Full-ISL clock offset estimation and prediction algorithm for BDS3

The Ka-band dual one-way measurements from Inter-Satellite Link (ISL) devices equipped on the third-generation Beidou Navigation Satellite System (BDS3) follow a time division multiple access (TDMA) structure and can calculate inter-satellite and satellite-ground clock offsets. L-band two-way satellite time and frequency transfer (TWSTFT) is also applied for time synchronization between satellites and ground master. We focus on a full-ISL clock offset estimation and prediction algorithm that estimates all satellite clock parameters simultaneously utilizing ISL clock observations and also synchronizes the constellation to the system time in Beidou Time (BDT) using Ka-band satellite-ground clock observations. We discuss the applications of this algorithm by assessing the clock performance of all BDS3 satellites equipped with a passive hydrogen maser (PHM) or rubidium atomic clock. After investigating the proper prediction model for each satellite, we use the full-ISL algorithm for 24-h clock predictions. The constant hardware delays in the ISL measurements are calibrated by comparing the derived clock parameters with TWSTFT measurements; the full-ISL clock products show high accuracy and continuity. The BDS3 PHMs and rubidium clocks both have a small clock rate drift of 10 –20 s/s 2 . The frequency stability of the BDS3 PHMs and some rubidium clocks is approximately 6–9 × 10 –15 at 1-day intervals. A linear model is suitable for these small-drift clocks, while a quadratic model is essential for the other rubidium clocks. Applying the full-ISL clock prediction method improves the RMS of the 24 h prediction error from 0.88 to 0.75 ns for PHMs and from 2.62 to 1.64 ns for rubidium clocks. The estimated ISL hardware delay STDs are less than 0.2 ns, and the prediction errors evaluated with TWSTFT clock observations are similar to those evaluated with Ka-band clock observations.