The geometry of the earth - Physical Geodesy - page 172

To repeat, the ellipsoidal coordinates ϕ, λ, h are defined such as to refer
to the ellipsoid exactly as the natural coordinates refer to the geoid, hence
their names.
Since the deviations of the geoid from the ellipsoid are small and com-
putable, it is convenient to add small reductions to the original coordinates
Φ , Λ ,H, so as to get values which refer to an ellipsoid. In this way we shall
find in Sect. 5.12:

ϕ =Φ − ξ,

λ =Λ η sec ϕ,

h = H + N ;

− (5-1)

ϕ and λ are the ellipsoidal coordinates on the ellipsoid, sometimes also called
geodetic latitude and geodetic longitude to distinguish them from the astro-
nomical latitude Φandthe astronomical longitude Λ. Astronomical and el-
lipsoidal coordinates differ by the deflection of the vertical (components ξ
and η ). The quantity h is the geometric height above the ellipsoid; it differs
from the orthometric height H above the geoid by the geoidal undulation N .
Geodetic measurements (angles, distances) are treated similarly. The
principle of triangulation is well known: historically, distances were obtained
indirectly by measuring the angles in a suitable network of triangles; only
one baseline was necessary in principle to furnish the scale of the network.
Triangulation was indispensable in former times, because angles could be
measured much more easily than long distances.
Nowadays, however, long distances can be measured directly just as eas-
ily as angles by means of electronic instruments, so that triangulation, using
angular measurements, is often replaced or supplemented by trilateration ,
using distance measurements. The computation of triangulations and trilat-
erations on the ellipsoid is easy. It is, therefore, convenient to reduce the
measured angles, baselines, and long distances to the ellipsoid, in much the
same way as the astronomical coordinates are treated. Then the ellipsoidal
coordinates ϕ, λ obtained (1) by reducing the astronomical coordinates and
(2) by computing triangulations or trilaterations on the ellipsoid can be
compared; they should be identical for the same point.
Today, of course, GPS is the best method for determining ϕ, λ ,and h
directly.

5.3 The Global Positioning System

The following sections on the Global Positioning System (GPS) are extracted
from Hofmann-Wellenhof et al. (2003: Sect. 9.3) which in return is based on