Bernese GPS Software Version 5.0 - Bernese GNSS Software

10. Station Coordinates and Velocities
10.2.2.2 Minimum Constraint Solution
Conditions based on Helmert constraints on coordinates of (a subset of) sites with respect
to a reference frame constitute an optimum way for the datum definition of a network. The
definition of the datum is not based on conditions imposed on single reference stations.
Rather, the conditions act on the barycenter of the reference sites or the mean orientation
of the network. This type of datum definition is called minimum constraint solution in the
Bernese GPS Software.
Usually it is sufficient to demand that the barycenter of the estimated reference coordinates
does coincide with the barycenter of the a priori coordinates (no-net-translation condition).
Because the orientation of the network is defined by the introduced orbits, this type of datum
definition is very closely related to the so-called inner constraint solution [Vaníček and
Krakiwsky, 1982]. In some cases, mainly when estimating orbits and EOPs in a global network,
it is necessary to additionally constrain the rotation of the network (no-net-rotation
condition). The scale of the net must only be constrained in very rare cases, e.g., when
estimating satellite antenna phase center variations. To setup the no-net-translation condition
in a global network or not coincides with the decision whether the coordinate origin of
the solution shall be enforced into the coordinate origin of the reference frame or into the
geocenter as it was realized by the solution (see also Section 15.4.4 for detail on estimating
the geocenter).
The advantage of a minimum constraint solution through three translation conditions on
the network’s barycenter is that (small) errors in the coordinates of a reference site do
neither distort the network geometry nor significantly degrade the datum definition per se.
It is thus the recommended method to estimate final results. Please note, that this option is
only available in program ADDNEQ2. The detailed mathematical background is described
in Section 9.3.9.
10.2.2.3 Constraining Reference Coordinates
The geodetic datum can be defined by constraining coordinates of reference stations to
their a priori values. Infinitely tight constraints correspond to fixing reference coordinates
whereas infinitely loose constraints are equivalent to a free network solution. By varying
the constraints you may smoothly shift between these two cases. Depending on the quality
of the reference site coordinates, tightly constraining of several sites may result in network
distortions (“over constraining”).
A solution with a single site constrained to its reference frame position is a particular
minimum constraint solution with the disadvantage that an error in the position of the
single reference site propagates into the positions of all other sites in the network.
The advantage of very tight constraints over fixing coordinates is that the constrained
station coordinates still remain in the resulting normal equation system. Thus it is possible
to change the datum definition later on in ADDNEQ2.
This datum definition type is in general well suited when saving normal equations in program
GPSEST.
Page 216 AIUB