Relativity effects of Galileo passive hydrogen maser satellite clocks

Abstract

As seen from comparisons of recent multi-GNSS experiment and pilot project (MGEX) clock solutions of November 23, 2018, and February 15, 2019, most Galileo satellite passive hydrogen maser (PHM) clocks, once corrected for daily drifts, can already show the small error of the conventional relativity correction (i.e., − 2 r.v/c²—negative twice the dot product of the satellite position and velocity vectors, divided by the light velocity squared). The Galileo satellite clock solutions, generated by the GRG and COD MGEX Analysis Centers, in most cases agree well with the simple analytical error approximation, based only on the most significant J₂ term of the earth’s gravitational potential expansion. The analytical error approximation is periodical with half an orbit period, and for the Galileo satellites it has an amplitude of 0.064 ns. It is subjected to residual periodical errors with amplitudes of up to 0.025 ns, which also have about half an orbital period. The residual periodical errors are likely caused by orbit perturbations, mostly due to the lunar attraction, which were neglected in the development of the analytical error approximation. Nevertheless, the application of the analytical error approximation to Galileo satellite clocks, corrected for daily drift, resulted in a significant reduction in clock RMS, from the average of 0.095–0.083 ns for GRG MGEX clock solutions on November 23, 2018, and from 0.084 to 0.075 ns on February 15, 2019, for COD MGEX clock solutions. The analytical relativity error approximation improves the linearity of Galileo PHM clocks, which, when accounted for, can result in significant improvements in clock solution precision, clock distributions and predictions. Furthermore, unlike for GPS and GLONASS, Galileo satellite clocks with samplings of 5 or 15 min can be safely interpolated, as demonstrated by Galileo-only kinematic PPP solutions with the MGEX tracking data of Feb. 15, 2019, at the station BRUX. When using the interpolated COD and GRG MGEX SP3 satellite clocks, rather than the 30-s clocks included in the respective clock files, the North/East/Up repeatability sigma’s of 10/8/16 mm increased by less than 10% for COD 5-min SP3 clock sampling. In the case of GRG’s 15-min sampling, the repeatability sigma’s of 8/8/14 mm increased by less than 20%.