Global Positioning System Reference
In-Depth Information
0.014
N
s
= 400
N
s
= 350
N
s
= 300
10°
0.012
0.01
N
s
= 400
N
s
= 350
N
s
= 300
45°
0.008
0.006
0.004
0.002
0
0
20
40
60
80
100
120
Horizontal separation (km)
Figure 8.4
Variation in tropospheric delay difference due to elevation angle.
small, negligible additional term in (8.3). However, the total delay difference is also
small. Even for extreme values of refractivity (400) and low angles (10º), the differ-
ences in delays are not much more than 2 cm.
Real-world data suggests that tropospheric delays vary more rapidly with dis-
tance than can be attributed solely to differences in viewing angle. Much larger dif-
ferences in tropospheric delay from location to location arise in reality because the
troposphere often differs significantly from the model, especially at an interface
between land and water or where the user and reference station are separated by a
weather front. In a study described in [4], differences in tropospheric delays as large
as 40 cm were observed over a 25-km baseline for satellites above 5º. This suggests a
vertical tropospheric delay difference on the order of 4 cm over this base-
line—leading to much larger slant differences than could be attributed to differences
in viewing angle alone. The smallest difference in tropospheric error observed in [4]
over a 25-km baseline was 10 cm.
A difference in heights between the user receiver and the reference station has a
greater effect than a horizontal displacement. Reference [3] develops the following
relationship between the tropospheric delay,
ε
Tropo
meters, experienced by the refer-
ence station and delay,
ε
Tropo
meters, experienced by a user at a height
h
kilometers
above the station (Figure 8.5):
083
.
⋅
(
)
h
2
−
0 0002
.
N
+
0 07
.
⋅
h
+
−
0 0017
.
S
Tropo
Tropo
N
ε
=
ε
⋅
e
S
h
m
At an altitude of 1 km above the reference station, the user experiences a delay of
083
360
.
⋅
(
)
1
2
−
0 0002
.
×
360
+
0 07
.
⋅ +
1
−
00017
.
Tropo
Tropo
ε
=
ε
⋅
e
h
m
ε
Tropo
=
045
.
×
=
045
.
×
36
.
mm
=
16
.
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