Global Positioning System Reference
In-Depth Information
Since the delay will be small compared to the satellite-to-user distance, we sim-
plify (7.17) and (7.18) by integrating the first term along the LOS path. Thus,
ds
changes to
dl
, and we now have
User
SV
User
SV
40 3
.
40 3
.
∫
∫
∆
S
=−
ndl
∆
S
=
n
e
dl
(7.19)
iono p
,
e
iono g
,
f
2
f
2
The electron density along the path length is referred to as the
total electron
count
(TEC) and is defined as
User
SV
TEC
=
∫
ndl
e
The TEC is expressed in units of electrons/m
2
or occasionally
TEC units
(TECU)
where 1 TECU is defined as 10
16
electrons/m
2
. The TEC is a function of time of day,
user location, satellite elevation angle, season, ionizing flux, magnetic activity, sun-
spot cycle, and scintillation. It nominally ranges between 10
16
and 10
19
, with the two
extremes occurring around midnight and mid-afternoon, respectively. We can now
rewrite (7.19) in terms of the TEC:
−
40 3
.
TEC
40 3
.
TEC
∆
S
=
∆
S
=
(7.20)
iono p
,
iono g
,
2
2
f
f
Since the TEC is generally referenced to the vertical direction through the iono-
sphere, the previous expressions reflect the path delay along the vertical direction
with the satellite at an elevation angle of 90° (i.e., zenith). For other elevation angles,
we multiply (7.20) by an
obliquity factor
. The obliquity factor, also referred to as a
mapping function
, accounts for the increased path length that the signal will travel
within the ionosphere. Various models exist for the obliquity factor. One example,
from [14], is (terms are defined in Figure 7.4):
1
2
−
2
R
Rh
cos
φ
F
=−
1
e
(7.21)
pp
+
e
I
The height of the maximum electron density,
h
I
, in this model is 350 km. With
the addition of the obliquity factor, the path delay expressions from (7.20) become
40 3
.
TEC
40 3
.
TEC
∆
S
=−
F
∆
S
=
F
iono p
,
pp
iono g
,
pp
f
2
f
2
Since the ionospheric delay is frequency dependent, it can be virtually eliminated
by making ranging measurements with a dual-frequency receiver. Differencing
pseudorange measurements made on both L1 and L2 enables the estimation of both
the L1 and L2 delays (neglecting multipath and receiver noise errors). These are
first-order
estimates,
since
they
are
based
on
(7.11).
An
ionospheric-free
pseudorange may be formed as [4]:
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