Home-made differential GPS

GPS information is deliberately "dumbed down" by adding an artificial error - only the military gets the exact data. The artificial error is random and changes every couple of minutes. So, what can be done to get more accurate positions?

A fixed base station with an exactly known location receives GPS data. It calculates the difference between the GPS location and the real location and transmits the error as a broadcast. A GPS receiver can receive the broadcast and deduct its exact position from its own GPS location and the error.

Neat! What what do you if you don't have a base station and a GPS-receiver that supports differential GPS? My laptop will serve as the base station. While I control the ship the laptop will stay put and receive GPS information. Any "jumping around" in the location is general GPS positioning error plus artifical error. The total error - how would I separate general from artifical error? - is transmitted to the ship via WLAN. The ship takes its own GPS measurements and uses the transmitted error information to improve the accuracy of the position.

That's the theory. Will it really improve the accuracy, or will the general errors of two receivers just add up and increase the blur? I am going to try this out by using two laptops with GPS receivers on a walk in the park.

Back to "how would I separate general from artifical error?". Maybe I could integrate the position of the base station over a longer amount of time. If the artificial error only changes every couple of minutes (verify that!), that might help.