Bernese GPS Software Version 5.0 - Bernese GNSS Software

9.3 Manipulation of Normal Equations
The free network condition thus may be imposed by adding the following fictitious observation
H p = 0 , (9.38)
where
H = (B ⊤ B) −1 B ⊤ . (9.39)
Because of the regularity of the matrix B ⊤ B it is even possible to use
H = B ⊤ . (9.40)
ADDNEQ2 uses the first of the two possible equations. It is not always necessary to constrain
all seven parameters ξ. The number of singularities (that have to be removed using the
constraints) depends on the solution type. In global solutions, when estimating orbits and/or
Earth orientation parameters, it is usually sufficient to constrain the rotation parameters
only (using the corresponding part of H). This is the minimum constraint for the GNSS
network. Minimum constraint conditions may be applied separately for coordinates and
velocities. We refer to Chapter 10 for more details.
9.3.10 Parameter Pre-Elimination and Deletion
Pre-elimination of parameters in ADDNEQ2 works in the same way as in GPSEST and as
described in Section 7.5.5. The different pre-elimination options implemented in ADDNEQ2
are described in Section 9.4.4. Parameters may be pre-eliminated before or after the stacking
of normal equations. Before pre-elimination, the parameters may be constrained and
transformed.
In ADDNEQ2 it is possible to eliminate (“delete”) parameters. This action is performed by
removing the rows and columns corresponding to the respective parameters from the normal
equation. As a result these parameters are fixed to their a priori values. The effect is the
same as if the parameters were pre-eliminated after applying infinitely heavy constraints or
if they were never set up.
9.3.11 Restrictions
All manipulations possible at normal equation level are based on linear transformations.
Only simple model changes are, therefore, possible with program ADDNEQ2. These include
setting up site velocities, geocenter coordinates, or stochastic parameters at boundaries of
the normal equations, and reduction of parameters for piece-wise linear representations.
Model changes that require access to the observations are not possible. In particular, in
case of changing
• the sampling rate,
• the analyzed linear combination of observations or frequency,
• the elevation cutoff,
• the troposphere model or mapping function,
• the satellite antenna offset or pattern group definition, or
• from relative to absolute antenna phase patterns.
The reanalysis of the observations with program GPSEST is required in order to get normal
equation files referring to the new model.
Bernese GPS Software Version 5.0 Page 195