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

Chapter 2 Observations of Orbit Determination
2.1.3 Carrier Phases
2.1.3.1 Basic Observation
The carrier-phase observations are biased on the integer number of cycles and oscillator frequency offsets
between transmitter and receiver. During a data processing session the initial ambiguities should be included as
parameters in the observation equations and solved with other parameters. The basic observation equation of
carrier phase measurement is written by
2π
L = ϕ r ( t)
−ϕt
( t)
= S1
+ 2πN1
+ ε
λ1
where
ϕ r local copy of the transmitted phase produced by the receiver
ϕ t received satellite phase at the nominal reception time t
initial integer ambiguity
N 1
λ 1
wavelength of signal frequency
c speed of light in vacuum,
ε carrier-phase measurement noises
1
1
10
(2-43)
From Figure 2-1 and Eq.(2-2), the linear observation L of carrier phase can be expressed as follows
0 2π
0 ∂L
∂L
∂L
L = L + δ L = S1
+ [ δr
( t1)
+ δS
( t2)]
+ δN1
λ1
∂r(
t1)
∂S
( t2)
∂N1
where
(2-44)
∂L
2π
∂S1
=
∂r
( t1)
λ1
∂r
( t1)
(2-45)
∂L
2π
∂S1
=
∂S
( t2)
λ1
∂S
( t2)
(2-46)
∂L
∂N
∂S1
= 2π
∂N
(2-47)
and
∂S1
[ r(
t1)
− S ( t2
)] [ r ( t1)
− S ( t 2 )]
=
=
∂r
( t ) || r(
t ) − S ( t ) || S
1
1
t2
1
1
T
2
T
t2)]
( t2)
∂S
[ r ( t1)
− S ( [ r ( t1)
− S ( t
= −
= −
∂S
( ) || r ( t ) − S || S
∂S
1 = I
∂N
1
1
1
T
2
)]
T
(2-48)
(2-49)
(2-50)
∂r(
t1)
∂r
( t1)
∂p(
t1)
δ r( t1)
= δr(
t0)
+
δp(
t0)
(2-51)
∂r(
t ) ∂p(
t ) ∂p(
t )
∂L
= I
∂N
1
0
1
0
(2-52)
Eq.(2-43) or Eq.(2-44) can also be expressed as
Li = f ( x,
y,
z,
x&
, y&
, z&
, N i )
(2-53)
where
x, yz , geocentric coordinates of satellite position
xyz &, &, & geocentric coordinates of satellite velocity
In Eq.(2-53) the tracking station coordinates are assumed to be known parameters. Eq.(2-53) shows that each
observation has an extra parameter, the initial integer ambiguity. Fortunately, the number of parameters will not
be increased if the observations are continuous. Therefore, the minimum number of parameters to be solved can
be described.
n=6 + m