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

Chapter 2 Observations of Orbit Determination
(2) Integrated Doppler Count
S(t 2 )
S(t 4)
S 2
S 1
8
r(t 3)
r(t 1)
Figure 2-3 Doppler Count Measurement
S(t 3)
S(t 1)
The equation of integrated Doppler count measurement can be written by
f0
L = ( f0
− ft
)( t3
− t1)
+ ( S2
− S1)
(2-27)
c
where
f0 ft the reference frequency of receiver
the transmitting frequency of satellite signal
From Figure 2-3,
1
1
2
1
2
T
1
2
1
2
S = || r ( t ) − S ( t ) || = {[ r ( t ) − S ( t )] [ r ( t ) − S ( t )]}
(2-28)
S
2
3
4
3
4
T
3
4
1
2
= || r ( t ) − S ( t ) || = {[ r ( t ) − S ( t )] [ r ( t ) − S ( t )]}
(2-29)
where
t )
r ( 1 satellite geocentric position vector at t1 r ( t3
) satellite geocentric position vector at t3 S ( t2
) the geocentric vector of ground tracking station at t 2
S ( t4
) the geocentric vector of ground tracking station at t 4
The basic linear observation L is expressed as
0
ft
0 0
L = L + δL
= ( f0
− ft
)( t3
− t1)
+ ( S2
− S1
)
c
ft
∂L
∂L
∂L
∂L
+ {[ δr
( t3)
+ δS
( t4)]
−[
δr(
t1)
+ δS
( t2)]}
c ∂r
( t3)
∂S
( t4)
∂r(
t1)
∂S
( t2)
where
(2-30)
∂L
=
∂r
t )
ft
∂S2
c ∂r
( t )
(2-31)
( 3
3
L ft
∂S2
( t4)
c ∂S
( t4
∂
∂S
=
)
(2-32)
∂L
=
∂rt
( )
ft
∂S1
c ∂rt
( )
(2-33)
∂
∂S
1
1
L ft
∂S1
( t2)
c ∂S
( t2
= (2-34)
)