原子钟钟差预测不确定度的建模与分析
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摘要
钟差预测是原子钟时标产生和原子钟驾驭的关键环节。原子钟作为精准的信号源,其信号由确定信号部分和固有噪声即随机部分组成。氢钟和铯钟主要包含两种噪声,即调频白噪声和调频随机游走噪声,这两种噪声是产生预测不确定度的主要因素。根据原子钟数学模型补充推导出原子钟时差数据预测不确定度的数学表达式,并得出了钟组的最小预测不确定度,分析了钟组的台数对预测不确定度的影响。最后通过数据仿真验证了理论的正确性。
Atomic clock difference prediction is the key step in atomic clock time scale generation and atomic clock control. The atomic clock is a precise signal source,and its signal consists of the determined signal part which is corrected by the prediction algorithm and the inherent noise,which is a random part. The hydrogen and cesium clock mainly contain two kinds of noise,that is,white frequency noise and random walk frequency noise. These two kinds of noise are the main factors that produce the uncertainty of prediction. The mathematical expression of the prediction uncertainty of the time difference data of the atomic clock is derived,based on the mathematical model of the atomic clock,and the minimum prediction uncertainty of the clock group is obtained. The influence of the number of clocks in the clock group on the prediction uncertainty is analyzed. Finally,the correctness of the theory is verified.
Atomic clock difference prediction is the key step in atomic clock time scale generation and atomic clock control. The atomic clock is a precise signal source,and its signal consists of the determined signal part which is corrected by the prediction algorithm and the inherent noise,which is a random part. The hydrogen and cesium clock mainly contain two kinds of noise,that is,white frequency noise and random walk frequency noise. These two kinds of noise are the main factors that produce the uncertainty of prediction. The mathematical expression of the prediction uncertainty of the time difference data of the atomic clock is derived,based on the mathematical model of the atomic clock,and the minimum prediction uncertainty of the clock group is obtained. The influence of the number of clocks in the clock group on the prediction uncertainty is analyzed. Finally,the correctness of the theory is verified.
引文
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[12] Zucca C, Tavella P. The clock model and its relationship with Allan and related variances[J]. IEEE Transactions on Ultrasonics Ferroelectrics&Frequency Control,2005,52(2):289-296.
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[16] Zhengming W. Experiments on a time scale algorithm for introducing hydrogen masers into an ensemble of caesium clocks[J]. Metrologia,2008,45(6):38-41.
[17]王玉琢,张爱敏,张越,等.一种原子钟频率稳定度的估计方法[J].计量学报,2018,39(3):397-400.Wang Y Z,Zhang A M,Zhang Y,et al. A Method for Estimating Frequency Stability of Atomic Clock[J].Acta Metrologica Sinica,2018,39(3):397-400.
[2]吴文娟,朱江淼,郭吉省.基于SVM对原子钟的钟差预测[J].信号处理,2012,12(28):31-34.Wu W J,Zhu J M,Guo J S. Clock error prediction of atomic clock based on SVM[J]. Signal Processing,2012,12(28):31-34.
[3]王宇谱,吕志平,陈正生,等.卫星钟差预报的小波神经网络算法研究[J].测绘学报,2013,42(3):323-330.Wang Y P,Lv Z P,Chen Z S,et al. Research on the Algorithm of Wavelet Neural Network to Predict Satellite Clock Bias[J]. Acta Geodaetica et Cartographica Sinica,2013,42(3):323-330.
[4]刘晓刚,吴晓平,田颜峰,等.利用切比雪夫多项式模型进行时间预报研究[J].大地测量与地球动力学,2010,30(1):77-83.Liu X G,Wu X P,Tian Y F,et al. Study on Automic Prediction of Time Based on Interpolation Model With Chebyshev Polynomiais[J]. Journal of Geodesy and Geody Namics,2010,30(1):77-83.
[5]刘晓刚,李建伟,李岩,等.基于最小二乘和卡尔曼滤波方法进行原子时预报的研究[J].海洋测绘,2008,28(3):24-26.Liu X G,Li J W, Li Y,et al. The Study of Time Prediction Based on the Methods of Least Square and Kalman Filter[J]. Hydrographic Surveying and Charting,2008,28(3):24-26.
[6]朱祥,维肖华,雍少为,等.卫星钟差预报的kalman算法及其性能分析[J].宇航学报,2008,29(3):965-970.Zhu X,W X H,Yong S W,et al. The Kalman Algorithm Used for Satellite Clock Offset Prediction and Its Performance Analysis[J]. Journal of Astronautics,2008,29(3):965-970.
[7] Huang G W,Zhang Q. Real-time estimation of satellite clock offset using adaptively robust Kalman filter with classified adaptive factors[J]. GPS Solutions,2012,16:531-539.
[8]宋会杰,侯娟.基于灰色模型和ARIMA模型的钟差预测[J].宇航计测技术,2012,32(1):26-29.Song H J,Hou J. Prediction of Clock Error Based on Grey Model and ARIMA Model[J]. Journal of Astronautic Metrology and Measurement,2012,32(1):26-29.
[9] Galleani L. A tutorial on the two-state model of the atomic clock noise[J]. Metrologia,2008,45(6):175-182.
[10] Galleani L,Sacerdote L,Tavella P, et al. A mathematical model for the atomic clock error[J].Metrologia,2003,40(3):257-264.
[11] Panfilo G,Tavella P. Atomic colck Prediction based on stochastic differential equations[J]. Metrologia,2008,45(6):108-111.
[12] Zucca C, Tavella P. The clock model and its relationship with Allan and related variances[J]. IEEE Transactions on Ultrasonics Ferroelectrics&Frequency Control,2005,52(2):289-296.
[13]朱江淼,孙盼盼,高源,等.原子钟频差数据去噪算法的研究[J].计量学报,2017,38(4):499-503.Zhu J M,Sun P P,Gao Y,et al. The Denoise of the Atomic Clock Frequency Differences[J]. Acta Metrologica Sinica,2017,38(4):499-503.
[14] Panfilo G,Harmegnies A, Tisserand L. A new prediction algorithm for the generation of international atomic time[J]. Metrologia,2012,49(1):49-56.
[15] Galleani L,Tavella P. Time and the Kalman filter[J].Control Systems IEEE,2010,30(2):44-65.
[16] Zhengming W. Experiments on a time scale algorithm for introducing hydrogen masers into an ensemble of caesium clocks[J]. Metrologia,2008,45(6):38-41.
[17]王玉琢,张爱敏,张越,等.一种原子钟频率稳定度的估计方法[J].计量学报,2018,39(3):397-400.Wang Y Z,Zhang A M,Zhang Y,et al. A Method for Estimating Frequency Stability of Atomic Clock[J].Acta Metrologica Sinica,2018,39(3):397-400.