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 .
Search WWH ::




Custom Search