Geoscience Reference
In-Depth Information
By substituting Eq.
20
into Eq.
29
, the ionospheric total delay for the phase observa-
tions is expressed as
C
X
8
f
4
C
X
2
f
2
C
X
C
Y
2
f
3
ion
ph
N
e
Δρ
=−
N
e
ds
±
N
e
B
0
cos
θ
ds
−
ds
+
κ,
(30)
−
ds
0
represents the curvature effect. The first three-terms of
Eq.
30
denote the first order and higher order ionospheric delays. Assuming that the
integrations are evaluated along the geometric path
s
0
for simplification, the curvature
effect is neglected; thus
ds
turns to
ds
0
and the equation results in
ds
where
κ
=
C
X
8
f
4
C
X
2
f
2
C
X
C
Y
2
f
3
ion
ph
N
e
Δρ
=−
N
e
ds
0
±
N
e
B
0
cos
θ
ds
0
−
ds
0
.
(31)
First Order Delay
In the first-order approximation, the ionospheric delay for phase measurements is
derived by neglecting the second and third terms of Eq.
31
and making use of Eq.
22
:
f
2
C
2
ion
1
ph
Δρ
=−
N
e
ds
0
,
(32)
by substituting
C
2
from Eq.
22
we get the phase delay
40
31
f
2
.
ion
1
ph
Δρ
=−
N
e
ds
0
.
(33)
The group delay is similarly obtained using Eq.
26
40
31
f
2
.
ion
1
gr
Δρ
=
N
e
ds
0
.
(34)
Second Order Delay
According to Eq.
31
, the second order ionospheric phase delay is
C
X
C
Y
2
f
3
ion
2
ph
Δρ
=
N
e
B
0
cos
θ
ds
0
.
(35)
Examining the constants
C
X
and
C
Y
,Eq.
35
can be written as
7527
c
2
f
3
ion
2
ph
Δρ
=−
N
e
B
0
cos
θ
ds
0
,
(36)
