Bernese GPS Software Version 5.0 - Bernese GNSS Software

12. Ionosphere Modeling and Estimation
f1,f2 are the frequencies associated with the carriers L1 and L2,
FI(z) is the mapping function evaluated at the zenith distance z ′ ,
E(β,s) is the vertical TEC (in TECU) as a function of geographic or geomagnetic latitude
β and sun-fixed longitude s, and
B4 = λ1 B1 − λ2 B2 is a constant bias (in meters) due to the initial phase ambiguities B1
and B2 with their corresponding wavelengths λ1 and λ2.
For each receiver, and satellite pass, at least one parameter B4 has to be solved for.
12.3.1.1 Ionosphere Mapping on Zero- and Double-Difference Level
Eqns. (12.10) are valid for zero-difference observations. In the double-difference case, the
“ionospheric” observation equations look similar, with the exception that B4, the phase bias
term, equals now λ1 N1 −λ2 N2 and that b4, the code bias term, vanishes. In the “ambiguityfixed”
case, where the integers N1 and N2 are known, it is obviously no longer necessary to
solve for B4.
Ionosphere mapping on both zero- and double-difference level may be performed using the
program GPSEST, considering GPS, GLONASS, or GPS/GLONASS-combined observations.
There is a second program for ionosphere mapping, IONEST. This program, however,
works only on the basis of GPS zero-difference observations and moreover does not take
into account DCBs.
The Bernese GPS Software supports three types of ionosphere models to represent the
deterministic component of the ionosphere:
(1) local models based on two-dimensional Taylor series expansions,
(2) global (or regional) models based on spherical harmonic expansions, and
(3) station-specific models, represented like (2).
Note that the numbers enclosed in brackets correspond to the model type numbers internally
used (see Figures 12.7 and 12.17).
12.3.1.2 Local TEC Model
The local TEC model – applicable in the vicinity of one or more dual-frequency station(s)
– is represented by
where
E(β,s) =
nmax
n=0
mmax
m=0
Enm (β − β0) n (s − s0) m , (12.11)
nmax,mmax are the maximum degrees of the two-dimensional Taylor series expansion in
latitude β and in longitude s,
Enm are the (unknown) TEC coefficients of the Taylor series, i.e., the local ionosphere
model parameters to be estimated, and
β0,s0 are the coordinates of the origin of the development.
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