Study on systematic errors of BDS-3 broadcast ephemeris and their effects with Helmert transformation

Previous studies have not evaluated the systematic errors implied in the third generation of BeiDou-3 Navigation Satellite System (BDS-3) broadcast ephemeris. In this paper we evaluate the systematic pattern described by the Helmert transformation parameters, including translations, rotations, and scale. BDS-3 broadcast and precise ephemerides from December 2019 to 2022 are collected, and the characteristics of the transformation parameters as well as their effects on the signal in space error are analysed. The annual variation in the z-translation is obtained, and the similar amplitudes of 5.5 cm and phases of approximate 300 days are obtained for different years. When the rotation parameters are considered in the orbit comparison, the Root Mean Square (RMS) errors of the along- and cross-track orbital differences decrease from 29.1 to 12.5 cm and from 30.6 to 9.2 cm, respectively, because the three rotation parameters compensate for the majority of the errors in the BDS-3 broadcast ephemeris. Moreover, the high correlations in the obtained rotation parameters among the three orbital planes suggest that the orientation of the BDS-3 broadcast ephemeris is influenced by common model errors, i.e., uncertainty of Earth Rotation Parameters (ERPs). Further research is required because an offset of 1.5 × 10–9 for the scale parameter is observed. A degraded User Range Error (URE) for epochs of up to 84% is attained when the systematic pattern is considered, though the impact of the systematic pattern indicated by the z-translation and rotation parameters on the URE is less than 5.0 cm. With the refinement of the ERPs implemented in the new generation of broadcast ephemeris, we anticipate that the broadcast ephemeris performance of BDS-3 will be improved.