Long-Term Frequency Stability Analysis for RRFM and Power-Law Noise Determination of the BeiDou-3 Satellite On-Board Atomic Clocks

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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 <inline-formula> <tex-math notation="LaTeX">$B1$ </tex-math></inline-formula> 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.