基于钟差预测的铯原子钟频率异常检测算法及性能分析

doi:10.11947/j.AGCS.2020.20190322

摘要/Abstract

摘要： 提出一种基于钟差预测的铯原子钟频率异常检测算法。将钟差预测不确定度的解析表达式作为理论依据，以预测误差作为检验统计量，对检验统计量做二元假设检验。在两种情况下，检验统计量都服从正态分布。通过约束虚警概率（P_FA），查询正态分布的分布函数，得到对应的检测门限值。根据在异常情况下的检验统计量分布函数和检测门限值，推导给出了求解平均频率跳变幅度（Y_a）对应的检测概率（P_D）的表达式。仿真试验和实测数据试验都验证了理论分析的结论。在此基础上总结了提高检测概率的方法。

关键词: 原子钟, 异常检测, 钟差预测, 检验统计量, 检测门限, 虚警概率, 检测概率

Abstract: A cesium atomic clock frequency anomaly detection algorithm based on clock prediction is proposed. The theory is based on the analytical expression of clock prediction uncertainty. Prediction errors are used as the test statistics and a binary hypothesis test is adopted. The test statistics all follow standard normal distributions. By means of setting a false alarm probability (P_FA) value and acquiring the distribution function of normal distributions, the detection threshold can be determined. According to the detection threshold and the distribution function of the test statistics when anomalies appear, the expression of the detection probabilities (P_D)s with different mean frequency jump levels (Y_a)s is derived. Simulations and experiments validate the theoretical analyses. Based on the analyses, the methods of improving the detection probability are summarized.

Key words: atomic clock, anomaly detection, clock prediction, test statistics, detection threshold, false alarm probability, detection probability

中图分类号:

P228

伍贻威. 基于钟差预测的铯原子钟频率异常检测算法及性能分析[J]. 测绘学报, 2021, 50(1): 52-60.

WU Yiwei. A cesium atomic clock frequency anomaly detection algorithm based on clock prediction and its performance analyses[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(1): 52-60.

参考文献

[1] WHIBBERLEY P B, DAVIS J A, SHEMAR S L.Local representations of UTC in national laboratories[J]. Metrologia, 2011, 48(4):S154-S164.
[2] LEWANDOWSKI W, ARIAS E F. GNSS times and UTC[J]. Metrologia, 2011, 48(4):S219-S224.
[3] 杨元喜.北斗卫星导航系统的进展、贡献与挑战[J].测绘学报, 2010, 39(1):1-6. YANG Yuanxi. Progress, contribution and challenges of compass/BeiDou satellite navigation system[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(1):1-6.
[4] 杨元喜.综合PNT体系及其关键技术[J].测绘学报, 2016, 45(5):505-510.DOI:10.11947/j.AGCS.2016.20160127. YANG Yuanxi. Concepts of comprehensive PNT and related key technologies[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5):505-510. DOI:10.11947/j.AGCS.2016.20160127.
[5] PANFILO G, ARIASE F.Algorithms for international atomic time[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2010, 57(1):140-150.
[6] PANFILO G, ARIAS E F.Studies and possible improvements on the EAL algorithm[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2010, 57(1):154-160.
[7] PANFILO G, HARMEGNIES A, TISSERAND L.A new prediction algorithm for the generation of international atomic time[J]. Metrologia, 2012, 49(1):49-56.
[8] PANFILO G, HARMEGNIES A, TISSERAND L.A new weighting procedure for UTC[J]. Metrologia, 2014, 51(3):285-292.
[9] GALLEANI L, TAVELLA P.Detection and identification of atomic clock anomalies[J]. Metrologia, 2008, 45(6):S127-S133.
[10] GALLEANI L, TAVELLA P.The dynamic Allan variance[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2009, 56(3):450-464.
[11] NUNZI E, GALLEANI L, TAVELLA P, et al.Detection of anomalies in the behavior of atomic clocks[J]. IEEE Transactions on Instrumentation and Measurement, 2007, 56(2):523-528.
[12] GALLEANI L.Detection of changes in clock noise using the time-frequency spectrum[J]. Metrologia, 2008, 45(6):143-153.
[13] LEES W, KIM J, LEEY J.Protecting signal integrity against atomic clock anomalies on board GNSS satellites[J]. IEEE Transactions on Instrumentation and Measurement, 2011, 60(7):2738-2745.
[14] GALLEANI L, TAVELLA P.Detection of atomic clock frequency jumps with the Kalman filter[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2012, 59(3):504-509.
[15] HUANG Xinming, GONG Hang, OU Gang.Detection of weak frequency jumps for GNSS onboard clocks[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2014, 61(5):747-755.
[16] GALLEANI L, TAVELLA P.Robust detection of fast and slow frequency jumps of atomic clocks[J].IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2017, 64(2):475-485.
[17] WU Yiwei, ZHU Xiangwei, HUANG Yangbo, et al.Uncertainty derivation and performance analyses of clock prediction based on mathematical model method[J].IEEE Transactions on Instrumentation and Measurement, 2015, 64(10):2792-2801.
[18] WU Yiwei, ZHU Xiangwei, HUANG Yangbo, et al.Optimal observation intervals for clock prediction based on the mathematical model method[J]. IEEE Transactions on Instrumentation and Measurement, 2016, 65(1):132-143.
[19] 伍贻威.GNSS时间基准关键技术研究[D].长沙:国防科技大学, 2016. WU Yiwei. Key technologies of GNSS time scale[D]. Changsha:National University of Defense Technology, 2016.
[20] 伍贻威. GNSS时间基准关键技术研究[J]. 测绘学报, 2017, 46(4):533. DOI:10.11947/j.AGCS.2017.20160660. WU Yiwei. Key technologies of GNSS time scale[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(4):533. DOI:10.11947/j.AGCS.2017.20160660.
[21] 伍贻威, 朱祥维, 龚航, 等. 建立GNSS时间基准的构想和思考[J]. 电子学报, 2017, 45(8):1818-1826. WU Yiwei, ZHU Xiangwei, GONG Hang, et al. Concepts and thoughts of forming a GNSS time scale[J]. Acta Electronica Sinica, 2017, 45(8):1818-1826.
[22] TAVELLA P.Statistical and mathematical tools for atomic clocks[J]. Metrologia, 2008,45(6):S183-S192.
[23] ZUCCA C, TAVELLA P.The clock model and its relationship with the Allan and related variances[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2005, 52(2):289-296.
[24] PANFILO G, TAVELLA P.Atomic clock prediction based on stochastic differential equations[J]. Metrologia, 2008, 45(6):S108-S116.
[25] 罗鹏飞, 张文明.随机信号分析与处理[M].北京:清华大学出版社, 2006. LUO Pengfei, ZHANG Wenming. Stochastic signal analysis and processing[M]. Beijing:Tsinghua University Press, 2006.
[26] 张小红, 陈兴汉, 郭斐. 高性能原子钟钟差建模及其在精密单点定位中的应用[J]. 测绘学报, 2015, 44(4):392-398. DOI:10.11947/j.AGCS.2015.20140287. ZHANG Xiaohong, CHEN Xinghan, GUO Fei. High-performance atomic clock modeling and its application in precise point positioning[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(4):392-398. DOI:10.11947/j.AGCS.2015.20140287.
[27] KASDIN N J.Discrete simulation of colored noise and stochastic processes and 1/f^α power law noise generation[J]. Proceedings of the IEEE, 1995, 83(5):802-827.
[28] 盛骤, 谢式千, 潘承毅.概率论与数理统计[M].4版. 北京:高等教育出版社, 2008. SHENG Zhou, XIE Shiqian, PAN Chengyi. Probability and mathematical statistics[M]. 4th ed. Beijing:Higher Education Press, 2008.
[29] WEI Ziqing, RUAN Rengui, JIA Xiaolin,et al.Satellite positioning and orbit determination system (SPODS):introduction and evaluation[J]. Journal of Geodesy and Geoinformation Science, 2018, 1(1):25-29.