Bernese GPS Software Version 5.0 - Bernese GNSS Software

9.3.9 Constraining of Parameters
9.3 Manipulation of Normal Equations
The old program ADDNEQ used the constraining technique rather extensively for almost
every parameter manipulation. To avoid numerical problems inherent in this approach,
ADDNEQ2 is based on parameter transformation instead of constraining technique wherever
possible. However, there are still quite a few situations where the constraining technique
has to be used or where a transformation is too complicated.
In the Bernese GPS Software the constraining of parameters is performed by adding fictitious
observations. The principles in ADDNEQ2 are the same as in GPSEST and are described
in Section 7.5.4. Nearly all parameters supported by ADDNEQ2 can be constrained. Relative
constraints (between successive parameters in time) may be applied for tropospheric zenith
path delay and gradient parameters as well as for global ionosphere parameters. A time interval
must be defined specifying the distance in time over which relative constraints shall act
(usually the nominal parameter spacing). Furthermore, relative constraints may be put to
pairs of station coordinates and/or velocities according to the entries in Section TYPE 004:
STATION COORDINATES AND VELOCITIES (ADDNEQ) of the station information file (see Section
10.3.5 for more details).
Parameters are constrained after parameter transformations took place. Parameters that
are pre-eliminated before stacking are constrained before pre-elimination. Parameters that
explicitly appear in the resulting normal equation are stored to file without any constraints in
order to avoid numerical problems. SINEX files generated by ADDNEQ2 have all constraints
of explicit parameters booked in the MATRIX/APRIORI block.
Station coordinates and velocities may be fixed (and deleted from the normal equation, not
recommended if saving normal equations or estimating velocities) or constrained to their
a priori values which are provided by input coordinate resp. velocity files. A free solution,
without any constraint on the station coordinates resp. velocities may be generated (not
recommended), or minimum network constraints may be imposed, see following section.
Minimum Constraint Conditions
GNSS is in principle an interferometric technique. Therefore it is in general not possible
to estimate the absolute position of all stations. Some of them (at least one) have to be
kept fixed on their a priori positions or so-called free network conditions have to be introduced.
Free network conditions (or minimum constraint conditions) are optimal to define
the geodetic datum with a minimum number of constraints, without fixing or constraining
particular site coordinates. This option is well-suited to analyze inconsistencies in the
reference site coordinates, see also Chapter 10.
Free network conditions are based on the assumption that there are two reference frames
(1) an a priori reference frame, and
(2) the reference frame of the resulting coordinates.
Bernese GPS Software Version 5.0 Page 193