Bernese GPS Software Version 5.0 - Bernese GNSS Software

12. Ionosphere Modeling and Estimation
To model the stochastic component of the ionosphere, you have the possibility to set up the
ionospheric term Ii k of the double-difference observation equation (Eqn. (2.37)) – rewritten
in a simpler way:
L i 1k = ̺i k − Ii k + ... + λ1 n i 1k (12.14a)
L i 2k = ̺ i k − f2 1
f 2 2
I i k + ... + λ2 n i 2k
(12.14b)
as an unknown parameter. This type of parameter, called Stochastic Ionosphere Parameter
(SIP), represents the double-difference ionospheric delay on L1 according to Eqn. (12.5).
One SIP per epoch and satellite (or satellite-pair) has to be estimated. To handle the
usually huge number of SIP parameters, an epoch-wise parameter pre-elimination has to be
performed (see Section 7.5.3 for the handling of epoch parameters in GPSEST).
This parameter type is particularly useful for “dual-band” ambiguity resolution when using
strategies like the General-Search or the Quasi-Ionosphere-Free (QIF) strategy, which
directly solve for L1/L2 ambiguities (see also Chapter 8). In the ambiguity-unresolved case,
where neither L1 and L2 ambiguities (N1 and N2) nor L5 ambiguities (N5 = N1 − N2) are
known, you have to impose a priori constraints on the SIP parameters to retain the integer
nature of the L1/L2 ambiguities, otherwise you will implicitly get real-valued ambiguity
parameters B3 according to Eqns. (2.43) and (2.44).
In addition, SIP parameters allow to smoothly switch between a pure L1/L2 solution and an
ionosphere-free (L3) solution. This is demonstrated in Figure 12.4 for a 20-kilometer baseline
Formal accuracy of coordinates/ambiguities in meters
10 1
10 0
10 -1
10 -2
10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2
A priori sigma for SIPs in meters
Figure 12.4: Coordinate and ambiguity parameters as function of SIP constraining.
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