Global Positioning System Reference
In-Depth Information
−
3
2
1.108
×
10
exp( 2.1844
−
β
)
TEC
Δ
TEC
=
(42)
bend
2
0.3
fHhm
where Δ
TEC
bend
is measured in TECU, atmospheric scale height
H
is in km, the maximum
ionization height
hm
is in km, signal frequency
f
is in GHz, TEC is in TECU and elevation
angle
β
is in radians. Again, it requires the knowledge of the ionospheric parameters
H
and
hm
. If actual parameters are not known, the formula may not be useful in practical purposes.
Therefore, in the present work, we have looked for a correction formula depending only on
the TEC, elevation angle and second order derivative of TEC with respect to the elevation.
We have found that the formula Eq. (41) can be used for such purposes multiplying simply
by
f
2
and determining new coefficients.
⎛
⎞
2
2
⎛
⎞
c
1
d TEC
⎜
⎟
2
1
Δ
TEC
=
−
1
TEC
+
⎜
c
cos
β
(43)
⎟
⎜
⎟
⎜
⎟
bend
3
2
(
)
1/2
2
f
d
β
2
⎜
⎟
⎝
⎠
1c s
−
c
β
2
⎝
⎠
where
c
1
= 1.2963,
c
2
= 0.8260,
c
3
= 0.0496. The Δ
TEC
bend
will be computed in TEC units when
β
is measured in radians,
f
is in MHz and TEC is in TEC units and
d
2
TEC
/
dβ
2
in TECU/deg
2
.
The polynomial coefficients are derived based on a nonlinear fit with ray tracing results in
least square senses as before.
ray tracing
Eq. (42)
Eq. (43)
Eq. (43) approx.
0.3
0.2
0.15
0.2
0.1
H = 60 km
0.1
H = 80 km
0.05
0
0
0 15 30 45
0 15 30 45
Elevation /deg
Elevation /deg
Fig. 11. Comparison of Δ
TEC
bend
correction formulas with ray tracing results
The elevation angle dependence of Δ
TEC
bend
has been plotted in Fig. 11 for the proposed
correction formula Eq. (43) as well as for the Eq. (42). Also ray tracing results are plotted for
comparisons. Comparing Δ
TEC
bend
computed by the Eq. (43) and Eq. (42) with ray tracing
results, we see that at higher
H
values (e.g.,
H
= 80 km) both correction results are
comparable. However, the performance of the new approach significantly degrades at lower
H
values (e.g.,
H
= 60 km).
As already mentioned, the derivative
d
2
TEC
/
dβ
2
is very sensitive to TEC gradients.
Considering this, another set of coefficients have been determined excluding the derivative
term in Eq. (43). In this case, we have found that
c
1
= 1.4563,
c
2
= 0.8260 and
c
3
is set to zero.
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