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

Chapter 2 Observations of Orbit Determination
ti+ 1 = ti−1+ ∆t1+ ∆ t2.
Then ∆t1+ ∆t2
will be converted to the range observation by multiplying with velocity of
light.
For two-way microwave measurement system, the received signal is reconstructed in a coherent transponder and
retransmitted. The advantage of a two-way system is that only frequency fluctuations that occur in the up-link
and down-link travel time are uncompensated and for time transfer it is unnecessary to know the precise
positions of satellite or ground stations. The disadvantage is that the propagation errors (ionosphere and
troposphere error) are increased twice.
In the following section the basic observations such as ranging, range rates (Doppler), carrier phases and laser
ranging used in two-way systems are discussed.
2.2.1 Range
S(t 1 )
S(t 4 )
S 2
S 1
12
r(t 3 )
r(t 2 )
Figure 2-4 Two-Way Range Measurement
S(t 3 )
S(t 2 )
2.2.1.1 Basic Observation
In a two-way system, assuming the signal is transmitted from a receiver and returned to the receiver in some
time later (see Figure 2-4), then two-way range observation can be expressed as
L = c(
t 4 − t1)
= S1
+ S 2 + ε
(2-54)
where
1
2
1
2
1
T
2
1
1
2
S = || r ( t ) − S ( t ) || = {[ r ( t ) − S ( t )] [ r ( t ) − S ( t )]}
(2-55)
S
2
and
3
4
3
4
T
3
4
1
2
= || r ( t ) − S ( t ) || = {[ r ( t ) − S ( t )] [ r ( t ) − S ( t )]}
(2-56)
r ( t 2 ) satellite geocentric position vector at t2 r ( t3
) satellite geocentric position vector at t3 S ( t1)
geocentric vector of ground tracking station at t1 S ( t4
) geocentric vector of ground tracking station at t4 The linear observation L is
0
0 0 ∂L
∂L
∂L
∂L
L = L + δ L = S1
+ S2
+ δr
( t2)
+ δS
( t1)
+ δr(
t3)
+ δS
( t4)
(2-57)
∂r
( t2)
∂S
( t1)
∂r(
t3)
∂S
( t4)
where
∂L
∂S1
= (2-58)
∂r
t ) ∂r(
t )
( 2 2