HAE, or Height Above Ellipsoid, or "elevation above surface of ellipsoid", is commonly the form of altitude a GPS receiver returns. It differs from AGL (height above ground level) and MSL (height above mean sea level).
Using HAE removes the undulation ("waviness") of the Earth, and presumably (I think) the gravitational effects of the moon and other celestial bodies pulling around on the mean sea level, allowing the Earth to be treated more like the oblate spheroid that it is.
From: https://nextnav.com/hae/ (emphasis added):
Have you ever heard the term Height Above Ellipsoid or HAE? It is a form of measurement common in GPS circles, but perhaps unknown for most lay people. Most people just use GPS for a horizontal location – standard latitude and longitude, or an x/y. That’s what we’re used to seeing on the maps on our phones. Yet tour GPS receiver might also display a height measurement, which sometimes appears in HAE. Understanding this vertical location measurement requires a little more information about how GPS systems produce their data.
The “ellipsoid” part of HAE refers to a mathematical model of the earth. (Remember that the Earth is not a sphere – it’s actually flatter at the poles, hence “ellipsoid”.) GPS scientists created these reference ellipsoids to represent a pristinely smooth version of the Earth’s surface. The ellipsoids used by GPS devices vary – most currently use a model called the WGS84 ellipsoid.
Here is a useful illustration (source; direct link):
- Here's a useful Google search for "height above ellipsoid", which is how I found the article I quoted above.
- WGS-84 ellipsoid: https://en.wikipedia.org/wiki/World_Geodetic_System#WGS_84