Ionospheric Propagation Effects on GNSS Signals and New Correction Approaches - Global Navigation Satellite Systems: Signal,Theory and Applications - page 396

Δ s len is negative in the dual-frequency combination and positive in the triple-frequency
combination. Again, the magnitude of Δ s TEC is higher than the magnitude of Δ s len for both
combinations. As a result, the triple-frequency (RRE) tr is found to be negative, i.e., the
corrected ρ is longer than the uncorrected one whereas the dual-frequency RRE is found
to be positive, i.e., the corrected ρ is shorter than the uncorrected ρ . Similarly, it can be
shown that (RRE gr ) tr is positive in the triple-frequency combination and RRE gr is negative
in the dual-frequency combination. These relations are true for combination frequencies
f 1 > f 2 > f 3 .

Fig. 8. Residual terms in the triple-frequency GPS L1-L2-L5 combination for an ionospheric
ionization of VTEC = 250 TEC units

4. Correction of higher order ionospheric terms
4.1 Second order term correction

The estimation of the second order term requires computation of the geomagnetic induction
and its direction with respect to the propagation direction along ray paths. Since this
computation is very cumbersome, a common practice is to assume the ionosphere as a single
thin layer at a certain altitude and compute B cosΘ at the IPP and consider it constant
throughout the propagation. Thus, the second order term coefficient q (Eq. 8) can be written
as

12 * *

q ≈ 2.2566 × 10 B cos Θ TEC (34)

where TEC is the total electron content along ray paths, B * is the magnitude of B , and Θ * is
the angle between the magnetic field vector and the wave direction at the IPP (the symbol *
denotes the values at the single layer).

Bassiri and Hajj (1993) were the first to propose such a single thin layered ionosphere for the
second order ionospheric correction; they choose the 300 km as a representative global