Global Positioning System Reference
In-Depth Information
2.2.3 World Geodetic System
The standard physical model of the Earth used for GPS applications is the DOD's
World Geodetic System 1984 (WGS 84) [5]. One part of WGS 84 is a detailed
model of the Earth's gravitational irregularities. Such information is necessary to
derive accurate satellite ephemeris information; however, we are concerned here
with estimating the latitude, longitude, and height of a GPS receiver. For this pur-
pose, WGS 84 provides an ellipsoidal model of the Earth's shape, as shown in Fig-
ure 2.7. In this model, cross-sections of the Earth parallel to the equatorial plane are
circular. The equatorial cross-section of the Earth has radius 6,378.137 km, which
is the mean equatorial radius of the Earth. In the WGS 84 Earth model, cross-sec-
tions of the Earth normal to the equatorial plane are ellipsoidal. In an ellipsoidal
cross-section containing the z -axis, the major axis coincides with the equatorial
diameter of the Earth. Therefore, the semimajor axis, a , has the same value as the
mean equatorial radius given previously. The minor axis of the ellipsoidal cross-sec-
tion shown in Figure 2.7 corresponds to the polar diameter of the Earth, and the
semiminor axis, b , in WGS 84 is taken to be 6,356.7523142 km. Thus, the eccen-
tricity of the Earth ellipsoid, e , can be determined by
b
a
2
e
=−
1
2
WGS 84 takes e 2
0.00669437999014. It should be noted that this figure is
extremely close, but not identical, to the Geodetic Reference System 1980 (GRS 80)
ellipsoid quantity of e 2
=
0.00669438002290. These two ellipsoids differ only by
0.1 mm in the semiminor axis, b .
Another parameter sometimes used to characterize the reference ellipsoid is the
second eccentricity,
=
e , which is defined as follows:
a
b
2
a
b e
e
′=
1
=
2
WGS 84 takes
e
2
=
0.00673949674228.
z
S
h
u
N
n
b
w
φ
O
P
A
Equatorial plane
a
Figure 2.7
Ellipsoidal model of Earth (cross-section normal to equatorial plane).
 
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