The key work this study is the power-law noises determination of 18 BeiDou-3 satellites (PRN19-PRN30 and PRN32-PRN37) on-board atomic clocks. First, for the noise determination of white frequency modulation (WFM), random-walk FM (RWFM), and random-run FM (RRFM), which are the basis of the ensemble timescale filter (ETF), we evaluated the Hadamard deviation with a maximum averaging time up to 30 days. To ensure the reliability of the evaluation, the Hadamard deviation was calculated by the relative clock offset determined from two independent techniques: orbit determination and time synchronization (ODTS) and the intersatellite link (ISL). This work shows that the noise characteristics of the clock offset obtained from ODTS and ISL are different, ODTS clocks are conducive to WFM determination because of low observation noise, and the ISL clocks are conducive to RWFM and RRFM determination because of independent to satellite orbit. Second, the lag 1 and $B1$ bias functions were employed to identify different noises, and the intensities of WFM, RWFM, and RRFM were determined by the Hadamard deviations above. The results of this study indicate that: 1) rubidium clocks (Rbs) always suffer from significant RRFM noise, which improves the magnitude component noise when the averaging time achieves several days; 2) the Rbs of BeiDou-3 satellites have distinctive characteristics of WFM, RWFM, and RRFM, different from the passive hydrogen masers (PHMs), which can only discover the WFM and RWFM noises; and 3) because of the RRFM, when the averaging time is greater than 2e5 s, the Hadamard deviation of Rbs is increased, which causes the frequency stability of Rbs to become an order of magnitude lower than PHMs. Last, simulation analyses and natural Kalman timescale (NKT) constructions using the actual ISL data were employed to verify the effectiveness of noises determination. Through this work, we can almost certainly identify the process noise of ETFs, which can become a reference for ETF construction in the future.

Precise point positioning can provide accurate coordinates to users without reference stations, and the high-precision real-time clock offset product is necessary for real-time precise point positioning application. As an integral part of the third generation BeiDou Navigation Satellite System, Precision Point Positioning Service provides dual systems (BDS-3 and GPS) real-time PPP services with centimeter- and decimeter-level accuracy for static and kinematic positioning users around China, respectively. However, there exist inconsistent biases in the clock offset of Precision Point Positioning Service, which will negatively affect the positioning and timing performance of the service. By comparing with the post-processing clock offset, this paper verifies that the broadcast clock offset has smaller and more stable biases in the long term and proposes a regional clock offset estimation strategy using broadcast clock offset for a priori constraint. The results show that the new algorithm can effectively reduce the bias in PPP-B2b clock offset. The new clock offset product could improve convergence speed by 25% and 10% in the horizontal and vertical directions. For positioning accuracy, the improvement is 22% and 17%. The absolute error of timing can also be reduced by 60%.

Slow and significant stochastic variations named “a2-drift” variations are observed in this contribution, which are discovered during the estimation of frequency aging of BeiDou-3 rubidium (Rb) clocks. The magnitude of the variations suffered on BeiDou-3 Rbs is distinctly larger than GPS and appears to exhibit a systematic drift associated with time. The phenomenon is widely ignored and will compromise the long-term (one day and beyond) autonomy of the onboard clock units. Random run frequency modulation (RRFM) noise, which may induce similar variations, can be detected and identified by lag 1 autocorrelation function (lag 1 ACF) and Hadamard deviation. To retrace the origin of the variations, the Hadamard deviations, broadcast clock model parameter $a1$ , and frequency drift of BeiDou-3 Rbs are estimated with reference to GPS. The variations result in long-term fluctuations on the broadcast clock parameters ( $a1$ and $a2$ ) and arise an increase in the Hadamard deviation when the averaging time is greater than 1e ⁵ s. Furthermore, the simulations of the power-law noises reproduce the variations, and the lag 1 ACF supports that the variations are caused by RRFM. Besides this, many conclusions are also related to this variation. Using two years of multi-global navigation satellite system (GNSS) experiment (MGEX) clock offsets from 2019 to 2021, the following conclusions are drawn: 1) the RRFM emerges as dominant noise and causes a decline in the frequency stability when the averaging time is greater than 1e ⁵ s; 2) the variations on the estimated series of BeiDou-3 Rbs broadcast clock model $a1$ and frequency drift are more visible than those of GPS; 3) when the averaging time is approximately one day, the frequency stability of BeiDou-3 Rbs is similar to that of GPS; however, when the averaging time reaches 1e ⁶ s, the frequency stability of BeiDou-3 Rbs deteriorates because of the RRFM and is nearly ten times lower than that of GPS Rbs; and 4) the GPS Rbs are free from RRFM, but the BeiDou-3 Rbs contain significant features of random-walk frequency modulation (RWFM) and RRFM noise.

Satellite clock offsets are the critical parameters for The Global Navigation Satellite Systems (GNSSs) to provide position and timing (PNT) service. Unlike other GNSSs, BDS-3 uses the two-way superimposition strategy to measure satellite clock offsets. However, affected by some deficiencies of the two-way superimposition strategy, the accuracy of BDS-3 clock offsets parameters is 1.29 ns (RMS), which is the main bottleneck for BDS-3 to improve its space signal accuracy. After analyzing problems in the clock offsets measurement process of BDS-3, the paper proposes a new strategy to real-time estimate high-accuracy satellite clock offsets. The clock offsets estimated by the new strategy show a good consistency with GBM clock offsets. The averaged STD of their differences in MEO is 0.14 ns, and the clock offsets estimated by the new strategy present less fluctuation in the 1-day fitting residuals. Applying the new clock offsets to prediction, BDS-3 can reduce its clock offsets errors from 1.05 ns to 0.29 ns (RMS), about 72%. The above results indicate that the new clock offsets estimated strategy can improve the accuracy of clock offsets parameters of BDS-3 effectively.