Ionospheric Propagation Effects on GNSS Signals and New Correction Approaches - Global Navigation Satellite Systems: Signal,Theory and Applications - page 399

d 2 TEC / dβ 2 have been plotted as functions of elevation angle in Fig. 9. The dTEC / dβ has been
calculated dividing the TEC difference between two measurement epochs by the
corresponding elevation angle difference. Then, d 2 TEC / dβ 2 has been calculated dividing the
dTEC / dβ difference between two measurement epochs by the corresponding elevation angle
difference.

Comparing plots in Fig. 9, we see that although the dependency of d len on the dTEC / dβ is not
straight forward, its dependency on the d 2 TEC / dβ 2 is obvious at low elevation angles
(< 20°). Thus, the magnitude of the d len depends on the magnitude of TEC as well as on the
magnitude of d 2 TEC / dβ 2 . Considering this, functional dependencies have been studied
separately for different parameters to develop correction formulas. For this, ray tracing
calculation has been carried out for different geometrical and ionospheric conditions
varying elevation and Chapman layer parameters H , Nm and hm . Thus, the following
formula has been obtained for the d I len correction.

4

ray tracing
Eq. (33)

ray tracing
Eq. (33)

3

3

2

2

1

H = 60 km

1

H = 80 km

0

0

0 30 60 90

0 30 60 90

Elevation /deg

Elevation /deg

20 1.5

500

H = 60 km
H = 80 km

H = 60 km
H = 80 km

15 1

375

0.5

250

10

125 0

5

0

-0.5

0

0 30 60 90

0 30 60 90

Elevation /deg

Elevation /deg

Fig. 9. Elevation angle dependence of d I len , TEC (see right scale), dTEC / dβ and d 2 TEC / dβ 2 for
the Chapman layer parameter H = 60 and 80 km

⎛ ⎞

2

⎛

2

⎞

a 1 d TEC

⎜ ⎟

len
I

2

(41)

1

d = − 1 TEC + ⎜ a cos β

⎟

⎜ ⎟

⎜ ⎟

3

4

( )

1/2 2

f d β

2

⎜ ⎟ ⎝ ⎠

1c s − a β

⎝

2

⎠