But do common aviation GPSs display HAE for "altitude"? Given that other elevations (e.g. terrain and obstacles) are referenced to mean sea level, it seems strange that GPS manufacturer would choose to ignore a relatively simple correction like geoid height.
I don't know what the standard is at display level, but at output level there are two different standards unfortunately. Internally, GPS usually works in WGS84, and calculates HAE. The output (through Arinc 743, label 076) can be either HAE or above MSL (743A). In the latter case the GPS unit must obtain the difference between MSL and HAE (geoid undulation), for example by looking up values in a database and interpolating between them.
If the GPS gives MSL on label 076, then it gives HAE on label 370, because some systems require HAE (for example GLS).
MSL is used for example by the EGPWS.
Latitude and longitude is always in WGS84 for aeronautical GPS units.
The
EGM96 model accurately defines the difference between HAE and MSL. The range is approx. +/- 100 meters.