Global Positioning System Reference
In-Depth Information
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The subscript
f
in (6.82) denotes the frequency of the carrier and the next subscript
identifies the sign and the unit. If that subscript is
P
, as in case of (6.82), the distance is
given in units of meters. The integral in (6.82) equals the total electron content (TEC)
according to (6.65). Using short notation, i.e., neglecting the subscript
k
(receiver) and
superscript
p
(satellite), we obtain
40
.
30
f
2
I
f,P
=
TEC
(6.83)
Th
e corresponding ionospheric time delay (codes) or time advance (phases) follows
as
I
f,P
c
40
.
30 TEC
cf
2
ν
f
=
=
(6.84)
[21
The time delay is proportional to the inverse of the frequency squared. Consequently,
the ionosphere affects transmissions at higher frequencies less.
The unit for the ionospheric code delay is in meters, whereas it is typically ex-
pressed in cycles for carrier phases, unless the carrier phases have explicitly been
scaled to distance. The following notation convention applies to identify sign and
units,
Lin
—
1.6
——
Nor
PgE
c
f
1
I
1
,ϕ
I
1
,P
=−
I
1
,
Φ
=−
(6.85)
c
f
2
=−
I
2
,
Φ
=−
I
2
,P
I
2
,ϕ
(6.86)
[21
I
1
,P
I
2
,P
=
f
2
f
1
(6.87)
I
1
,ϕ
I
2
,ϕ
=
f
2
f
1
(6.88)
Figure 6.14 shows the ionospheric delays for GPS frequencies as a function of TEC.
Typically the TEC values range from 10
16
to 10
18
. Often the total electron content is
expressed in terms of TEC units (TECU), with one TECU being 10
16
electrons per
1-square-meter column.
Even though they are very important, phase advancement and group delay are
not the only manifestations of the ionosphere on the signal propagation. Some of the
phase variations are converted to amplitude variation by means of diffraction. The re-
sult can be an irregular but rapid variation in amplitude and phase, called scintillation.
The signal can experience short-term fading by losing strength. Scintillations might
occasionally cause phase-lock problems to occur in receivers. A receiver's bandwidth
must be sufficiently wide not only to accommodate the normal rate of change of the
geometric Doppler shift, (up to 1 Hz), but also the phase fluctuations due to strong
