Digital Signal Processing Reference
In-Depth Information
GNSS electromagnetic wave signal goes through the ionosphere, the phase advance
and code delay will occur, and the travel path will be changed slightly. Currently the
ionospheric delay is one of main error sources in GNSS measurement, which should
be considered carefully for higher accuracy GNSS applications. Here the theory and
estimate of ground-based GNSS ionospheric delay are introduced.
Firstly, the refractive index for electromagnetic wave propagation in Earth's
ionosphere is introduced (e.g., Bassiri and Hajj
1993
). Appleton equation is shown
as follow.
X
n
P
2
h
Y
T
4
4
.
1
C
Y
L
2
i
D
1
(2.9)
Y
T
2
1
iZ
˙
2
.
1
iZ
/
iZ
/
X
X
p
1, X
!
0
2
!
H
!
where
n
P
is complex phase refra
ctiv
e index, i
D
D
!
2
, Y
D
, Z
D
q
Ne
2
"
0
m
, and !
H
B
0
j
e
m
, where ¤ stands
for electron collision frequency, ! is radial frequency,
f
is wave frequency, !
0
is
electron plasma frequency, !
H
is electron gyro frequency, "
0
is permittivity of free
space,
B
0
is ambient magnetic field strength,
e
is electron charge,
m
is electron mass,
and
N
is electron density. When we assume the damping term Z
D
0, Eq. (
2.9
) can
be written as
!
, !
D
2
f
, !
0
D
2f
0
D
D
2f
H
D
X.1
X/
n
P
2
D
1
(2.10)
2
Y
2
sin
2
2
C
.1
X /
2
Y
2
cos
2
1
2
1
2
Y
2
sin
2
˙
1
X
where is the angle between the magnetic field direction and the wave propagation
direction. Usually, a Taylor expansion about the signal frequency
f
and a series of
approximations are made for simplification. Then we could get Eq. (
2.11
)
4
XY
2
cos
2
C
sin
2
(2.11)
1
2
X
1
2
XY
j
cos
j
1
8
X
2
1
4
XY
2
cos
2
1
n
P
D
1
With substituting X, Y and Z into Eq. (
2.11
),
n
L
can be expressed as:
Ne
2
8
2
"
0
mf
B
0
Ne
3
.cos /
16
3
"
0
m
2
f
3
N
2
e
4
128
4
"
0
2
m
2
f
4
n
P
D
1
˙
2
(2.12)
4
XY
2
cos
2
C
sin
2
1
4
XY
2
cos
2
1
C
And group index
n
G
has relationship with
n
P
as follow:
dn
P
dn
G
D
1
C
1
2
X
C
XY cos
C
3
8
X
2
3
4
XY
2
cos
2
C
3
4
XY
2
(2.13)
n
G
D
n
P
C
f
C
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