Ionospheric Propagation Effects on GNSS Signals and New Correction Approaches - Global Navigation Satellite Systems: Signal,Theory and Applications - page 393

For a GNSS user in the northern hemisphere the magnitude of the second order term is the
largest when the signal is received from a satellite in southward direction. However, for a
user in the southern hemisphere the scenario is reversed, i.e., the largest effect is observed
when the signal is received from a satellite in northward direction. Figure 4 shows that the
magnitude of the second order term and its sign differ depending on the user location on
the earth and direction of the signal reception. Therefore, such non systematic effects cannot
be cancelled out by averaging GNSS measurements over long period at a certain user location.

3.1.2 Third order term
The third order term depends on the integral 2

nd ∫ (see Eq. 9) which can be simplified as
0.6577 N m TEC (obtained by analytical integration of the Chapman layer, Hoque & Jakowski,
2008, see also Brunner & Gu, 1991; Hartmann & Leitinger, 1984; Leitinger & Putz, 1988)
where N m is the maximum ionospheric ionization. Therefore, assuming the worst case
condition with f g = 1.4 MHz and Θ = 0, the third order term can be simplified as (using Eqs.
5 and 9)

TEC

() (

)

3

14

d = 1602.81 N + 2.37 × 10 (31)

Igr m

4

f

()

3
Ig d is measured in meters, TEC is the slant TEC and measured in electrons/m 2 , f in
Hz and N m is measured in m -3 . If the vertical TEC is known, N m can be computed assuming a
Chapman profile for the ionosphere by the following expression (Hoque & Jakowski, 2007).

where

VTEC = 4.13 HN (32)

m

where VTEC is the TEC in vertical direction and H is the atmospheric scale height. The
parameter H can be assumed as 70 km for a rough estimation of the third order ionospheric
term. Using the above approximations (Eqs. 31 and 32) the frequency dependence of the
third order term at different levels of ionospheric ionization and elevation angles has been
plotted in Fig. 5.

()

3
Igr

Fig. 5. Frequency dependence of the third order term d at different levels of ionospheric

ionization and elevation angles