Time scale algorithm based on cesium atomic fountain clock and optically pumped small cesium clocks

SONG Huijie; DONG Shaowu; WANG Xiang; ZHANG Yu; GUO Dong; WU Wenjun; WU Dan; WANG Xinliang; LIU Dandan

doi:10.7498/aps.74.20250642

Abstract

Realizing the independent control of the national standard time has important practical significance under the current international situation. In this work, an independent time scale that does not rely on external references is developed by studying the self-developed cesium fountain primary frequency standard and domestically-produced optically-pumped small cesium clocks. The specific approach is to use the cesium fountain primary frequency standard as a frequency reference to predict the frequency drift of the optically pumped small cesium clocks. By analyzing the noise characteristics of the optically pumped small cesium clocks, the state equation of the atomic clock is established, and the state of the optically pumped small cesium clock is estimated based on the Kalman filtering algorithm. The calculation of the time scale is based on the frequency state estimation and frequency drift state estimation of atomic clocks, which serve as the forecast values, and is achieved through the weight algorithm. The weight algorithm based on prediction error and the weight algorithm based on noise characteristics are studied. The results show that in the case of using Kalman filtering state estimation, the weight algorithm based on prediction error significantly improves the accuracy of the independent time scale. The cesium fountain primary frequency standard is chosen as the frequency reference to predict the frequency drift of the optically pumped small cesium clock. The accuracy and long-term stability of the independent time scale calculated are much better than those when the time scale itself is used as the frequency reference. Taking the international standard time (UTCr) as the reference, the accuracy of the independent time scale is maintained within 15 ns. The frequency stability is 1.57×10^–14 for a sampling interval of 1 day, 4.29×10^–15 for a sampling interval of 15 days, and 2.87×10^–15 for a sampling interval of 30 days is showing that its stability can meet the current national time demand.

Keywords:

Authors and contacts

1.
National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China
2.
Key Laboratory of Time Reference and Applications, Chinese Academy of Sciences, Xi’an 710600, China
3.
School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: DONG Shaowu, sdong@ntsc.ac.cn

Funds: Project supported by the “Western Light” Talents Trainining Program, Chinese Academy of Sciences, China (Grant No. XAB2021YN22), the Major Program of the National Natural Science Foundation of China (Grant No. 62394352), and the Open Fund of Beijing Institute of Radio Metrology and Testing, China (Grant No. JLJK2021001A002).

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References

[1]	Greenhall C A 2003 Metrologia 40 S335 Google Scholar
[2]	Panfilo G, Harmegnies A, Tisserand L 2012 Metrologia 49 49 Google Scholar
[3]	Panfilo G, Harmegnies A, Tisserand L 2014 Metrologia 51 285 Google Scholar
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[10]	梁悦, 谢勇辉, 陈鹏飞, 帅涛, 裴雨贤, 徐昊天, 赵阳, 夏天, 潘晓燕, 张朋军, 林传富 2023 物理学报 72 013702 Google Scholar Liang Y, Xie Y H, Chen P F, Shuai T, Pei Y X, Xu H T, Zhao Y, Xia T, Pan X Y, Zhang P J, Lin C F 2023 Acta Phys. Sin. 72 013702 Google Scholar
[11]	邵晓东, 韩海年, 魏志义 2021 物理学报 70 134204 Google Scholar Shao X D, Han H N, Wei Z Y 2021 Acta Phys. Sin. 70 134204 Google Scholar
[12]	He X, Yuan Z C, Chen J Y, Fang S W, Chen X Z, Wang Q, Qi X H 2022 Front. Phys. 10 970030 Google Scholar
[13]	Shi H B, Qin X M, Chen H J, Yan Y F, Lu Z Q, Wang Z Y, Liu Z J, Guan X L, Wei Q, Shi T T, Chen J B 2025 Phys. Rev. Appl. 23 034018 Google Scholar
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[17]	Shi J R, Wang X L, Yang F, Bai Y, Guan Y, Fan S C, Liu D D, Ruan J, Zhang S G 2023 Chin. Phys. B 32 040602 Google Scholar
[18]	Wang X L, Ruan J, Liu D D, Guan Y, Shi J R, Yang F, Bai Y, Zhang H, Fan S C, Wu W J, Zhao S H, Zhang S G 2023 Metrologia 60 065012 Google Scholar
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[26]	Wang X B, Shi F F, Gong D L, Xu S Y, Li Z N, Fu G T, Li Q 2020 Metrologia 57 065009 Google Scholar
[27]	Greenhall C A 2001 33rd Annual Precise Time and Time Interval Systems and Applications Meeting, Long Beach, CA, November 27–29, 2001 p445
[28]	Wu Y W, Liu S R 2023 Metrologia 60 065009 Google Scholar

Cited By

图 1 氢原子钟HM5085相对于铯基准钟测量频率偏差的Allan偏差曲线

Figure 1. Allan deviation curves of the measurement frequency deviation of the hydrogen atom clock HM5085 relative to cesium atomic fountain clock.

DownLoad: Full-Size Img PowerPoint

图 2 光抽运守时小铯钟的Allan偏差曲线

Figure 2. The Allan deviation curves of optically pumped small cesium clocks.

DownLoad: Full-Size Img PowerPoint

图 3 Cs3059的频率漂移估计

Figure 3. Frequency drift estimation of Cs3059.

DownLoad: Full-Size Img PowerPoint

图 4 Cs2025的频率漂移估计

Figure 4. Frequency drift estimation of Cs2025.

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图 5 基于预测误差计算权重的时间尺度的相位偏差

Figure 5. Phase deviation curve of the time scale with weights calculated based on the prediction error.

DownLoad: Full-Size Img PowerPoint

图 6 基于预测误差计算权重的时间尺度与原子钟的Allan偏差曲线

Figure 6. Allan deviation curve of the time scale based on the weight of prediction error and Allan deviation curves of atomic clocks.

DownLoad: Full-Size Img PowerPoint

图 7 基于噪声特性计算权重的时间尺度的相位偏差

Figure 7. Phase deviation curve of the time scale with weights based on the noise characteristics.

DownLoad: Full-Size Img PowerPoint

图 8 两种不同取权算法的时间尺度的Allan偏差曲线

Figure 8. Allan deviation curves of the time scale of two different weighting algorithms.

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图 9 基于不同参考预报频率漂移的时间尺度的相位偏差

Figure 9. Phase deviation of the time scale based on different reference forecast frequency drifts.

DownLoad: Full-Size Img PowerPoint

图 10 基于不同参考预报频率漂移的时间尺度的Allan 偏差曲线

Figure 10. Allan deviation curves based on the time scale of different reference forecast frequency drifts.

DownLoad: Full-Size Img PowerPoint

图 11 时间尺度(光抽运小铯钟)相对于UTCr的相位偏差

Figure 11. Phase deviation curve of the time scale (optically pumped small cesium clocks) relative to UTCr.

DownLoad: Full-Size Img PowerPoint

图 12 时间尺度(光抽运小铯钟)相对于UTCr的稳定度曲线

Figure 12. Stability curve of the time scale (optically pumped small cesium clocks) relative to UTCr.

DownLoad: Full-Size Img PowerPoint

图 13 时间尺度(磁选态小铯钟)相对于UTCr的相位偏差

Figure 13. Phase deviation curve of the time scale (magnetically selected small cesium clocks) relative to UTCr.

DownLoad: Full-Size Img PowerPoint

图 14 时间尺度(磁选态小铯钟)相对于UTCr的稳定度曲线

Figure 14. Stability curve of the time scale (magnetically selected small cesium clocks) relative to UTCr.

DownLoad: Full-Size Img PowerPoint

表 1 不同取权方法的时间尺度的准确度比较

Table 1. Comparison of time scale accuracy of different weighting methods.

不同取权方法	最大误差/ns	最小误差/ns	均值/ns	标准偏差/ns
预测误差取权	9.44	–12.25	–0.17	4.22
噪声特性取权	8.43	–18.22	–6.12	5.51

DownLoad: CSV

表 2 不同取权方法的时间尺度的稳定度比较

Table 2. Comparison of time scale stability of different weighting methods.

平均时间/d	1	5	10	20	30
预测误差取权	1.56×10^–14	8.11×10^–15	5.15×10^–15	3.24×10^–15	2.59×10^–15
噪声特性取权	1.49×10^–14	7.13×10^–15	4.61×10^–15	2.94×10^–15	2.51×10^–15

DownLoad: CSV

表 3 原子钟与时间尺度相对于UTCr的Allan偏差

Table 3. The Allan deviation of atomic clocks and time scale relative to UTCr.

取样间隔/d	Cs3050	Cs3059	时间尺度
1	3.80×10^–14	3.39×10^–14	1.57×10^–14
5	2.06×10^–14	1.36×10^–14	8.81×10^–15
10	1.23×10^–14	1.30×10^–14	4.91×10^–15
15	1.85×10^–14	1.58×10^–14	4.29×10^–15
30	—	—	2.87×10^–15

DownLoad: CSV

[1]	Greenhall C A 2003 Metrologia 40 S335 Google Scholar
[2]	Panfilo G, Harmegnies A, Tisserand L 2012 Metrologia 49 49 Google Scholar
[3]	Panfilo G, Harmegnies A, Tisserand L 2014 Metrologia 51 285 Google Scholar
[4]	Song H J, Dong S W, Zhang Y, Wang X, Guo D, An W, Qi Y, Zhang S G 2025 Phys. Scr. 100 015217 Google Scholar
[5]	宋会杰, 董绍武, 王翔, 姜萌, 章宇, 郭栋, 张继海 2024 物理学报 73 060201 Google Scholar Song H J, Dong S W, Wang X, Jiang M, Zhang Y, Guo D, Zhang J H 2024 Acta Phys. Sin. 73 060201 Google Scholar
[6]	Song H J, Dong S W, Qu L L, Wang X, Guo D 2021 J. Instrum. 16 P06032 Google Scholar
[7]	宋会杰, 董绍武, 王翔, 章宇, 王燕平 2020 物理学报 69 170201 Google Scholar Song H J, Dong S W, Wang X, Zhang Y, Wang Y P 2020 Acta Phys. Sin. 69 170201 Google Scholar
[8]	Song H J, Dong S W, Wu W J, Jiang M, Wang W X 2018 Metrologia 55 350 Google Scholar
[9]	刘云, 王文海, 贺德晶, 周勇壮, 沈咏, 邹宏新 2023 物理学报 72 184202 Google Scholar Liu Y, Wang W H, He D J, Zhou Y Z, Shen Y, Zou H X 2023 Acta Phys. Sin. 72 184202 Google Scholar
[10]	梁悦, 谢勇辉, 陈鹏飞, 帅涛, 裴雨贤, 徐昊天, 赵阳, 夏天, 潘晓燕, 张朋军, 林传富 2023 物理学报 72 013702 Google Scholar Liang Y, Xie Y H, Chen P F, Shuai T, Pei Y X, Xu H T, Zhao Y, Xia T, Pan X Y, Zhang P J, Lin C F 2023 Acta Phys. Sin. 72 013702 Google Scholar
[11]	邵晓东, 韩海年, 魏志义 2021 物理学报 70 134204 Google Scholar Shao X D, Han H N, Wei Z Y 2021 Acta Phys. Sin. 70 134204 Google Scholar
[12]	He X, Yuan Z C, Chen J Y, Fang S W, Chen X Z, Wang Q, Qi X H 2022 Front. Phys. 10 970030 Google Scholar
[13]	Shi H B, Qin X M, Chen H J, Yan Y F, Lu Z Q, Wang Z Y, Liu Z J, Guan X L, Wei Q, Shi T T, Chen J B 2025 Phys. Rev. Appl. 23 034018 Google Scholar
[14]	Guo G K, Li C, Hou D, Liu K, Sun F Y, Zhang S G 2023 Appl. Sci. 13 9155 Google Scholar
[15]	Domnin Y S, Baryshev V N, Boyko A I, Elkin G A, Novoselov A V, Kopylov L N, Kupalov D S 2013 Meas. Tech. 55 1155 Google Scholar
[16]	Levi F, Calonico D, Calosso C E, Godone A, Micalizio S, Costanzo G A 2014 Metrologia 51 270 Google Scholar
[17]	Shi J R, Wang X L, Yang F, Bai Y, Guan Y, Fan S C, Liu D D, Ruan J, Zhang S G 2023 Chin. Phys. B 32 040602 Google Scholar
[18]	Wang X L, Ruan J, Liu D D, Guan Y, Shi J R, Yang F, Bai Y, Zhang H, Fan S C, Wu W J, Zhao S H, Zhang S G 2023 Metrologia 60 065012 Google Scholar
[19]	Rovera G D, Bize S, Chupin B, Guéna J, Laurent P H, Rosenbusch P, Uhrich P, Abgrall M 2016 Metrologia 53 S81 Google Scholar
[20]	Bauch A, Weyers S, Piester D, Staliuniene E, Yang W 2012 Metrologia 49 180 Google Scholar
[21]	Galleani L, Signorile G, Formichella V, Sesia I 2020 Metrologia 57 065015 Google Scholar
[22]	宋会杰, 董绍武, 王翔, 王燕平, 张继海, 屈俐俐, 赵书红, 张首刚 2022 时间频率学报 45 270 Google Scholar Song H J, Dong S W, Wang X, Wang Y P, Zhang J H, Qu L L, Zhao S H, Zhang S G 2022 J. Time Freq. 45 270 Google Scholar
[23]	Zucca C, Tavella P 2005 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52 289 Google Scholar
[24]	Stein S R 1992 24th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting McLean, VA, December 1–3, 1992 p289
[25]	Coleman M J, Beard R L 2020 Navigation 67 333 Google Scholar
[26]	Wang X B, Shi F F, Gong D L, Xu S Y, Li Z N, Fu G T, Li Q 2020 Metrologia 57 065009 Google Scholar
[27]	Greenhall C A 2001 33rd Annual Precise Time and Time Interval Systems and Applications Meeting, Long Beach, CA, November 27–29, 2001 p445
[28]	Wu Y W, Liu S R 2023 Metrologia 60 065009 Google Scholar

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