Ionospheric Propagation Effects on GNSS Signals and New Correction Approaches - Global Navigation Satellite Systems: Signal,Theory and Applications - page 397

average peak height. Later Kedar et al. (2003) assumed the ionosphere as a single layer at a
400 km altitude for estimating the effect of the second order GPS ionospheric correction on
receiver positions. Hernandez-Pajares et al. (2007) considered the ionosphere as a single

layer at a 450 km altitude to estimate the impact of the second order ionospheric term on
geodetic estimates.

The computation of co B Θ along ray paths requires the knowledge of the ionospheric
profile shape which is not available to the GNSS users; they only have TEC information
along ray paths. Therefore, assumptions of a thin ionospheric layer and co B Θ computation
at the IPP are very suitable for practical use. However, such assumptions lead up to 2 mm
errors in the second order ionospheric term computation (Hoque & Jakowski, 2008).

As an alternative approach, we (Hoque & Jakowski, 2007) assume an average value co B Θ
for the magnetic field component and consider it constant through out the propagation.
Based on simulation studies we derived a correction formula for the co B Θ computation
along any receiver-to-satellite link geometries inside European geographic latitude 30 - 65°
N and longitude 15° W - 45° E.

12

1.1283 × 10

Δ s = ⋅ B cos Θ ⋅ TEC (35)

2

ff f ( + f )

12 1 2

In which

2 2 2

α ′ B cos Θ =− y cos α + r − y sin α − 2 r cos (36)

1 1 1 2

( )

r =

=
=

ςβφλ
ςβφ
ςβφ

,,,
,,
,,

a

1 i

( )

r b (37)

2 i

( )

y c

1 i

The parameters r 1 , r 2 and y 1 are the functions of the receiver-to-satellite elevation angle β ,
geographic latitude φ and longitude λ at the receiver position. The quantity α is the receiver-
to-satellite azimuth angle and α' is the modified azimuth angle. The quantities a i , b i and c i
are the polynomial coefficients. Thirty polynomial coefficients have been derived for the
European region (30° - 65° N, 15° W- 45° E) by least squares fitting of ray tracing results.
Inside the ray tracing program, the IGRF model has been used to compute co B Θ along ray
paths. For details and values of the polynomial coefficients we refer to Hoque & Jakowski
(2007). Using such a correction formula and knowing the TEC value, the second order term
can be corrected to the 2-3 millimeter accuracy level for a vertical TEC level of 100 TEC
units. The formula can be adapted for other geographic regions too after deriving new set of
polynomial coefficients.

4.2 Third order term correction

It has been found that the second term of Eq. (9) is less than the first term by about 1-2
orders of magnitude. As already discussed in the section 3.1.2, the integral

2
nds

∫

can be