I don't know whether GPS altitude is measured against an estimate of local sea level with reference to the Earth's centre - 'sea level' is not the same world-wide. Or whether an assumed perfect oblate spheroid provides the GPS datum?
Beagle is absolutely right to raise this point.
It is best explained by starting with how LNAV works. LNAV is based on a ellipsoid (a perfect, regular geometric shape) model of the earth. Both GPS and aviation charts (at least in most developed countries) use the same ellipsoid datum (WGS84, the ICAO standard).
VNAV is measured against a different kind of shape, a geoid. This is irregular and takes into account variations in the earth's composition and form which, in turn, cause local variations in gravity and mean sea level.
GPS altitude is initiallly calculated with reference to the WGS84 ellipsoid as a coordinate and then translated into an altitude using the EGM96 geodetic model for the mean sea level datum.
However, EGM96 is NOT the standard for aviation charts and instrument procedures. There is no standard - a local MSL datum tends to be used. This varying datum is of no relevance to pilots using barometric altimetry, because they will be using a QNH which is referenced to the same local datum as the charts. However, the difference between the local datum and EGM96 could be quite sigificant. Whether the your GPS is accurate to 1ft or 5ft or 10ft doesn't matter if the datums vary by 100ft.
Hence why we have to use barometric altimetry in aviation, for the time being....
brgds
421C
see page 52 of the following link
http://www.pplir.org/images/stories/...vmanual1_8.pdf