A very basic question here, what are gps coordinates?
GPS coordinates (latitude, longitude) are related to an elipsoid (WGS84), so not a perfect sphere. Since the difference to a sphere is very little most formulas use the spherical approach, or even linear cartesian mathematics.
For regions outside the poles (< latitude 80) and for traces which do not overlap the datum limit (border between longitude -180 and 180) and for an interpolation / regression range that do not exceed 10km, a linear apporoach can be used. At least a simple transformation to cartesian space is needed to overcome the fact that 1 degree of longitude corresponds to a different number of meters as one degree of latitude. Such simple transformation multiply the longitude value with cos(medium latitude).
If the traces exceed the range of 10km, a more complex transformation is needed. E.g UTM transofrmtaion gives cartesian coordinate in the span of 3 degrees of longitude.
This is all is valid as long as you don't need to consider the altitude value of a GPS coordinate. (Aero plane traces would need that). In the later case a ECEF (Earth centered, Earth fixed) transformed coordinatres can be used to make a linear interpolation and to use standard cartesian coordinate mathematics.