Comparison of Different Combination Strategies Applied for the Computation of Terrestrial Reference Frames and Geodetic Parameter Series

The combination of space geodetic techniques is today and becomes in future more and more important for the computation of Earth system parameters as well as for the realization of reference systems. Precision, accuracy, long-term stability and reliability of the products can be improved by the combination of different observation techniques, which provide an individual sensitivity with respect to several parameters. The estimation of geodetic parameters from observations is mostly done by least squares adjustment within a Gauß-Markov model. The combination of different techniques can be done on three different levels: on the level of observations, on the level of normal equations and on the level of parameters. The paper discusses the differences between the approaches from a theoretical point of view. The combination on observation level is the most rigorous approach since all observations are processed together ab initio, including all pre-processing steps, like e.g. outlier detection. The combination on normal equation level is an approximation of the combination on observation level. The only difference is that pre-processing steps including an editing of the observations are done technique-wise. The combination on the parameter level is more different: Technique-individual solutions are computed and the solved parameters are combined within a second least squares adjustment process. Reliable pseudo-observations (constraints) have to be applied to generate the input solutions. In order to realize the geodetic datum of the combined solution independently from the datum of the input solutions, parameters of a similarity transformation have to be set up for each input solution within the combination. Due to imperfect network geometries, the transformation parameters can absorb also non-datum effects. The multiple parameter solution of the combination process leads to a stronger dependency of the combined solution on operator decisions and on numericalaspects.