I found a lot of pieces of an answer to this question, but no complete and good one.
How does a GPS System calculate it's own accuracy at the moment?
Where does it get the known position to compare measured positions to?
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There are many many factors that affect the accuracy of the GPS. However they all go down to there is no "correct" but a more accurate value. Of course you might add some more accurate values to compare your results to - e.g. by using differential GPS which uses a base-station of a very accurate measued (e.g by geodetic information) location.
However a usual GPS calculates its own accuracy based on usual statistics. It gets a number of locations for one single point and calculates its arithmetic mean as well its the standard deviation and many other parameters.
Having said this the accuracy of a GPS-device is mostly determinded by the number of signals (sensors) that measure a given location. On most deviced you have therefor the number of satellites displayed which are currently used/can be seen by your device.
EDIT: Unfortunetaly the US-military (which invented GPS) has a disturbing signal which reduces accuracy from 20cm to 1-2meter.