Precise Orbit Determination of Global Navigation Satellite System of ...

Chapter 4 Major Error Sources of Satellite Observations
The effects of the atmosphere on radio signal propagation are mainly from two parts of the atmosphere, one is
called troposphere and another is ionosphere.
4.1.1 Tropospheric Error
The troposphere is composed of dry gases and water vapor. Water vapor exists only below altitude of 12 km
above sea level. Water vapor density varies widely with position and time and is much more difficult to predict
than dry gases. Fortunately, however, water vapor effects represent only a relatively small fraction (≈1/10) of
total tropospheric error (Spiker, 1996). Dry gases are relatively uniform in its constituents. For L-band
frequencies, oxygen, which is part of dry gases, is the dominant source of attenuation. Tropospheric errors cause
the radio signal delay.
The signal from the satellite is refracted by the troposphere as it travels to the users on or near the Earth’s
surface. Tropospheric refraction causes a delay that depends upon the actual path of the ray and the refractive
index of the gases along that path. For troposphere symmetric in azimuth about the user antenna, the delay
depends only upon the vertical profile of the troposphere and elevation angle to the satellite.
There are several empirical models for computation of signal delay due to the tropospheric effects. Among them,
Saastamoinen total delay model, Hopfield two quartic models and Black and Eisner model are more popularly
used (Hofmann-Wellenhof et al 1992, Leick 1995, Spiker, 1996).
1)Saastamoinen model (Spiker, 1996)
Tropospheric error which produces a signal delay and thus causes an increase in the observed range can be
calculated by using Saastamoinen standard model as follows
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∆Strop = 0. 002277( 1 + D)sec ψ 0[ P0
+ ( + 0005 . ) e0− Btan ψ 0 ] + δ Rm
(4-1)
T
0
where ∆Strop is the delay correction in meters; P0 e0
water vapor at sea level in millibars; T0 is the absolute temperature at sea level in °Kelvin; The correction term
, are the atmospheric pressure and the partial pressure of
B and δ R are given in Table 4-2 (Spilker, 1996) for various tracking station heights h. The apparent zenith angle
0
ψ 0 = 90 − E in which E is the elevation of satellite related to the tracking station; the value D is
D = 0. 0026cos 2ϕ + 0. 00028h,
where ϕ is the local latitude, and h is the tracking station height in km.
Table 4-2 Correction Terms for Saastamoinen Standard Model
Apparent Zenith Tracking Station Height Above Sea Level
Angle 0 km 0.5 km 1 km 1.5 km 2 km 3 km 4 km 5 km
60°00’ 0.003 0.003 0.002 0.002 0.002 0.002 0.001 0.001
66°00’ 0.006 0.006 0.005 0.005 0.004 0.003 0.003 0.002
70°00’ 0.012 0.011 0.010 0.009 0.008 0.006 0.005 0.004
73°00’ 0.020 0.018 0.017 0.015 0.013 0.011 0.009 0.007
75°00’ 0.031 0.028 0.025 0.023 0.021 0.017 0.014 0.011
δR m 76°00’ 0.039 0.035 0.032 0.029 0.026 0.021 0.017 0.014
77°00’ 0.050 0.045 0.041 0.037 0.033 0.027 0.022 0.018
78°00’ 0.065 0.059 0.054 0.049 0.044 0.036 0.030 0.024
78°30’ 0.075 0.068 0.062 0.056 0.051 0.042 0.034 0.028
79°00’ 0.087 0.079 0.072 0.065 0.059 0.049 0.040 0.033
79°30’ 0.102 0.093 0.085 0.077 0.070 0.058 0.047 0.039
79°45’ 0.111 0.101 0.092 0.083 0.076 0.063 0.052 0.043
80°00’ 0.121 0.110 0.100 0.091 0.083 0.068 0.056 0.047
B mb 1.156 1.079 1.006 0.938 0.874 0.757 0.654 0.563
2) Hopfield Model (Hofmann-Wellenhof et al 1992)
Hopfield’s empirical representation of the dry refractivity as a function of the height h above the surface can be
written as
�hd−h�
Nd( h) = Nd,
0 � �
� hd
�
4
for h≤ hd= 43 km (4-2)
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