Screenshot from the Display Geo Data App, showing the Causeway bridge over the Lake Pontchartrain at New Orleans.
The data points were measured by Jesse Kozlowski, a geodetic surveyor, to about 5 cm accuracy, using his Differential GPS equipment. The points were measured in earth centered earth fixed (ECEF) vectors in cartesian (x,y,z) coordinates by Multilateration of distances to multiple satellites in view at the same time, e.g. NAVSTAR and Galileo. The NAVSTAR satellites orbit the earth in an altitude of 20,200 km. So no measured distance to any satellite was less than 20,200 km and the received signals can not be emitted by transmitters on earth.
GPS does not assume the shape of the earth, no refraction and no perspective is involved. The App shows the vectors as they were measured. All cartesian coordinates gathered are listet in the table at the bottom of the App. If the earth were flat, all points would lie on a plane. But the coordinates for a typical point are (−12,248.083, −5,518,473.705, 3,187,193.785) in meters. If you calculate the length of this vector l = √x2 + y2 + z2 = 6,372,747.153 m, which is the distance of the point from the center of the earth or about the radius of the earth.
The radius of the earth can also be be measured by selecting any 3 data points in a row at the same elevation as shown in the image. In this example the radius calculated is (6362 ± 21) km, which is better than 0.5% accuracy.