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

Chapter 2 Observations of Orbit Determination
∂S1
[ r(
t1)
− S ( t2
)] [ r ( t1)
− S ( t 2 )]
=
=
∂r
( t ) || r(
t ) − S ( t ) || S
1
2
t3
1
∂S
[ r ( t3)
− S ( t [ r(
t3)
− S ( t
=
=
∂r
( ) || r ( t ) − S ( || S
1
t2
3
1
T
2
T
4)]
t4)
T
( t2)]
S ( t2)
||
T
S ( t 4 )]
∂S
[ r ( t1)
− S [ r ( t1)
− S ( t
= −
= −
∂S
( ) || r ( t ) −
S
∂S
2 [ r ( t3
) −
[ r ( t3
) − S ( t4
)]
= −
= −
∂S
( t ) || r ( t ) − S ( t ) || S
4
3
4
2
1
4
1
)]
T
2
T
2
)]
T
T
9
(2-35)
(2-36)
(2-37)
(2-38)
∂r(
t1)
∂r
( t1)
∂p(
t1)
δ r( t1)
= δr(
t0)
+
δp(
t0)
(2-39)
∂r(
t ) ∂p(
t ) ∂p(
t )
0
1
0
∂r
( t3)
∂r
( t3)
∂p(
t3)
δ r( t3)
= δr(
t0)
+
δp(
t0)
(2-40)
∂r(
t0)
∂p(
t3)
∂p(
t0)
where
p satellite dynamical model parameters
2.1.2.2 Error Budget
Doppler shift measurement is indirectly made by Phase-Lock-Loop (PLL). PLL measures the difference in the
carrier phase between the incoming carrier and a reference carrier generated by local receiver. The standard error
of phase measurement by PLL is given by
B L
λ
σ ϕ = (2-41)
2π C / N
0
where
λ carrier wave-length
C/N0 carrier-to-noise ratio in 1 Hz bandwidth
Because Doppler shift is the difference between the instantaneous phases at two continuous epochs, the standard
error of Doppler measurement can be evaluated by following a simple formular
σ ϕ
σ D = 2
(2-42)
Ti
where
Doppler integration time constant
Ti
The errors of Doppler measurements are composed of ionospheric, tropospheric, multipath, satellite clock and
receiver errors. Table 2-2 shows the error budget for integrated Doppler count measurement of the TRANSIT
satellite system.
Table 2-2 Error Budget for One-Way Doppler Count Measurement (Seeber, 1993)
* not determined
Error Source Error (m)
Ionosphere 1-5
Troposphere 2
Multipath *
Satellite Clock *
Receiver Error 1-6
Total (1σ) >8
The accuracy listed in Table 2-2 does not look good. For the precise Doppler shift measurements, please refer to
Chapter 3.