GPS receiver doesn't know where the ground is and they don't need to be "calibrated". It just know the receiver location calculated from satellite messages it received. Satellites are traveling in fixed orbits. Receiver then calculates its position from the satellite positions with respect to absolute time. Each satellite is essentially a 3rd order time standard. First order being the universal time standard in Paris, 2nd order being the US National time standard at NIST near Denver.

GPS receiver calculates the travel speed from the next position and elapsed time. Each location point is recorded as altitude, longitude, latitude and time. So no calibration on the "ground" is needed. Once it got a fix anywhere, on the ground or in a plane, it is "calibrated" if you want to call it that.

GPS maps are overlays and tied to receiver location via datum set by USGS and other national surveying agencies. The latest one in use in the US is from 1984 thus called WGS84.

Below is a recorded track FRA-SFO. The GPS device was turned on after the plane took off and left on for the entire flight until near SFO. Each leg recorded represents the distance between two points (Alt, Long, Lat, time) and speed is calculated from it.

FRA-SFO