Global Positioning System Reference
In-Depth Information
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TABLE 2.2
Example of Fourteen-Parameter Transformation between Geocentric
Frames
T
x
(m)
T
y
(m)
T
z
(m)
ε
x
(mas)
ε
y
(mas)
ε
z
(mas)
s
(ppb)
−
0.0256
−
0.030
−
0.003
−
0.140
0.0047
0.0028
1.48
±
±
±
±
±
±
±
0.0005
0.0006
0.0008
0.025
0.021
0.021
0.09
T
x
(m/y)
T
y
(m/y)
T
z
(m/y)
˙
ε
x
(mas/y)
ε
y
(mas/y)
˙
˙
ε
z
(mas/y)
˙
s
(ppb/y)
−
0.0004
−
0.0008
−
0.0016
0.003
−
0.001
−
0.030
0.03
±
0.0003
±
0.0003
±
0.0004
±
0.012
±
0.011
±
0.011
±
0.05
Note:
Transformation from IGS(ITRF00) to IGS(ITRF97) at epoch
t
k
=
2001
.
5 (Ferland, 2002, p. 26).
Anticlockwise rotations are positive (mas
=
milliarc seconds, ppb
=
part per billion).
[18
be 2001.5 (the fraction of the year is given to one decimal). Soler and Marshall (2002)
derive the following fourteen-parameter transformation for transforming ITRFyy to
ITRFzz
Lin
—
6.0
——
Cus
PgE
t
t
k
+
1
s
t
k
I
R
ε
t
k
x
t,
ITRFyy
x
t,
ITRFzz
=
+
−
(2.3)
t
k
)
t
+
−
1
s
t
k
R
(
s
I
R
ε
t
k
x
t,
ITRFyy
+
(t
−
+
ε
)
+˙
−
Th
e
x
t,
ITRFyy
positions on the right side of (2.3) can be computed from
x
t,
IRTFyy
=
x
t
0
,
IRTFyy
+
(t
−
t
0
)
v
t
0
,
IRTFyy
(2.4)
[18
In
terms of notation,
t
k
is the epoch at which the transformation parameters are given,
t
0
is the epoch of the initial frame IRTFyy, and
t
is the epoch of the final transformed
fra
me ITRFzz (
t
could be the actual time of the GPS observations). The vector
t
k
co
ntains the Cartesian coordinates of the origin of ITRFyy in the frame ITRFzz, i.e.,
it
is the shift between the two frames.
[
ε
x
ε
y
ε
z
]
T
denotes three differential
co
unterclockwise rotations around the
x
,
y
, and
z
axes of the ITRFyy frame, to
es
tablish parallelism with the ITRFzz frame. The symbol
s
denotes the differential
sc
ale change. When applying (2.3), the units must be conformable. The simplified
fo
rm of Equation (2.3) assumes that the velocities
v
t
k
ε
=
v
t
0
are in the same frame.
Th
e transformation parameters are available from the IERS or research institutions
th
at maintain their own realization of the ITRF. Respective software is also readily
av
ailable on the web, e.g., Kouba (2001).
=
2.1.3 Solid Earth Tides
Ti
des are caused by the temporal variation of the gravitational attraction of the sun
an
d the moon on the earth due to orbital motion. While the ocean tides are very much
in
fluenced by the coastal outlines and the shape of the near-coastal ocean floor, the
so
lid earth tides are accurately computable from relatively simple earth models. Their
