Bernese GPS Software Version 5.0 - Bernese GNSS Software

7. Parameter Estimation
contains a factor equal or larger than unity. Sigma factors may be specified independently
for each measurement type and are annotated with a time window. For missing stations,
values are automatically set to unity.
A station sigma file may be generated by program RESRMS based on the station-specific
histogram of observation residuals (see Section 6.6.2). For the majority of stations the factors
should be close to unity. Use the same station sigma file for all processing steps (CODSPP
and GPSEST).
In general, station observation sigma factors are only important for processing of pseudorange
observations. For phase measurements or smoothed code measurements (generated by
RNXSMT) station sigma factors are not required.
7.4.3 Elevation-Dependent Weighting of Observations
Observations at low elevations are generally much more susceptible to tropospheric refraction
and multipath effects than those at high elevations. The unmodeled systematic errors
decrease the quality of results. Using low-elevation observations, however, may also improve
the estimation of tropospheric zenith delays and, consequently, the vertical component of
station positions [Rothacher et al., 1997], [Meindl et al., 2004]. In order to optimize the use
of low-elevation observations, program GPSEST allows for an elevation-dependent weighting
of observations. The weight function w(z) adopted is
w(z) = cos 2 (z) (7.14)
where z is the zenith angle of the satellite. Thus, an observation at zenith has unit weight.
The user has the possibility to enable elevation-dependent weighting of observations in panel
“GPSEST 3.1: General Options 1” (see Figure 7.1). Incidentally, users may easily implement
other weighting models into subroutine${LG}/WGTELV.f. Whichever model you test, w(0) =
1 should still hold. Elevation-dependent weighting is recommended when processing data
from elevations below 10 o .
With elevation-dependent weighting enabled, it is necessary to reduce the a priori sigma in
option “A priori sigma” of panel “GPSEST 3.1” from 0.002 m to 0.001 m. The a priori sigma
of unit weight corresponds to the weight of the zero-difference L1 phase observable at
zenith if elevation-dependent weighting is enabled, whereas it corresponds to the weight of
the observable averaged over all zenith angles if no elevation-dependent weighting is active.
The adaptation of the unit weight is necessary in order not to bias the weights of a priori
constraints.
7.4.4 Real and Normalized Residuals
According to their definition in Eqn. (7.8), the residuals correspond to the difference adjusted
minus actual observations. Vice versa, the sum of actual observation vector plus the
residual vector gives the adjusted observation vector. In the Bernese GPS Software these
residuals are called real residuals.
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