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Atomic Clock Ensemble Configuration and Performance Analysis
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摘要: 针对原子钟的技术指标，对比分析了不同钟组配置的时标性能。根据典型原子钟的技术指标和实际运行情况对氢钟和铯钟钟差数据进行仿真，应用ALGOS算法计算了铯钟组、氢钟组、氢铯联合钟组的原子时标，从时间偏差、时间稳定度、频率偏差、频率稳定度四个方面考察了钟组时标性能。结果表明，180台仿真铯钟的守时天频率稳定度相当于1台氢钟的守时天频率稳定度；由于铯钟频率稳定度与氢钟相差较大，原子时计算过程中，铯钟权重远低于氢钟，对原子时的贡献有限；氢钟占比高的钟组，时标稳定性较好，溯源状态下时间偏差和频率偏差也较小。时标稳定性好的钟组在守时状态下的时间保持能力也更好。Abstract: The time scale performance of different clock ensemble configurations is compared and analyzed concerning the technical specifications of atomic clocks. Simulations of hydrogen maser and cesium clock differential data were performed based on the technical specifications and actual operation of typical atomic clocks. The atomic time scales of the cesium clock ensemble, hydrogen clock ensemble, and combined hydrogen-cesium clock ensemble were calculated by applying the ALGOS algorithm, and the clock ensemble time scale performance was examined in four aspects: time deviation, time stability, frequency deviation, and frequency stability. The results showed that the frequency stability of the clock ensemble of 180 cesium clocks is equivalent to the frequency stability of 1 hydrogen maser. Due to the large difference between the frequency stability of cesium clocks and hydrogen masers, the weight of cesium clocks is much lower than that of hydrogen masers in the atomic time calculation process, and the contribution to the atomic time is limited. The clock ensembles with a high proportion of hydrogen maser have better time scale stability, and the time deviation and frequency deviation in the traceability state are also smaller. The clock ensembles with good time scale stability also have better timekeeping ability in the timekeeping state.
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Key words:
- clock ensemble /
- frequency stability /
- time stability /
- timekeeping ability /
- atomic clock
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图 2 实际铯钟运行情况与仿真铯钟稳定度情况
Figure 2. Actual cesium clock operation and simulated cesium clock stability
图 3 实际氢钟运行情况与仿真氢钟稳定度情况
Figure 3. Actual hydrogen maser operation and simulated hydrogen maser stability
图 4 溯源状态下，不同钟组频率稳定度变化情况
Figure 4. Frequency stability of different clock ensemble in the traceability state
图 5 溯源状态下，不同钟组时间稳定度变化情况
Figure 5. Time stability of different clock ensemble in the traceability state
图 6 溯源状态下，不同钟组时间偏差变化情况
Figure 6. Time difference of different clock ensemble in the traceability state
图 7 溯源状态下，不同钟组频率偏差变化情况
Figure 7. Fractional frequency difference of different clock ensemble in the traceability state
图 8 不同钟组自主守时情况。
注：红线代表溯源情况下时间偏差，黑线代表守时状态下时间偏差
Figure 8. Timekeeping ability of different clock ensemble
表 1 典型原子钟技术指标
Table 1. Technical indicators of typical atomic clock manufacturers
$\tau $ MHM-2010 VCH1003A VCH1003M 5071A 1 s ≤8.0E-14 ≤2.0E-13 ≤8.0E-14 ≤5.0E-12 10 s ≤1.5E-14 ≤2.0E-14 ≤1.4E-14 ≤3.5E-12 100 s ≤4.0E-15 ≤7.0E-15 ≤4.0E-15 ≤8.5E-13 1 000 s ≤2.0E-15 ≤3.0E-15 ≤1.5E-15 ≤2.7E-13 3 600 s — ≤1.5E-15 ≤1.3E-15 — 10 000 s ≤1.5E-15 — — ≤8.5E-14 86 400 s ≤2.0E-15 ≤2.0E-15 ≤5.0E-16 — 100 000 s — — — ≤2.7E-14 5 d — — — ≤1.0E-14 30 d — — — ≤1.0E-14 
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表 2 铯钟仿真参数
Table 2. Cesium clock simulation parameters
噪声类型 参数设置 RW-FM 1.0E-19 F-FM 6.0E-15 W-FM 8.0E-12
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表 3 氢钟仿真参数
Table 3. Hydrogen maser simulation parameters
噪声类型 参数设置 RW-FM 5.5E-19 F-FM 7.5E-16 W-FM 6.0E-14
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表 4 铯钟数量与钟组时标频率稳定度关系
Table 4. The relationship between the number of cesium clocks and the frequency stability of time scale in the clock ensemble
铯钟数量（台） 钟组频率稳定度${\sigma }_{y}\left(1\;\mathrm{d}\right)$ 理论值 计算值 10 7.68E-15 9.11E-15 30 4.47E-15 5.24E-15 60 3.17E-15 3.58E-15 90 2.59E-15 2.95E-15 120 2.24E-15 2.46E-15 150 2.01E-15 2.19E-15 160 1.94E-15 2.10E-15 170 1.89E-15 2.05E-15 180 1.83E-15 1.99E-15
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表 5 铯钟数量对氢铯联合钟组时标稳定度影响
Table 5. The influence of the number of cesium clocks on the stability of time scale in the combined cesium hydrogen clock ensemble
钟组构成 钟组频率稳定度${\sigma }_{y}\left(1\;\mathrm{d}\right)$ 理论值 计算值（不限权） 计算值（A/N限权） 5HM 3.78E-16 4.00E-16 4.00E-16 5HM + 30Cs 3.76E-16 3.73E-16 3.00E-15 5HM + 60Cs 3.75E-16 3.74E-16 2.77E-15 5HM + 90Cs 3.74E-16 3.75E-16 2.50E-15 5HM + 120Cs 3.73E-16 3.74E-16 2.17E-15 5HM + 150Cs 3.71E-16 3.71E-16 1.98E-15 5HM + 180Cs 3.70E-16 3.70E-16 1.84E-15 注：5HM + 30Cs表示5台氢钟30台铯钟的联合钟组
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表 6 不同钟组配置的性能情况
Table 6. The performance of different clock ensemble configurations
钟组配置 频率稳定度$ {\sigma }_{y}\left(\tau \right) $(溯源状态) 时间稳定度$ {\sigma }_{x}\left(\tau \right) $/ns（溯源状态） 时间偏差(取绝对值) /ns（自主守时） 5 d 15 d 30 d 5 d 15 d 30 d 6 m 12 m 18 m 10Cs 3.39E-15 2.50E-15 1.74E-15 0.84 1.46 1.70 −299.1 −722.9 −1461.6 9Cs+1HM 2.91E-15 2.13E-15 1.50E-15 0.73 1.25 1.49 −283.2 −683.2 −1349.6 7Cs+3HM 1.62E-15 1.20E-15 8.19E-16 0.40 0.70 0.82 −215.1 −441.0 −795.4 3Cs+7HM 2.50E-16 2.85E-16 2.53E-16 0.06 0.18 0.27 −40.8 −86.8 −166.9 1Cs+9HM 2.32E-16 2.59E-16 2.33E-16 0.06 0.16 0.26 −40.3 −93.7 −144.8 10HM 2.21E-16 2.66E-16 2.34E-16 0.05 0.17 0.25 −40.7 −79.9 −114.1
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