Bernese GPS Software Version 5.0 - Bernese GNSS Software

12.3 Ionosphere Modeling
β is the geographic latitude of the intersection point of the line receiver–satellite with the
ionospheric layer and s is the sun-fixed longitude of the ionospheric pierce point (or subionospheric
point). s is related to the local solar time (LT) according to
s = LT − π ≈ UT + λ − π. (12.12)
UT is Universal Time and λ denotes the geographical longitude of the sub-ionospheric
point. For satellites at elevation angles of 15/20 o with widely different azimuth, these subionospheric
points can be separated by up to 3000/2000 kilometers. Nevertheless, the representation
(12.11) is not well suited for regional or even global applications because of
limitations in the (β,s)-space. More information concerning local ionosphere modeling may
be found in [Wild, 1994].
12.3.1.3 Global TEC Model
The global TEC model – which may be used for regional applications also – may be written
as
nmax n
E(β,s) = Pnm(sin β) (anm cos ms + bnm sinms), (12.13)
where
nmax
n=0 m=0
is the maximum degree of the spherical harmonic expansion,
Pnm = Λ(n,m)Pnm are the normalized associated Legendre functions of degree n and order
m, based on normalization function Λ(n,m) and Legendre functions Pnm,
and
anm,bnm are the (unknown) TEC coefficients of the spherical harmonics, i.e., the global
ionosphere model parameters to be estimated.
Here, we may use the geographic latitude β and the sun-fixed longitude s, or an equivalent
set in a solar-geomagnetic frame, as independent arguments. Further information concerning
global and regional ionosphere modeling may be found in [Schaer et al., 1995], [Schaer et al.,
1996], and [Schaer, 1999].
12.3.1.4 Station-Specific TEC Models
Station-specific TEC models are treated exactly in the same way as global models. One full
set of ionosphere parameters is estimated with respect to each station involved, however.
12.3.2 Stochastic Component
Short-term TEC variations are not modeled by Eqns. (12.11) and (12.13). When evaluating
these observation equations, they are interpreted as noise of the geometry-free observable.
Bernese GPS Software Version 5.0 Page 261