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

Chapter 2 Observations of Orbit Determination
∂r(
t4)
∂r
( t4)
∂p(
t4)
δ r( t4)
= δr(
t0)
+
δp(
t0)
∂r
( t0)
∂p(
t4)
∂p(
t0)
(2-93)
r&
( t1)
r&
∂
δ ( t1)
= r&
( t0)
r&
δ
∂ ( t0)
(2-94)
r&
( t4
)
r&
∂
δ ( t4
) = δr&
( t0
)
∂r&
( t )
(2-95)
0
∂S
( t2)
δ S ( t2)
= δS
( t0)
(2-96)
∂S
( t )
0
∂S
( t3)
δ S ( t3)
= δS
( t0)
(2-97)
∂S
( t0)
where
p satellite dynamical model parameters
2.2.2.2 Error Budget
Like two way range observations, for the two-way Doppler observation, the atmosphere errors are increased
twice. Using error propagation law, the accuracy of two-way Doppler observation can be given by
2
ion
2
trop
2
multi
2
r
2
noise
md = 2m
+ 2m
+ m + 2m
+ 2m
≈ 2mo
(2-98)
where
md two way Doppler error
one way Doppler error
m o
2.3 Conclusion
In this chapter the major observations of one-way and two-way systems such as ranges, range rates (Doppler),
carrier phases and laser ranges were discussed. One-way observations require two clocks, one in the receiver and
another on-board the satellite. This introduces clock synchronization errors to the observations. Two-way
observations do not have such a problem. Another advantage of two-way observations is that for time transfer no
accurate position coordinates of satellite and ground station are needed to compute the signal propagation delays
of the mainly reciprocal paths and the clock offset respectively (Hahn, 1996). Significant drawbacks of two-way
observations are that atmospheric errors are introduced twice due to the signal traveling around the propagation
path.
As an orbit tracking system for GNSS-2, range observations are one of the best choices for orbit determination,
because a range observation is simple in mathematical form, easily processed and well modeled for the various
error sources. It is very important that range observations can be used in real time. If SLR is used for orbit
determination of GNSS-2 satellites, in addition to the advantages mentioned above, there is another advantage,
high accuracy. The disadvantage is that SLR is strongly dependent on the weather, which can not be used in
routine operation.
Carrier phase observations are highly accurate measurements, but they are complicated to process due to initial
ambiguity and cycle slips, especially in real-time applications. If two L-band frequencies just like the GPS
system are used, it is difficult to determine GEO satellite orbits using carrier phase observations because the
initial ambiguity is not sensitive to GEO satellite.
Doppler measurement is also a good choice due to its high accuracy. It can also be used in real time applications.
For GEO satellite orbit determination, the problem is that the position change of GEO satellite related to the
earth is so small that the accuracy of Doppler measurement will not be good.
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