving at a position where it wasn't, or now is. Consequently,
the position where it is, is now the position where it wasn't; thus, it
follows logically that the position where it was is the position where
the event that the position where the aircraft now is, is not the position
where it wasn't, the GPS has acquired a variation. Variations are caused by
external factors, the discussions of which are beyond the scope of this
variation is the difference between where the aircraft is and where the
aircraft wasn't. If the variation is considered to be a factor of
significant magnitude, a correction may be applied by the use of the
autopilot system. However, use of this correction requires that the aircraft
now knows where it was because the variation has modified some of the
information which the aircraft has, so it is sure where it isn't.
Nevertheless, the aircraft is sure where it isn't (within reason) and it
knows where it was. It now subtracts where it should be from where it
isn't, where it ought to be from where it wasn't (or vice versa) and
integrates the difference with the product of where it shouldn't be and
where it was; thus obtaining the difference between its deviation and
its variation, which is variable constant called "error".