Digital Signal Processing Reference
In-Depth Information
Usually, only the first order of the phase refractive index and group refractive
index are considered during ionospheric delay estimation (Datta-Barua et al.
2008
).
Then, phase velocity
V
P
and group velocity
V
G
can be obtained easily as
1
40:3
f
2
c
1
C
40:3
N
f
2
c
n
P
c
D
V
P
(2.14)
1
C
40:3
f
2
c
1
40:3
N
c
n
G
c
V
G
D
(2.15)
f
2
As we know, GPS observation equations are expressed as:
P
1
D
C
I
G
.f
1
/
(2.16)
P
2
D
C
I
G
.f
2
/
(2.17)
L
1
D
C
I
P
.f
1
/
C
N
1
1
(2.18)
L
2
D
C
I
P
.f
2
/
C
N
2
2
(2.19)
where is the sum of the true geometry range between the satellite and the receiver
and frequency-independent errors,
I
stands for ionospheric delay,
N
is integer
ambiguity, and is the wavelength of the GPS signal. If the traveling time of GPS
signal is
t
, the geometry range can be written as follow:
c
1
C
40:3
N
f
2
dt
D
ct
C
Z
Z
f
2
Z
f
2
Z
40:3
40:3
D
V
P
dt
cNdt
D
ct
C
Nds
t
t
t
s
Z
Z
c
1
40:3
N
f
2
dt
D
ct
f
2
Z
f
2
Z
40:3
40:3
D
V
G
dt
cNdt
D
ct
Nds
t
t
t
s
(2.20)
Then, ionospheric delay
I
P
and
I
G
can be derived from Eq. (
2.20
).
Z
40:3
f
2
I
P
D
Nds
s
Z
40:3
f
2
I
G
D
Nds
(2.21)
s
The total electron content (TEC) of the ionosphere can be calculated as the
integration of
N
along the signal path:
Z
TEC
D
Nds
(2.22)
s
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