基于稳定度加权和Kalman滤波算法相融合的多级时间比对融合算法

doi:10.12305/j.issn.1001-506X.2026.08.28

摘要/Abstract

摘要：

针对卫星双向时间频率传递（two-way satellite time and frequence transfer，TWSTFT）和精密单点定位（precise point positioning，PPP）等单一技术难以同时满足高精度和高稳定度的需求，提出一种多级时间比对融合算法。模型一基于稳定度权重融合TWSTFT、GALILEO P3和全球定位系统（global positioning system，GPS）P3码，再利用Kalman滤波将融合结果与GPS PPP进行二次融合，模型二优先融合TWSTFT与GPS PPP，再通过两级Kalman滤波逐级融合GALILEO P3和GPS P3码。仿真结果表明，两种模型均能改善时间比对的精度和稳定度，模型一适合对稳定度要求较高的长期钟差分析场景，模型二适合实时监测和动态环境下的时间比对需求。数据失效测试进一步表明，模型二在GPS PPP缺失时表现更好，两种模型对GALILEO P3和GPS P3码缺失时均表现出良好的容错性，验证了算法设计的容错能力。

关键词: 时间比对, 数据融合, Kalman滤波, 稳定度加权

Abstract:

For the single techniques such as two-way satellite time and frequence transfer （TWSTFT） and precise point positioning （PPP）, which are difficult to satisfy the demands of high accuracy and high stability at the same time, a multi-level time comparison fusion algorithm is proposed. Model 1 fuses TWSTFT, GALILEO P3, and global positioning system （GPS） P3 codes with stability weighting, and then fuses the weighted results with GPS PPP using Kalman filtering, while Model 2 prioritizes the fusion of TWSTFT and GPS PPP, and then fuses GALILEO P3 and GPS P3 codes step by step by two-level Kalman filtering. Simulation results show that both models can improve the accuracy and stability of time comparison, and Model 1 is suitable for long-term clock difference analysis scenarios with high stability requirements, while Model 2 is suitable for real-time monitoring and time comparison needs in dynamic environments. The data failure test further shows that Model 2 performs better when GPS PPP is missing, and both models show good fault tolerance for GALILEO P3 and GPS P3 code missing, which verifies the fault tolerance of the algorithm design.

Key words: time comparison, data fusion, Kalman filtering, stability weighting

中图分类号:

宁学友, 刘强, 胡邓华, 张爽. 基于稳定度加权和Kalman滤波算法相融合的多级时间比对融合算法[J]. 系统工程与电子技术, 2026, 48(8): 2833-2840.

Xueyou NING, Qiang LIU, Denghua HU, Shuang ZHANG. Multi-level time comparsion fusion algorithm based on the intergration of stability weighting and Kalman filtering algorithm[J]. Systems Engineering and Electronics, 2026, 48(8): 2833-2840.

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参考文献 28

1	FENG F, CHEN Z K, CHEN L J, et al. Rapid detection of GNSS time synchronization attacks via the enhanced code and carrier Doppler consistency test[J]. GPS Solutions, 2023, 28 (1): 38. doi: 10.1007/s10291-023-01583-6
2	LIU W X, YUAN H, GE J. Local-area nanosecond-accuracy time synchronisation based on GPS L1 observations[J]. IET Radar Sonar and Navigation, 2019, 13 (5): 824- 829. doi: 10.1049/iet-rsn.2018.5283
3	SUN H Y, HANG G, PENG J, et al. Kalman filter based pseudo-code ranging and carrier phase measurement for fiber optical time transfer method[J]. Photonics, 2023, 10 (9): 981- 993. doi: 10.3390/photonics10090981
4	LIU M Y, TU R, LI F X, et al. GPS + 5G fusion for high-precision time transfer[J]. Measurement Science and Technology, 2024, 35 (4): 045024. doi: 10.1088/1361-6501/ad1d2f
5	WANG X, DONG S W, SONG H J, et al. Time transfer link fusion algorithm based on wavelet multi-resolution analysis[J]. Measurement, 2024, 232, 114599. doi: 10.1016/j.measurement.2024.114599
6	QIN W J, YANG H Y, ZHANG Z, et al. The analysis on time transfer of GPS/Galileo/BDS PPP with integer ambiguity resolution[J]. Physica Scripta, 2024, 99 (2): 025011. doi: 10.1088/1402-4896/ad19bb
7	ZHANG V, PARKER T, YAO J. Long-term uncertainty in time transfer using GPS and TWSTFT techniques[C]// Proc. of the Joint Conference of the IEEE International Frequency Control Symposium & the European Frequency and Time Forum, 2015: 723−727.
8	WANG W X, DONG S W, WU W J, et al. Combining TWSTFT and GPS PPP using a Kalman filter[J]. GPS Solutions, 2021, 25 (4): 138. doi: 10.1007/s10291-021-01173-4
9	ZHANG P F, TU R, GAO Y P, et al. Improving the performance of multi-GNSS time and frequency transfer using robust Helmert variance component estimation[J]. Sensors, 2018, 18 (9): 2878. doi: 10.3390/s18092878
10	VERHASSELT K, DEFRAIGNE P. Multi-GNSS time transfer based on the CGGTTS[J]. Metrologia, 2019, 56 (6): 065003. doi: 10.1088/1681-7575/ab3ed7
11	DEFRAIGNE P, BAIRE Q. Combining GPS and GLONASS for time and frequency transfer[J]. Advances in Space Research, 2011, 47 (2): 265- 275. doi: 10.1016/j.asr.2010.07.003
12	DARMIAN K, KRZYSZTOF K. Performance of the precise point positioning method along with the development of GPS, GLONASS and Galileo systems[J]. Measurement, 2020, 164, 108009. doi: 10.1016/j.measurement.2020.108009
13	GUO D, DONG S W, WU S W, et al. Galileo E3 total time delay calibration in NTSC time and frequency comparison[J]. Chinese Astronomy and Astrophysics, 2024, 48 (1): 206- 221. doi: 10.1016/j.chinastron.2024.03.001
14	PETIT G, JIANG Z. Stability and accuracy of GPS P3 TAI time links[C]// Proc. of the European Frequency and Time Forum, Guildford, 2004: 287−291.
15	YANG C F. Innovation and development of BeiDou navigation satellite system （BDS） project management mode[J]. Frontiers of Engineering Management, 2021, 8 (2): 312- 320. doi: 10.1007/s42524-021-0155-3
16	YANG Y X, REN X, JIA X L, et al. Development trends of the National secure PNT system based on BDS[J]. Science China Earth Sciences, 2023, 66 (5): 929- 938. doi: 10.1007/s11430-022-1069-7
17	张虹, 广伟, 袁海波, 等. TWSTFT与北斗共视数据融合算法研究[C]//第九届中国卫星导航学术年会, 2018: 85−88.
	ZHANG H, GUANG W, YUAN H B, et al. Research on fusion algorithm of TWSTFT and Beidou common view[C]// Proc. of the 9th China Satellite Navigation Academic Annual Conference, 2018: 85−88.
18	王威雄, 董绍武, 武文俊, 等. 时间比对融合算法分析与比较[J]. 天文学报, 2020, 61 (6): 118- 127.
	WANG W X, DONG S W, WEU W J, et al. Analysis and comparison for fusion algorithms of time transfer[J]. Acta Astronomica Sinica, 2020, 61 (6): 118- 127.
19	王威雄, 董绍武, 武文俊, 等. Vondrak-Cepek组合滤波在北斗共视和卫星双向时间比对融合中的应用[J]. 国防科技大学学报, 2021, 43 (6): 17- 25. doi: 10.11887/j.cn.202106003
	WANG W X, DONG S W, WEU W J, et al. Application of Vondrak-Cepek combined filtering in the fusion of Beidou CV and TWSTFT[J]. Journal of National University of Defense Technology, 2021, 43 (6): 17- 25. doi: 10.11887/j.cn.202106003
20	刘强, 孙浩冉, 胡邓华, 等. 基于Vondrak-Cepek组合滤波和注意力机制加权的时间比对融合算法[J]. 系统工程与电子技术, 2025, 47 (2): 673- 679.
	LIU Q, SUN H R, HU D H, et al. Time alignment fusion algorithm based on Vondrak-Cepek combined filtering and attention mechanism weighting[J]. Systems Engineering and Electronics, 2025, 47 (2): 673- 679.
21	JIANG Z H, ZHANG V, PARKER T E, et al. Accurate TWSTFT time transfer with indirect links[C]// Proc. of the Precise Time and Time Interval Systems and Applications Meeting, 2017: 243−255.
22	JIANG Z, PETIT G. Combination of TWSTFT and GNSS for accurate UTC time transfer[J]. Metrologia, 2009, 46 (3): 305- 314. doi: 10.1088/0026-1394/46/3/019
23	GUYENNON N, GERRETTO G, TAVELLA P, et al. Further characterization of the time transfer capabilities of precise point positioning （PPP）: the sliding batch procedure[J]. IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control, 2009, 56 (8): 1634- 1641. doi: 10.1109/TUFFC.2009.1228
24	JIANG Z, PETIT G. Combination of GPS PPP and two-way time transfer for TAI computation[C]// Proc. of the 39th Annual Precise Time and Time Interval Systems and Applications Meeting, 2007: 195−202.
25	黄艳. GPS P3码共视算法的研究[D]. 北京: 北京工业大学, 2009.
	HUANG Y. The research on tne common-view comparison system based on GPS P3 code recriver[D]. Beijing: Beijing University of Technology, 2009.
26	张越, 高小珣, 高源, 等. 多通道GPS共视法时频传递接收机的研制[J]. 宇航计测技术, 2004, 24 (5): 35- 39. doi: 10.3969/j.issn.1000-7202.2004.05.009
	ZHANG Y, GAO X X, GAO Y, et al. Research on multi−channel GPS common−view method time & frequency transfer receiver[J]. Joumal of Astronautic Metrology and Measurement, 2004, 24 (5): 35- 39. doi: 10.3969/j.issn.1000-7202.2004.05.009
27	GUTMAN P, VELGER M. Tracking targets using adaptive Kalman filtering[J]. IEEE Trans. on Aerospace and Electronic Systems, 1990, 26 (5): 691- 699. doi: 10.1109/7.102704
28	LI Q, GUO J, LIU W Y, et al. An enhanced time synchronization method for a network based on Kalman filtering[J]. Scientific Reports, 2024, 14 (1): 21271. doi: 10.1038/s41598-024-71929-8

链路	最大值	最小值	均值	标准差
TWSTFT-GPS PPP	1.894 4	0.144 3	0.985 0	0.303 6
GPS P3-GPS PPP	2.170 6	−2.815 2	−0.241 8	1.017 6
GALILEO P3-GPS PPP	2.274 3	−0.283 2	1.029 4	0.397 1
模型一-GPS PPP	0.198 4	−0.163 1	0.029 0	0.054 2
模型二-GPS PPP	0.325 4	−0.073 6	0.143 9	0.064 1

模型	单一数据缺失	均方根误差	最大偏移量
模型一	GPS P3缺失	0.002 8	0.134 9
	GPS PPP缺失	0.632 3	1.072 8
	GALILEO P3缺失	0.000 4	0.073 2
模型二	GPS P3缺失	0.007 9	0.522 5
	GPS PPP缺失	0.153 2	0.755 5
	GALILEO P3缺失	0.001 2	0.098 9

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