<trans-title xml:lang="en">An improved Kalman filter time scale algorithm for atomic clock noise variation</trans-title>

Hui-Jie Song; Shao-Wu Dong; Xiang Wang; Yu Zhang; Yan-Ping Wang

doi:10.7498/aps.69.20191920

Acta Physica Sinica, Volume. 69, Issue 17, 170201-1(2020)

An improved Kalman filter time scale algorithm for atomic clock noise variation

Hui-Jie Song1...2,*, Shao-Wu Dong1,2,3, Xiang Wang1,2, Yu Zhang1,2, and Yan-Ping Wang12 |Show fewer author(s)

Author Affiliations

¹National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China

²Key Laboratory of Time and Frequency Primary Standards, Chinese Academy of Sciences, Xi’an 710600, China

³School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(11)

Fig. 1. The corrected time deviations of modeling AHM1 based on two algorithms:　(a) The corrected time deviations of modelling AHM1 based on Kalman filter algorithm; (b) the corrected time deviations of modelling AHM1 based on modified Kalman filter algorithm.

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Fig. 2. The corrected time deviations of modelling AHM2 based on two algorithms:　(a) The corrected time deviations of modelling AHM2 based on Kalman filter algorithm; (b) the corrected time deviations of modelling AHM2 based on modified Kalman filter algorithm.

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Fig. 3. Time scale based on two Kalman filter algorithms.

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Fig. 4. The overlapping Allan deviation of time scale based on two Kalman filter algorithms.

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Fig. 5. Time scales based on two Kalman filter algorithms.

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Fig. 6. Time scale stabilities based on two Kalman filter algorithms.

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Table 1.
The overlapping Allan deviations of time scale based on two Kalman filter algorithms.
基于两种Kalman滤波算法的时间尺度的重叠Allan偏差
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Table 1.
The overlapping Allan deviations of time scale based on two Kalman filter algorithms.
基于两种Kalman滤波算法的时间尺度的重叠Allan偏差
取样时间/10² s KF scale/10^–14 R-KF scale/10^–14
3 9.85 13.80
6 6.73 8.75
12 4.38 5.20
30 2.50 2.70
60 1.76 1.85
120 1.22 1.24
300 0.85 0.73
600 0.88 0.57
1200 0.89 0.63

Table 2.
Relative weights of atomic clocks.
原子钟的相对权重
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Table 2.
Relative weights of atomic clocks.
原子钟的相对权重
原子钟编号 HM4926 HM4967 HM0296 Cs3436 Cs2098
相对权重 0.30 0.30 0.14 0.19 0.07

Table 3.
Noise intensity of atomic clocks.
原子钟的噪声强度

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Table 3.
Noise intensity of atomic clocks.
原子钟的噪声强度

原子钟编号	q_1WFM/10^–36 [s²/s]	q_2RWFM/10^–50 [s²/s³]	q_3RWFM/[s²/s⁵]
HM4926	4.64	4.99	4.27 × 10^–60
HM4967	5.88	4.60	3.87 × 10^–60
HM0296	2.01	4.10	6.80 × 10^–49
Cs3436	26.90	0	0
Cs2098	5.43	0	0

Table 4.
Statistical values based on two Kalman filter algorithms.
基于两种Kalman滤波算法的统计值
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Table 4.
Statistical values based on two Kalman filter algorithms.
基于两种Kalman滤波算法的统计值
计算方法最大偏差值/ns 最小值偏差值/ns 平均偏差值/ns
KF scale 4.36 –3.13 0.98
R-KF scale 1.11 –2.65 –0.47

Table 5.
The overlapping Allan deviations of time scale based on two Kalman filter algorithms.
基于两种Kalman滤波算法的时间尺度的重叠阿伦偏差值
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Table 5.
The overlapping Allan deviations of time scale based on two Kalman filter algorithms.
基于两种Kalman滤波算法的时间尺度的重叠阿伦偏差值
Sample time/10³ s KF scale/10^–14 R-KF scale/10^–14
3.60 1.94 1.64
7.20 1.34 1.17
14.40 1.03 0.92
36.00 0.92 0.85
72.00 0.74 0.69
144.00 0.53 0.51
360.00 0.27 0.25

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Hui-Jie Song, Shao-Wu Dong, Xiang Wang, Yu Zhang, Yan-Ping Wang. An improved Kalman filter time scale algorithm for atomic clock noise variation[J]. Acta Physica Sinica, 2020, 69(17): 170201-1

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Paper Information

Category:

Received: Dec. 18, 2019

Accepted: --

Published Online: Jan. 4, 2021

The Author Email:

DOI:10.7498/aps.69.20191920

Topics

Nuclear physics

Particles and fields

Particle and nuclear astrophysics and cosmology

Table 1. The overlapping Allan deviations of time scale based on two Kalman filter algorithms.基于两种Kalman滤波算法的时间尺度的重叠Allan偏差

Table 1. The overlapping Allan deviations of time scale based on two Kalman filter algorithms.基于两种Kalman滤波算法的时间尺度的重叠Allan偏差

Table 2. Relative weights of atomic clocks.原子钟的相对权重

Table 2. Relative weights of atomic clocks.原子钟的相对权重

Table 3. Noise intensity of atomic clocks.原子钟的噪声强度

Table 3. Noise intensity of atomic clocks.原子钟的噪声强度

Table 4. Statistical values based on two Kalman filter algorithms.基于两种Kalman滤波算法的统计值

Table 4. Statistical values based on two Kalman filter algorithms.基于两种Kalman滤波算法的统计值

Table 5. The overlapping Allan deviations of time scale based on two Kalman filter algorithms.基于两种Kalman滤波算法的时间尺度的重叠阿伦偏差值

Table 5. The overlapping Allan deviations of time scale based on two Kalman filter algorithms.基于两种Kalman滤波算法的时间尺度的重叠阿伦偏差值

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Table 1.
The overlapping Allan deviations of time scale based on two Kalman filter algorithms.
基于两种Kalman滤波算法的时间尺度的重叠Allan偏差

Table 1.
The overlapping Allan deviations of time scale based on two Kalman filter algorithms.
基于两种Kalman滤波算法的时间尺度的重叠Allan偏差

Table 2.
Relative weights of atomic clocks.
原子钟的相对权重

Table 2.
Relative weights of atomic clocks.
原子钟的相对权重

Table 3.
Noise intensity of atomic clocks.
原子钟的噪声强度

Table 3.
Noise intensity of atomic clocks.
原子钟的噪声强度

Table 4.
Statistical values based on two Kalman filter algorithms.
基于两种Kalman滤波算法的统计值

Table 4.
Statistical values based on two Kalman filter algorithms.
基于两种Kalman滤波算法的统计值

Table 5.
The overlapping Allan deviations of time scale based on two Kalman filter algorithms.
基于两种Kalman滤波算法的时间尺度的重叠阿伦偏差值

Table 5.
The overlapping Allan deviations of time scale based on two Kalman filter algorithms.
基于两种Kalman滤波算法的时间尺度的重叠阿伦偏差值