Global Positioning System Reference
In-Depth Information
hence the covariance matrix for the local coordinates is according to (8.44):
⎡
⎤
7
.
37
4
.
14
−
13
.
96
⎣
⎦
.
enu
=
4
.
14
4
.
56
−
9
.
38
−
13
.
96
−
9
.
38
33
.
07
From this we get
σ
e
=
2
.
7m,
σ
n
=
2
.
1m, and
σ
u
=
5
.
7m.
8.10
World Geodetic System 1984
The ellipsoid in WGS 84 is defined through four parameters; see Anonymous
(1997):
1. the semi-major axis
a
=
6,378,137 m,
2. the Earth's gravitational constant (including the mass of the Earth's atmo-
sphere)
GM
10
8
m
3
s
2
,
=
3,986,004.418
×
/
3. the flattening
f
=
1
/
298
.
257223563,
10
−
11
rad
ω
=
×
/
4. the Earth's rotational rate
7,292,115
s.
10
−
11
rad
ω
e
=
×
/
The International Astronomical Union uses
7,292,115.1467
s,
ω
e
with four extra digits, together with a new definition of time, and this value for
is used for GPS. The speed of light in vacuum is taken as
c
=
299,792,458 m/s.
Conceptually, WGS 84 is a very special datum as it includes a model for the
gravity field. The description is given by spherical harmonics up to degree and
order 180. This adds 32,755 more coefficients to WGS 84 allowing for determi-
nation of the global features of the geoid. A truncated model (
n
18) of the
geoid is shown in Figure 8.11. For a more detailed description; see Anonymous
(1997).
In North America the transformation from NAD 27 to WGS 84 is given as
⎡
=
m
=
⎤
⎡
⎤
X
WGS 84
Y
WGS 84
Z
WGS 84
X
NAD 27
+
9m
⎣
⎦
=
⎣
⎦
.
Y
NAD 27
−
161 m
Z
NAD 27
−
179 m
A typical datum transformation into WGS 84 only includes changes in the semi-
major axis of the ellipsoid and its flattening and three translations of the origin of
the ellipsoid.
WGS 84 is a global datum, allowing us to transform between regions by means
of GPS. The importance of WGS 84 is undoubtedly to provide a
unified global
datum
.
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