Global Positioning System Reference
In-Depth Information
national Terrestrial Reference Frame (ITRF), administered by the International
Association of Geodesy. For example, the WGS 84 (G1150) matches the ITRF2000
frame to better than 1 cm, one sigma [7].
The fact that there have been four realizations of WGS 84 has led to some confu-
sion regarding the relationship between WGS 84 and other reference frames. In par-
ticular, care must be used when interpreting older references. For example, the
original WGS 84 and NAD 83 were made coincident [8], leading to an assertion that
WGS 84 and NAD 83 were identical. However, as stated above, WGS 84 (G1150) is
coincident with ITRF2000. It is known that NAD 83 is offset from ITRF2000 by
about 2.2m. Hence, the NAD 83 reference frame and the current realization of WGS
84 can no longer be considered identical.
2.2.4 Height Coordinates and the Geoid
The ellipsoid height, h , is the height of a point, P, above the surface of the ellipsoid,
E, as described in Section 2.2.3.1. This corresponds to the directed line segment EP
in Figure 2.8, where a positive sign denotes point P further from the center of the
Earth than point E. Note that P need not be on the surface of the Earth, but could be
above or below the Earth's surface. As discussed in the previous sections, ellipsoid
height is easily computed from Cartesian ECEF coordinates.
Historically, heights have not been measured relative to the ellipsoid but,
instead, relative to a surface called the geoid . The geoid is that surface of constant
geopotential, W
W 0 , which corresponds to global mean sea level in a least squares
sense. Heights measured relative to the geoid are called orthometric heights, or, less
formally, heights above mean sea level. Orthometric heights are important, because
these are the type of height found on innumerable topographic maps and in paper
and digital data sets.
The geoid height, N , is the height of a point, G, above the ellipsoid, E. This cor-
responds to the directed line segment EG in Figure 2.8, where positive sign denotes
point G further from the center of the Earth than point E. And, the orthometric
height, H , is the height of a point P, above the geoid, G. Hence, we can immediately
write the equation
=
P
Topography
H
G
Geoid
N
Ellipsoid
E
Figure 2.8
Relationships between topography, geoid, and ellipsoid.
 
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