Global Positioning System Reference
In-Depth Information
FIGURE 2.4 An octet of an ideal spherical earth.
2.9 EARTH GEOMETRY ( 4-6 )
The earth is not a perfect sphere but is an ellipsoid; thus, the latitude and alti-
tude calculated from Equations (2.18) and (2.20) must be modified. However,
the longitude l calculated from Equation (2.19) also applies to the nonspherical
earth. Therefore, this quantity does not need modification. Approximations will
be used in the following discussion, which is based on references 4 through 6.
For an ellipsoid, there are two latitudes. One is referred to as the geocentric
latitude L c , which is calculated from the previous section. The other one is the
geodetic latitude L and is the one often used in every-day maps. Therefore, the
geocentric latitude must be converted to the geodetic latitude. Figure 2.5 shows
a cross section of the earth. In this figure the x -axis is along the equator, the
y -axis is pointing inward to the paper, and the z -axis is along the north pole of
the earth. Assume that the user position is on the x - z plane and this assumption
does not lose generality. The geocentric latitude L c is obtained by drawing a line
from the user to the center of the earth, which is calculated from Equation (2.18).
The geodetic latitude is obtained by drawing a line perpendicular to the surface
of the earth that does not pass the center of the earth. The angle between this
line and the x is the geodetic latitude L . The height of the user is the distance h
perpendicular and above the surface of the earth.
The following discussion is used to determine three unknown quantities from
two known quantities. As shown in Figure 2.5, the two known quantities are
the distance r and the geocentric latitude L c and they are measured from the
ideal spherical earth. The three unknown quantities are the geodetic latitude
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