On theoretical and practical analyses of BDS-3/Galileo/GPS all-in-view and PPP time transfer with the consideration of satellite clock biases

Benefited from the advantage of high precision, wide area and low cost, the time transfer method based on precise point positioning (PPP) has become a popular technique for the remote clock comparisons. Although the time reference to which satellite clocks are referred can be eliminated by the difference between stations, the effect of satellite clock biases on the estimation of receiver clock offset is always ignored for PPP time transfer. Considering the PPP technique is extended from the all-in-view (AV) by the full use of precise carrier phase observables, a method to evaluate the effects of satellite clock biases on AV and PPP time transfer is proposed first. Then, the GPS, Galileo and BDS-3 time transfer results with different international GNSS Service (IGS) precise products are compared to verify the negative effects of satellite clock biases on AV and PPP time transfer. In our experiment, precise orbit and clock products provided by GFZ (German Research Centre for Geosciences), ESA (European Space Agency) and COD (Center for Orbit Determination in Europe) are used to obtain the clock comparison results of nine time links, including three short baselines, three medium baselines and three long baselines. The results show that the effects of satellite clock biases on AV and PPP time transfer are related to the magnitude of satellite clock biases and the baseline distance between stations. After removing the satellites with larger satellite clock biases, we assess the negative effects of satellite clock biases on AV and PPP time transfer for GPS, Galileo and BDS-3, respectively. By using GFZ, COD and ESA precise products for AV time transfer, the inconsistency of GPS and Galileo time transfer results caused by satellite clock biases is below 0.2 ns for long baseline. Due to the larger satellite clock biases for BDS-3, the inconsistency of BDS-3 AV time transfer results caused by satellite clock biases could reach 0.3 ns for medium baseline and even reach 0.9 ns for long baseline. For GPS and Galileo PPP time transfer, the inconsistency of time transfer results is below 0.05 ns for long baseline. However, the inconsistency of BDS-3 PPP time transfer results can only achieve 0.11 ns for medium baseline and 0.3 ns for long baseline. Thus, it is concluded that the satellite clock biases of BDS-3 precise satellite clock products need refining to improve the performance of BDS-3 PPP time transfer.