Optimal distribution of VLBI transmitters in the Galileo space segment for frame ties

Equipping Galileo satellites with a VLBI transmitter (VT) will allow to observe satellites next to quasars with Very Long Baseline Interferometry (VLBI) radio telescopes. This concept will facilitate the direct estimation of the satellite orbits in the celestial reference frame. Moreover, these observations along with usual Galileo observations can be used to transfer the space tie between the VT and the antenna on the Galileo satellite to the Earth surface realizing the frame tie at the geodetic site with VLBI radio telescope and Galileo antenna. In this study, we assess the accuracy of that frame tie by simulating the estimation of station coordinates from VLBI observations to Galileo satellites next to quasars. We find that at least two or three satellites need to be equipped with a VT with the best results if all satellites with a VT are placed in the same plane. Concerning the ratio between satellite and quasar observations within a schedule, the results suggest that the optimal ratio is around 30% to 40% satellite observations out of the total number of observations in order to have enough observations for the estimation of the station coordinates but still enough quasar observations to ensure a sufficient sky-coverage for the estimation of troposphere parameters. The best scenario with two satellites yields repeatabilities for the east and north components between 7.5 and 10 mm, and for the up component between 9.5 and 12 mm. In case there is a third satellite with a VLBI transmitter in the same plane, the repeatabilities are reduced by up to 2 mm for the horizontal components and up to 3 to 4 mm for the up component. Rotating the schedules over the constellation repeat cycle of Galileo of 10 days reveals that there are differences between the individual days, but there are no days with a significantly worse precision of the estimated station coordinates.