Bernese GPS Software Version 5.0 - Bernese GNSS Software

where:
E0 is the night time electron content,
E1 is the day time variation of the ionosphere.
17.7 Statistical Information
E0 (“Night time electron number”), E1 (“Day time electron number”) are input parameters to be
specified in panel “GPSSIM 3.3: Simulation Options”. No azimuth dependence is modeled here.
In addition to this deterministic component an irregular part may be superposed. The
following term is added at epoch i:
where:
δEi = (Ei1 cos a + Ei2 sin a) d/200
δEi is the random part of the electron content in the atmosphere,
d is the distance in km between the station considered and the ionosphere
“Reference station” (panel “GPSSIM 3.3: Simulation Options”),
a is the azimuth of the station considered with respect to the ionosphere reference
station,
Eik ,k = 1,2 is the result of the following random walk:
E1k = 0 , var(Ei+1,k − Eik) = ∆ti · var1min ,
where ∆ti is the time between observations i,i+1 in minutes, var1min is the
variance of the difference of the electron contents at time t and t + 1 minute.
var1min has to be specified in panel “GPSSIM 3.3: Simulation Options”, option
“Variance of irreg. change of ionosphere content in 1 min. at 200 km from the reference
site”.
This model certainly is a crude simplification for the random behavior of the true ionosphere.
It shares, however, important aspects with the real situation: (1) the irregular contribution
increases linearly with the baseline length, for distances > 200 km this distance dependence
“stops”, (2) baselines which are close to each other geometrically will show similar random
contributions. The strength of the irregular contribution may be tuned by option “Variance
of irreg. change of ionosphere content in 1 min. at 200 km from the reference site”.
If you do not want to model the ionosphere at all, specify 0 for the three numbers and * for
the “Reference station”.
17.7 Statistical Information
Error free observations are certainly desirable for several applications. But if a good approximation
to reality is needed, the options in “GPSSIM 3.4: Simulation Options” (Figure 17.3)
offer the possibility to inflict errors on the simulated observations. A priori sigmas can be selected
for both frequencies and both observation types independently. A normal distributed
random error with the specified sigma is added to each simulated measurement.
Bernese GPS Software Version 5.0 Page 351