Understanding GPS
The US GPS system is a collection of 24 space vehicles placed in an approximately 12 hour orbit at +/- 55 degrees lattitude around the earth. By knowing exactly where these satalites are with regard to the earth, comunication with a GPS device can be trilaterated to calculate it's postition as well. GPS delivers to us 4 peices of data. Longitude, Latitude, Altitude, and Time.
Earth is a rock
The Earth is not spherical. Neither is it an ellipsoid, although we use an ellipsoid to approximated it. The Earth is actually a geoid, or shaped like a rock.

The System
The standard for this is constantly in a state of flux, but at this moment, the system is defined by the WGS-84 standard.
[WGS84 Implementation Manual]


Europe has been working on developing their own Galileo GPS system, mainly in the interest on not relying on a US system that can be locked out as a negotiating tactic. Russia uses it's own GLONASS system.
Mathmatics

The earth surface can be approximated as an Oblate Sphereoid or Oblate Ellipsoid. The GPS system uses a definition contained in WGS-84. This model has an equitorial radius of 20925646 feet and a polar radius of 20855487 feet.
F = (x/a)^2 + (y/b)^2 + (z/c)^2 where a = b = 20925646 and c = 20855487.

Hardware Suppliers
Garmin
Megellen
Trimble - Highly accurate GPS. Survey grade.
