Evaluation of GPS and BDS-3 broadcast earth rotation parameters: a contribution to the ephemeris rotation error

Due to errors of earth rotation parameters (ERPs) adopted when generating the broadcast ephemeris, GNSS broadcast ephemeris suffers orientation deficiencies called constellation rotation errors. Moreover, significant rotation inconsistencies are indicated among different GNSS ephemerides as they utilize different sets of ERPs. Based on the ERP datasets from broadcast navigation messages, we investigate the correlation between broadcast ERPs and ephemeris rotation errors for GPS and BDS-3, and then explore orbital rotation correction using broadcast ERPs. Evaluation of the broadcast ERPs indicates the average root mean square errors (RMSEs) of GPS xp, yp, and UT1-UTC are 1.00, 0.67 mas, and 0.17 ms, respectively, while those of BDS-3 are 2.52, 1.51 mas, and 0.44 ms. BDS-3 performs about 2–3 times worse due to its longer update latency. Comparing to the rotation parameters derived from Helmert transformation between broadcast and precise ephemerides, we demonstrate that the GPS and BDS-3 broadcast ERPs exhibit a prominent correlation with orbital orientation. The correlation coefficients between polar motion errors and X/Y-axis rotation parameters exceed 0.88 for GPS and 0.77 for BDS, whereas no significant correlation is found between the UT1-UTC error and the Z-axis rotation. We propose to correct the orbital orientation inconsistencies between BDS-3 and GPS by aligning their broadcast ERPs, explicitly the polar motion. The GPS ERPs are utilized as a reference due to higher precision and real-time availability. The BDS-3 broadcast orbit after correction reveals precision improvement of approximately 3.0 and 1.0 cm in the along-track and cross-track components, respectively. Static precise point positioning test with GPS and BDS-3 ephemerides also indicates a remarkable positioning improvement in north direction of 21.9% when BDS-3 ephemeris is corrected by the ERP alignment approach.