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

Chapter 2 Observations of Orbit Determination
where
n total number of parameters to be solved
6 number of coordinate components of position and velocity of satellite
m number of tracking stations
For example, if eight tracking stations are tracking one satellite at the same time, at least 6+8=14 parameters
should be solved. For one epoch, only 8 observations are available. That means in order to solve the orbit
determination problem using carrier-phase observations, from the theoretical point of view, at least two epochs
of observation are necessary.
2.1.3.2 Error Budget
For dual frequency carrier phase observations, ionospheric error will be significantly decreased. Another
advantage of carrier phase observations is that the receiver noise is much smaller due to high resolution of carrier
phase measurement.
The carrier phase processed in the receiver is mainly affected by following error sources
• Observation resolution
• Variation of the antenna phase center
• Variation of phase delay in the receiver
• Instability of the oscillator
• Interchannel bias
Interchannel bias for each hardware channel can be of order of ±2.5 mm r.m.s. Phase delay variations depend on
the satellite signal strength. The influence can be reduced by processing observations from many satellites.
Oscillator instabilities play only a minor role in carefully designed receivers if the timing signal is taken from the
satellite clock or a well-behaved atomic clock. The phase center variation is minimized and reproducible for
well-designed antenna. For a modern microstrip antenna the variation is a few mm (Seeber, 1993). Observation
resolution depends on the signal to noise ratio from the satellite signals. Currently, the observation resolution is
about 1% of the signal wavelength according to rule of thumb.
Using GPS as an example, the error budget of one-way carrier phase measurements are listed in Table 2-3.
Table 2-3 Error Budget of One-Way Carrier Phase Measurements (GPS, L1)
Error Source Error (m)
Ionosphere 0.1
Troposphere 2.0*
Multipath 0.1
Satellite Clock 3.0*
Receiver Error 0.002
Total (1σ) 3.6
* based on Table 2-1
From Table 2-3, the accuracy of a carrier phase observation is not much better than that of a range observation.
Usually a carrier phase observation is used in differential way. Under this situation, the accuracy of the carrier
phase observation is much higher than that of the range observation. See Chapter 7 for details. Another problem
for carrier phase observations are initial ambiguities. It is difficult to solve initial ambiguites in real-time
applications such as navigaion.
2.2 Two-Way System
In a two-way system, the signal is transmitted and received by the same station. A typical two-way system is
satellite laser ranging (SLR). Supposing that the signal is transmitted by the ground station at ti-1 and is reflected
by the satellite at t = t + ∆ t . The same signal is returned and received at the ground station at
i i−1
1
11