Bernese GPS Software Version 5.0 - Bernese GNSS Software

9. Combination of Solutions
files are combined to one set of parameters. If we want to stack the parameters pi and pi+1
into one parameter pi, we can use following parameter transformation:
⎛
⎛ ⎞ 1 · · ·
⎜ . ⎜
⎟ ⎜ .
⎜ ⎟ ⎜ . ..
⎜ pi ⎟ ⎜
⎜ ⎟ ⎜ 0 · · ·
⎜ pi+1 ⎟ = ⎜
⎜ ⎟ ⎜ 0 · · ·
⎜ pi+2 ⎟ ⎜
⎝ ⎠ ⎜ .
⎝ . ..
.
0 · · ·
.
. ..
1 · · ·
1 · · ·
.
. ..
⎞
0
⎟
. ⎟
0
⎟
0 ⎟
. ⎠
⎛ ⎞
⎜ . ⎟
⎜ ⎟
⎜ pi ⎟
⎜ ⎟ .
⎜ pi+2 ⎟
⎝ ⎠
.
(9.28)
0 · · · 0 · · ·
C
1
The transformation of the normal equation system is performed using Eqn. (9.22). Sometimes,
parameters are stacked immediately after reading the normal equation system. But
usually some type of parameter transformation precedes the stacking.
Stacking is performed automatically for same parameters from different normal equation
files, e.g., coordinates of the same station, troposphere parameters referring to the same
station and the same epoch, or dynamic orbit parameters for the same satellite and the
same osculating epoch.
Stacking may be suppressed for station coordinates (e.g., in case of anomalous behavior) by
marking the station as bad in the station information file (see Section 9.4.6). The coordinates
for the marked station will then not be stacked but pre-eliminated before stacking for normal
equation files within the time interval specified without any constraining.
Orbital elements may be stacked after transformation to the same osculating epoch according
to [Beutler et al., 1996]. For details see Section 15.3.2.
9.3.7 Reduction of the Number of Parameters
Stacking reduces the number of unknown parameters in the normal equations. An important
application is the reduction of the number of parameters used to represent a piece-wise
linear function, see example in Figure 9.2. The operation is performed in two steps: first, the
validity interval of each parameter is adjusted to the new interval according to Section 9.3.5.
Then transformed parameters are stacked according to Section 9.3.6.
A typical example is the reduction of number of troposphere parameters. If you have, e.g.,
estimated (and stored into normal equation files) 12 troposphere parameters per site and
day, you have the possibility to reduce the number of parameters to 1, 2, 3, 4, or 6 values
per day and site. See Section 9.4.5 for details on how to use this option.
9.3.8 Introducing Additional Parameters
The introduction of additional parameters is possible in some specific cases, even if these
parameter types have not been set up in the individual normal equations. Site motion
parameters, or site velocities, are an example for such parameter types. It is necessary that
the influence of these parameters can be neglected within the individual normal equations.
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