Methods and assessments of two-way time synchronization based on BDS-3 Ka-band satellite-ground link observations

The Beidou-3 system (BDS-3) satellites are deployed, equipped with an inter-satellite link (ISL) payload, so that the satellite–satellite or satellite-ground time synchronization is available. The satellite-ground link (GSL) can be used in conjunction with the ISL if proper attention is paid to all corrections and the biases are fitted. We execute methods to synchronize the clocks of BDS-3 satellites to an accurate reference clock on the ground, by estimating relative clock offsets obtained via Ka-band GSL observations. We solve for the relative biases using the closure properties of the redundant biases and the Ka-band (Ka-mode) satellite-ground two-way data. We find the biases, relative to the GSL hardware delay, are relatively stable in the short term. This makes it feasible to estimate them as a constant every few hours, and the standard deviation of the hardware delay estimations within 24 h is slightly less than 0.7 ns. The frequency stability of Ka-mode estimated clock offset shows a negative short-term performance because of the dominant effect of the white phase noise in the relative clock offsets from the Ka-mode, but the long-term performance seems to be improved to a higher level. The time synchronization accuracy of Ka-mode is proven to be better than 0.3 ns (RMS), whereas the accuracy for the high-orbit satellite is slightly worse.