Geoscience Reference
In-Depth Information
or
N
e
f
2
31
N
e
n
ion
gr
=
1
+
C
2
=
1
+
40
.
f
2
.
(26)
It can be seen from Eqs.
23
and
26
that the group and phase refractive indices have
the same diversity from one but with an opposite signs. As
n
gr
>
n
ph
it is simply
concluded that
v
gr
<
v
ph
. As a consequence of the different velocities, when a signal
travels through the ionosphere, the carrier phase is advanced and the modulated code
is delayed. In the case of GNSS, code measurements which propagate with the group
velocity are delayed and the phase measurements that propagate with phase velocity
are advanced. Therefore, compared to the geometric distance between a satellite and
a receiver, the code pseudo-ranges are measured too long and phase pseudo-ranges
are measured too short. The amount of this difference is in both cases the same
(Hofmann-Wellenhof et al.
1993
).
High Order Refractive Index
The first order refractive index only accounts for the electron density within the
ionosphere, while the effect of the Earth's magnetic field and its interactions with the
ionosphere are considered in the higher order terms; i.e. the third and fourth terms
of Eq.
20
. For precise satellite positioning, these terms have to be considered as they
will introduce an ionospheric delay error of up to a few centimeters (Brunner and
Gu
1991
; Bassiri and Hajj
1993
).
3 Ionospheric Delay
According to Fermat's principle (Born and Wolf
1964
), the measured range
s
is
defined by
s
=
nds
,
(27)
where the integration is performed along the path of the signal. The geometric dis-
tance
s
0
between the satellite and the receiver may be obtained analogously by setting
n
=
1:
s
0
=
ds
0
.
(28)
The delay (or advance) experienced by signals traveling through the ionosphere is
the difference between measured and geometric range. This is called the ionosphere
delay or ionospheric refraction:
ion
Δρ
=
nds
−
ds
0
.
(29)
