GPS measurements are comprised of a 2D surface coordinate system (e.g. lat/long) and an altitude above mean sea level. So, "speed" as measured by GPS is speed along the Earth's surface.

EDIT: assuming a constant altitude flight

No, GPS measurements are taken as receiver distance from orbiting satellites whose orbits are calculated in a 3-D+t inertial reference frame (ECI), which is then converted to an earth-centered-earth-fixed (ECEF) coordinate. From there an end user devices can transform to desired Datum reference (a model of the Earth's surface) depending on the application. Everything about GPS is inherently 3D+t.

Guys I am talking about how commercial aircraft GPS reports speed. I understand how it gets its fix from satellites; what it reports to the human is speed along the reference horizontal datum AKA "the ground."

If you fly from point A to point B in one hour at 10,000 feet, and then fly from point A to point B in one hour at 30,000 feet, GPS will report the same speed for both flights. It does not bother to correct for the slightly longer path at 30,000 feet because that level of precision is simply not needed for commercial aviation.

>> GPS measurements are comprised of a 2D surface coordinate system

GPS is inherently 3 dimensional.

There's some interesting stuff going on behind the scenes. GPS inherently gives you a 3-dimensional coordinate, which is useless for most applications. So the coordinate gets converted to a 2D surface coordinate (latitude/longitude) plus an altitude, which is what you generally want. However, since the Earth isn't a perfect sphere, this conversion is not well-defined.

The solution is a datum, a model of the Earth's surface that is used for the conversion. WGS84 is the datum used by GPS, and approximates the Earth as a specified ellipsoid. However, maps can use use different datums (data?), so there can be a discrepancy of many meters between what GPS says the location is, and what the map says the location is, and they can both be right relative to their datum.

> and an altitude above mean sea level

Nah, you're clearly misunderstanding how GPS works.

GPS allows you to directly measure displacement of any 2 points in 3 dimensions.

You're speaking of the altitude + lat/lon instead, which is in polar coordinates.