Neglected issues of terrestrial datum definition in VLBI

Very Long Baseline Interferometry (VLBI) observations describe the relative relationship between the stations
within the observing network, resulting in a precise three-dimensional point cloud at a specific epoch. A geodetic
datum describes the absolute location, orientation and scale of this point cloud with respect to a target frame by
introducing certain conditions. This additional information ensures that the normal equations are regular, invertible
and therefore solvable.
Today, the ”no-net-translation (NNT) and no-net-rotation (NNR)” approach is widely used. In this case, a condition
matrix is formed to map a set of coordinates (and velocities) onto a conventional system, not allowing any
net translation or rotations. Another widely used approach is ”Helmert rendering”, in which the Helmert parameters
of the transformation are added to the system and are forced to be zero. This results in the determination of
coordinates that deviate from the reference frame in a way such that the sum of the translations and the rotations
with respect to the reference frame is zero. In both cases, the datum-free normal matrix is regularized with a
datum matrix which needs to belong to the same family as that of a spectral decomposition into an Eigenvector
system. A permitted alternative is scaling of the datum matrix so that the length of each column is one. In this
presentation, we explain the background and discuss the implications of proper scaling and approximations.