Kern, L. M., Krasna, H., Nothnagel, A. G., Böhm, J., & Madzak, M. (2023). Issues of terrestrial geodetic datum definition in VLBI data analysis [Poster Presentation]. 28th IUGG General Assembly, Berlin, Germany.
E120-04 - Forschungsbereich Höhere Geodäsie E120 - Department für Geodäsie und Geoinformation
28th IUGG General Assembly
11-Jul-2023 - 20-Jul-2023
VLBI; geodetic datum; NNT/NNR
The geodetic datum describes the absolute location, orientation and scale of the observed system with respect to
a target frame. Since Very Long Baseline Interferometry (VLBI) observations only provide information on the
relative relationships between the participating radio telescopes, the introduction of datum conditions is neces-
sary to ensure that the normal equation system is invertible and thus solvable.
For some time, ”Helmert rendering” or the ”no-net-translation (NNT) and no-net-rotation (NNR)” approach are
applied to datum-free VLBI normal matrices to regularize the normal matrix system. When using ”Helmert
rendering”, the transformation parameters are added to the system and are forced to be zero. In this case, the
condition matrix is used to expand the normal equation system. The results are retrieved in such a way that the
sum of translation and rotations with respect to the reference frame are zero. A similar condition matrix is formed
with the NNT/NNR approach, which is then weighted and added to the singular normal matrix. 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 the scaling of the datum matrix
so that the length of each column is one. In this poster, we explain the background and discuss the implications
of proper scaling and approximations.