Relation between Geoidal separation and antenna altitude in GGA sentence?

The geoidal separation just reports the height difference between the ellipsoidal surface and the geoid model's surface. Natively, GNSS calculates ellipsoidal height (height above ellipsoid surface) but it's usually more useful to have a geoidal height, approximately a height above mean sea level.

The geoidal height is often called an altitude or elevation.

The relationship is

h = N + H

where 

h = height above ellipsoid
H = elevation, orthometric height
N = geoidal separation (some books call this the geoidal height)

The GPS/GNSS device will have some geoid model that it's using to calculate the N value which is the 2nd "z" value given in a GGA NMEA sentence. The first is the calculated orthometric height value, H. Here's the layout of the GGA sentence:

eg3. $GPGGA,hhmmss.ss,llll.ll,a,yyyyy.yy,a,x,xx,x.x,x.x,M,x.x,M,x.x,xxxx*hh
1    = UTC of Position
2    = Latitude
3    = N or S
4    = Longitude
5    = E or W
6    = GPS quality indicator (0=invalid; 1=GPS fix; 2=Diff. GPS fix)
7    = Number of satellites in use [not those in view]
8    = Horizontal dilution of position
9    = Antenna altitude above/below mean sea level (geoid)
10   = Meters  (Antenna height unit)
11   = Geoidal separation (Diff. between WGS-84 earth ellipsoid and
       mean sea level.  -=geoid is below WGS-84 ellipsoid)
12   = Meters  (Units of geoidal separation)
13   = Age in seconds since last update from diff. reference station
14   = Diff. reference station ID#
15   = Checksum

from Glenn Bladdeley GPS NMEA sentence information