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Thomas Artz
Type of contribution: oral

Numerical issues of VLBI data analysis

Thomas Artz, University of Bonn Sebastian Halsig, University of Bonn Andreas Iddink, University of Bonn Axel Nothnagel, University of Bonn

In recent years, the VLBI Global Observing System (VGOS) has been developed. The advent of VGOS, will lead to increasing observational precisions and new opportunities for the determination of geophysical or technical process parameters. However, numerical issues of data analysis also play an important role for the quality of the derived parameters. Thus, conditioning as well as stability of the solution have to be investigated. While conditioning refers to numerical problems and it has no connection to the solution strategy, numerical stability refers to the algorithms which are used. Thus, a numerically stable algorithm does not amplify the errors of the observations. In this paper, a linearized least squares adjustment on the basis of a Gauss-Markov-Model is used to estimate the VLBI parameters. It is essential to note that the involved matrices are not only affected by the design of the measurement process, but also by the characteristics of the functional description and, thus, even more by the numerical characteristics of the equation system. For VLBI, the equation system of the least squares adjustment is typically ill-conditioned. Thus, errors of the observations are amplified during the adjustment process. This paper focuses on the impact of numerical conditioning. We present methods to reveal the relationship between numerical characteristics of the normal equation matrix and parameter types as well as network properties and the presence of data gaps. Furthermore, we show the impact of the algorithm which is used to solve the equation system on the estimated parameters.