基于频差估计值修正的Kalman滤波钟差预报算法

doi:10.11947/j.AGCS.2025.20250055

测绘学报 ›› 2025, Vol. 54 ›› Issue (9): 1596-1607.doi: 10.11947/j.AGCS.2025.20250055

基于频差估计值修正的Kalman滤波钟差预报算法

沈聪¹^,²(), 王国成¹(), 柳林涛¹, 胡辉雯¹^,², 蔡志武³

^1.中国科学院精密测量科学与技术创新研究院精密大地测量与定位全国重点实验室，湖北　武汉　430077
^2.中国科学院大学，北京　101408
^3.北京卫星导航中心，北京　100094

收稿日期:2025-02-13 修回日期:2025-07-08 出版日期:2025-10-10 发布日期:2025-10-10
通讯作者: 王国成 E-mail:shencong@apm.ac.cn;guocheng96@apm.ac.cn
作者简介:沈聪（1996—），男，博士生，研究方向为钟差数据处理与分析。E-mail：shencong@apm.ac.cn
基金资助:
国家自然科学基金(42074011);中国科学院重大科技任务局重点部署科研专项(T24Y6303)

Kalman filter-based satellite clock bias prediction algorithm with frequency difference estimation correction

Cong SHEN¹^,²(), Guocheng WANG¹(), Lintao LIU¹, Huiwen HU¹^,², Zhiwu CAI³

^1.State Key Laboratory of Precision Geodesy, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China
^2.University of Chinese Academy of Sciences, Beijing 101408, China
^3.Beijing Satellite Navigation Center, Beijing 100094, China

Received:2025-02-13 Revised:2025-07-08 Online:2025-10-10 Published:2025-10-10
Contact: Guocheng WANG E-mail:shencong@apm.ac.cn;guocheng96@apm.ac.cn
About author:SHEN Cong (1996—), male, PhD candidate, majors in clock bias processing and analysis. E-mail: shencong@apm.ac.cn
Supported by:
The National Natural Science Foundation of China(42074011);The Key Projects Deployed by the Major Scientific and Technological Mission Bureau of the Chinese Academy of Sciences(T24Y6303)

摘要/Abstract

摘要：

卫星钟差预报在时间同步、实时定位及自主导航等方面具有重要意义，其精度直接影响导航系统的服务质量。传统卡尔曼滤波模型（KFM）因其最小方差估计特性，能够得到时差、频差和频漂的最优估计值而被广泛应用于钟差预报。然而，KFM未显式建模钟差中的周期项，导致时差、频差和频漂估计值中存在周期性波动。这种周期性估值偏差将增大KFM的预报误差，并会随着时间累积进一步放大。针对这一问题，本文提出基于频差估计值修正的改进卡尔曼滤波模型（IKFM）。该模型首先通过频谱分析识别频差估计值中的周期项，并利用最小二乘拟合其参数，随后从估计值中扣除周期性波动，以消除周期项对状态估计的干扰，最终基于修正后的频差进行时差的外推预报。基于GPS卫星钟的试验结果表明：与KFM相比，IKFM在1～24 h预报中的误差最高降低了32.14%；且相较于灰色模型、二次多项式模型和谱分析模型，IKFM在所有预报时长上均表现出最佳的准确性和稳定性。IKFM通过有效抑制周期项干扰，为高精度卫星钟差预报提供了可靠解决方案，尤其适用于周期性波动显著的卫星钟。

关键词: 卫星钟差预报, 卡尔曼滤波, 预报精度, 原子钟状态估计, 周期项

Abstract:

Satellite clock bias prediction is of great significance for time synchronization, real-time positioning, and autonomous navigation, and its accuracy directly affects the service quality of navigation systems. The traditional Kalman filter model (KFM) is widely used in clock bias prediction because of its minimum variance estimation characteristics, which enable it to obtain optimal estimates of time difference, frequency difference, and frequency drift. However, KFM does not explicitly model the periodic terms in clock bias, resulting in periodic fluctuations in the estimated values of time difference, frequency difference, and frequency drift. This periodic estimation bias increases the prediction error of KFM and further amplifies it over time. To address this issue, this paper proposes an improved Kalman filter model (IKFM) based on frequency difference estimation correction. This model first identifies the periodic terms in the frequency difference estimates through spectral analysis and fits their parameters using least squares. Then, periodic fluctuations are subtracted from the estimated values to eliminate the interference of periodic terms on the state estimation. Finally, the time difference is extrapolated based on the corrected frequency differences. The experimental results based on GPS clock bias data show that, compared with KFM, IKFM reduced the error in 1~24 h predictions by up to 32.14%; and compared with the gray model, quadratic polynomial model, and spectral analysis model, IKFM showed the best accuracy and stability for all prediction durations. By effectively suppressing periodic term interference, IKFM provides a reliable solution for high-precision satellite clock bias prediction, especially for spaceborne atomic clocks with significant periodic fluctuations.

Key words: satellite clock bias prediction, Kalman filter, prediction accuracy, atomic clock state estimation, periodic terms

中图分类号:

P228

沈聪, 王国成, 柳林涛, 胡辉雯, 蔡志武. 基于频差估计值修正的Kalman滤波钟差预报算法[J]. 测绘学报, 2025, 54(9): 1596-1607.

Cong SHEN, Guocheng WANG, Lintao LIU, Huiwen HU, Zhiwu CAI. Kalman filter-based satellite clock bias prediction algorithm with frequency difference estimation correction[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(9): 1596-1607.

图/表 10

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卫星类型	原子钟类型	卫星钟编号
ⅡR	Rb	G02、G13、G16、G19、G20、G21、G22
ⅡRM	Rb	G05、G07、G12、G15、G17、G29、G31
IIF	Rb	G01、G03、G06、G09、G10、G25、G26、G27、G30、G32
IIF	Cs	G08、G24
ⅢA	Rb	G04、G11、G14、G18、G23、G28

f=1/86 400 Hz	f=1/43 200 Hz	f=1/21 600 Hz
0.004 5	0.005 0	0.004 9
－90.760 7	－90.234 0	－90.091 9
－218.925 5	－218.398 2	－218.258 7
－0.001 2	－0.002 7	－0.005 5
0.399 6	0.206 0	0.101 9
0.404 9	0.208 7	0.103 3

模型	ⅡR	ⅡR-M	ⅡF-Rb	ⅡF-Cs	ⅢA	均值
GM	0.604 6	0.837 3	1.744 7	2.702 7	1.501 7	1.311 1
QPM	0.953 4	0.995 3	1.110 4	3.693 3	0.399 0	1.078 9
SAM	0.953 3	0.996 0	1.099 9	3.633 6	0.393 7	1.071 0
KFM	0.670 8	0.740 2	0.804 3	3.594 6	0.277 2	0.836 6
IKFM	0.575 3	0.639 0	0.543 1	1.836 2	0.236 2	0.594 4
均值	0.751 5	0.841 6	1.060 5	3.092 1	0.561 6

统计指标	模型	3 h预报	6 h预报	12 h预报	24 h预报
RMS/ns	GM	0.644 1	0.783 3	1.185 4	2.391 1
	QPM	0.541 2	0.695 3	1.027 5	1.957 6
	SAM	0.528 6	0.681 3	1.004 2	1.936 1
	KFM	0.557 1	0.724 8	1.033 3	1.687 1
	IKFM	0.509 6	0.611 8	0.783 6	1.144 8
预报提升率/（%）	IKFM vs. GM	20.87	21.89	33.89	52.12
	IKFM vs. QPM	5.82	12.01	23.73	41.51
	IKFM vs. SAM	3.57	10.20	21.97	40.87
	IKFM vs. KFM	8.51	15.59	24.16	32.14

测站	E方向RMS			N方向RMS			U方向RMS
测站	IGUP	KFM	IKFM	IGUP	KFM	IKFM	IGUP	KFM	IKFM
FALK	9.5	5.7	2.9	9.7	7.0	7.3	7.4	6.9	5.8
LROC	12.9	12.9	6.2	5.4	8.7	6.0	11.3	16.9	11.0
MAR6	9.4	8.5	7.9	4.5	9.1	4.4	8.6	9.6	5.2

基于频差估计值修正的Kalman滤波钟差预报算法

Kalman filter-based satellite clock bias prediction algorithm with frequency difference estimation correction

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