Just to put in my two cents, Civilian GPS are at MOST accurate to 1m in horizontal position. This is due to the wavelength the signal is broadcast in, and the position, and number of satellites each unit can track. Much more error is found in vertical measurements, and is greatly increased when only three or four satellites are being tracked.
When A GPS tracks a route, it takes the differences in successive positions and adds them up. Looking at a map of the route only gives you half the picture, the sampled profile will appear much more jagged than the true profile. The longer, GPS profile will lead to longer than measured courses EVEN IF THE ROUTE LOOKS IDENTICAL on a map.
Civilian units that can be purchased for $30k or so will reduce the error significantly, but they require two receivers; one fixed, one rover. This is called "Differential GPS". By comparing differences in the signals received by the rover from the base and the satellites, corrections can be made to reduce horizontal and vertical error to less than 1cm. I use these in my profession as a Civil Engineer, and find the accuracy astoundingly repeatable.
Military units achieve the same 1cm accuracy with only one receiver. This is simply a matter of decoding a number (28-36) of differently coded messages coming from the individual (28-36) satellites, on 3 frequencies, in real-time. Each satellite broadcasts correction information to each other satellite, and is in turn repeated by each and every satellite. This correction is updated about 3 times a week per satellite, and is computed by measuring each satellites position with a laser from a few places on the earth at the same time. Also, radio-interferometry is used to check velocities and direction constantly, to correct the corrections between adjustments. The upshot is they have to know, within a cm, where all of the satellites are at all times, or be able to correct for the positional error. Corrections are made for weather, gravitational fluctuations, ionospheric events, altitude and velocity of the receiver, and many, many more. About 20 corrections in all to get to centimeter-level accuracy.
The built-in innacuracy (Called spoofing) was reportedly turned off in the first Gulf War to enable troops to carry cheap, and accurate enough, commercial grade GPS units onto the battlefield. It is the assumpion of all GPS users that this is has stayed off, because it has not been announced that it was ever turned back on.
There are a couple good book on the subject, I'd recommend "GPS For Surveyors", as it is easily read, and lacks the lenghty mathematical proofs others include.