改进ABC算法优化BP神经网络的短期钟差预报及其应用

doi:10.11947/j.AGCS.2025.20240318

测绘学报 ›› 2025, Vol. 54 ›› Issue (8): 1404-1415.doi: 10.11947/j.AGCS.2025.20240318

改进ABC算法优化BP神经网络的短期钟差预报及其应用

潘雄¹(), 张龙杰¹, 艾青松³, 金丽宏²(), 蔡茂¹

^1.武汉纺织大学计算机与人工智能学院，湖北　武汉　430200
^2.武汉纺织大学数学与统计学院，湖北　武汉　430200
^3.长江空间信息技术工程有限公司（武汉），湖北　武汉　430010

收稿日期:2024-08-01 修回日期:2025-07-03 出版日期:2025-09-16 发布日期:2025-09-16
通讯作者: 金丽宏 E-mail:pxjlh@163.com;2022018@wtu.edu.cn
作者简介:潘雄（1973—），男，博士，教授，研究方向为深度学习、卫星导航定位。E-mail：pxjlh@163.com
基金资助:
国家自然科学基金(42174010);湖北省自然科学基金(2023AFB435)

Improved ABC algorithm for optimizing BP neural network in short-term clock bias prediction and application

Xiong PAN¹(), Longjie ZHANG¹, Qingsong AI³, Lihong JIN²(), Mao CAI¹

^1.School of Computer Science and Artificial Intelligence, Wuhan Textile University, Wuhan 430200, China
^2.School of Mathematics and statistics, Wuhan Textile University, Wuhan 430200, China
^3.Changjiang Space Information Technology Engineering Co., Ltd., (Wuhan), Wuhan 430010, China

Received:2024-08-01 Revised:2025-07-03 Online:2025-09-16 Published:2025-09-16
Contact: Lihong JIN E-mail:pxjlh@163.com;2022018@wtu.edu.cn
About author:PAN Xiong (1973—), male, PhD, professor, majors in deep learning and satellite navigation positioning. E-mail: pxjlh@163.com
Supported by:
The National Natural Science Foundation of China(42174010);The Hubei Province Natural Science Foundation(2023AFB435)

摘要/Abstract

摘要：

针对BP神经网络在处理非线性与复杂环境时易陷入局部最优解，且收敛速度较慢的问题，本文提出一种改进的人工蜂群（ABC）算法用于优化反向传播神经网络模型，并将其应用于钟差短期预报中。首先，从增强步长的随机性、提升搜索效率及维持种群多样性出发，引入莱维飞行策略、教与学优化算法及适应度-距离平衡机制，改进ABC算法，有效提高算法的全局搜索能力，避免陷入局部最优解。其次，将改进的ABC算法与BP神经网络相结合，应用于卫星钟差短期预报，并给出相应的计算步骤。然后，选用GFZ提供的高精度卫星钟差产品，从算法效率、稳定性及精度等方面进行单天和多天预报对比分析，验证模型的适用性。最后，验证优化模型的预报结果在PPP中的应用效果。结果表明，改进后的人工蜂群算法能够快速逼近最优解，精度提升明显，与二次多项式（quadratic polynomial，QP）模型、BP和ABC-BP模型相比，平均精度分别提升了56.55%、25.11%和7.07%，且MEO-PHM钟的提升效果优于MEO-Rb钟；改进人工蜂群算法与BP组合模型残差分布更加集中，中位数更接近零，极值更小，在6、12 h的预报中具有较高的准确性和稳定性；使用预报钟差序列进行精密单点定位测试，改进组合模型的结果在E、N、U方向的精度，分别较ABC-BP模型和BP模型提升了42.07%、31.07%，41.79%和45.42%、50.16%、46.18%。

关键词: 适应度-距离平衡, 教与学优化, 短期预报, 精密单点定位

Abstract:

In order to solve the problem that BP neural network is easy to fall into the local optimal solution and the convergence speed is slow when dealing with nonlinear and complex environments, an improved artificial bee colony algorithm is proposed to optimize BP neural network and apply it to short-term prediction of clock deviation. Firstly, from the perspective of enhancing the randomness of the step size, improving the search efficiency and maintaining the diversity of the population, the Lévy flight strategy, the teaching and learning optimization algorithm and the fitness-distance balance mechanism were introduced to improve the artificial bee colony algorithm, which effectively improved the global search ability of the algorithm and avoided falling into the local optimal solution. Secondly, the improved artificial bee colony algorithm is combined with BP neural network to be applied to the short-term prediction of satellite clock deviation, and the corresponding calculation steps are given. Then, the high-precision satellite clock products provided by GFZ are selected to compare and analyze the single-day and multi-day forecasts from the aspects of algorithm efficiency, stability and accuracy, so as to verify the applicability of the model. Finally, the prediction results of the optimization model are verified to be applied in PPP. Compared with the QP, BP and ABC-BP models, the average accuracy is increased by 56.55%, 25.11% and 7.07%, respectively, and the improvement effect of MEO-PHM clock is better than that of MEO-Rb clock. The improved artificial bee colony algorithm and the BP combined model have a more concentrated residual distribution, a median closer to zero, and a smaller extreme value, which has high accuracy and stability in the 6 and 12 h prediction. The accuracy of the combined model in the E, N and U directions was improved by using the forecast clock error sequence to improve the accuracy of the results in the E, N and U directions, which were improved by 42.07%, 31.07%, 41.79% and 45.42%, 50.16%, 46.18% compared with the ABC-BP model and the BP model, respectively.

Key words: fitness-distance balance, teaching-learning-based optimization, short-term prediction, precision point positioning

中图分类号:

P228

潘雄, 张龙杰, 艾青松, 金丽宏, 蔡茂. 改进ABC算法优化BP神经网络的短期钟差预报及其应用[J]. 测绘学报, 2025, 54(8): 1404-1415.

Xiong PAN, Longjie ZHANG, Qingsong AI, Lihong JIN, Mao CAI. Improved ABC algorithm for optimizing BP neural network in short-term clock bias prediction and application[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(8): 1404-1415.

图/表 14

图1

表1

图2

图3

图4

表2

图5

表3

表4

表5

表6

图6

表7

表8

参考文献 26

[1]	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.
[2]	YANG Yuanxi. Resilient PNT concept frame[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(3): 1-7.
[3]	YAO Yibin, YANG Yuanxi, SUN Heping, et al. Geodesy discipline: progress and perspective[J]. Journal of Geodesy and Geoinformation Science, 2021, 4(4): 1-10.
[4]	CHEN Jun, LI Zhilin, LI Songnian, et al. From digitalized to intelligentized surveying and mapping: fundamental issues and research agenda[J]. Journal of Geodesy and Geoinformation Science, 2022, 5(2): 148-160.
[5]	毛亚, 王潜心, 胡超, 等. BDS-3卫星钟差特性分析[J]. 武汉大学学报(信息科学版), 2020, 45(1): 53-61.
	MAO Ya, WANG Qianxin, HU Chao, et al. Analysis of the characterization for BDS-3 satellite clock error[J]. Geomatics and Information Science of Wuhan University, 2020, 45(1): 53-61.
[6]	潘雄, 赵万卓, 黄伟凯, 等. 基于优化自注意力神经网络的卫星钟差短期预报[J]. 中国惯性技术学报, 2023, 31(11): 1092-1101.
	PAN Xiong, ZHAO Wanzhuo, HUANG Weikai, et al. Short-term prediction of satellite clock bias based on improved self-attention model[J]. Journal of Chinese Inertial Technology, 2023, 31(11): 1092-1101.
[7]	XI Chao, CAI Chenglin, LI Simin, et al. Long-term clock bias prediction based on an ARIMA model[J]. Chinese Astronomy and Astrophysics, 2014, 38(3): 342-354.
[8]	YAN Xiong, LI Wentao, YANG Yufeng, et al. BDS satellite clock offset prediction based on a semiparametric adjustment model considering model errors[J]. Satellite Navigation, 2020, 1(1): 11.
[9]	潘雄, 杨玉锋, 欧吉坤, 等. BDS-2卫星钟设计年限末期阶段性能评估与分析[J]. 大地测量与地球动力学, 2020, 40(10): 991-999, 1033.
	PAN Xiong, YANG Yufeng, OU Jikun, et al. Performance evaluation and analysis of the final stage of BDS-2 satellite clock design period[J]. Journal of Geodesy and Geodynamics, 2020, 40(10): 991-999, 1033.
[10]	潘雄, 黄伟凯, 赵万卓, 等. 基于BiLSTM模型的BDS-3短期钟差预报精度研究[J]. 测绘学报, 2024, 53(1): 65-78. DOI: . doi: 10.11947/j.AGCS.2024.20230082
	PAN Xiong, HUANG Weikai, ZHAO Wanzhuo, et al. Research on short-term prediction accuracy of BDS-3 clock bias based on BiLSTM model[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(1): 65-78. DOI: . doi: 10.11947/j.AGCS.2024.20230082
[11]	李方能, 梁益丰, 许江宁, 等. 基于鲁棒双参数指数平滑法的BDS卫星钟差预报[J]. 中国惯性技术学报, 2024, 32(7): 645-653.
	LI Fangneng, LIANG Yifeng, XU Jiangning, et al. Prediction of BDS satellite clock bias based on robust two-parameter exponential smoothing method[J]. Journal of Chinese Inertial Technology, 2024, 32(7): 645-653.
[12]	李文涛, 颜雄, 夏磊, 等. BDS卫星钟差半参数平差模型异常数据探测与处理[J]. 测绘学报, 2020, 49(1): 55-64. DOI: . doi: 10.11947/j.AGCS.2020.20180384
	LI Wentao, YAN Xiong, XIA Lei, et al. Abnormal data detection and process by using BDS satellite offset semiparametric adjustment model[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(1): 55-64. DOI: . doi: 10.11947/j.AGCS.2020.20180384
[13]	HE Shaofeng, LIU Jiulong, ZHU Xiangwei, et al. Research on modeling and predicting of BDS-3 satellite clock bias using the LSTM neural network model[J]. GPS Solutions, 2023, 27(3): 108.
[14]	黄观文, 崔博斌, 张勤, 等. 附加周期和神经网络补偿的实时钟差预报模型[J]. 宇航学报, 2018, 39(1): 83-88.
	HUANG Guanwen, CUI Bobin, ZHANG Qin, et al. Real-time clock offset prediction model with periodic and neural network corrections[J]. Journal of Astronautics, 2018, 39(1): 83-88.
[15]	YANG Yuanxi, MAO Yue, SUN Bijiao. Basic performance and future developments of BeiDou global navigation satellite system[J]. Satellite Navigation, 2020, 1(1): 1.
[16]	ZHU Jiangmiao, SUN Panpan, GAO Yuan, et al. Clock differences prediction algorithm based on EMD-SVM[J]. Chinese Journal of Electronics, 2018, 27(1): 128-132.
[17]	LÜ Dong, LIU Genyou, OU Jikun, et al. Prediction of GPS satellite clock offset based on an improved particle Swarm algorithm optimized BP neural network[J]. Remote Sensing, 2022, 14(10): 2407.
[18]	WANG Xu, CHAI Hongzhou. Developing an innovative high-precision approach to predict medium-term and long-term satellite clock bias[J]. Journal of Geodesy and Geoinformation Science, 2023, 6(1): 47-58.
[19]	黄博华, 杨勃航, 李锡瑞, 等. 顾及一次差分数据结构特征的钟差预报模型[J]. 武汉大学学报(信息科学版), 2021, 46(8): 1161-1169.
	HUANG Bohua, YANG Bohang, LI Xirui, et al. Prediction of navigation satellite clock bias considering structure characteristics of single difference data[J]. Geomatics and Information Science of Wuhan University, 2021, 46(8): 1161-1169.
[20]	吕栋, 欧吉坤, 于胜文. 基于MEA-BP神经网络的卫星钟差预报[J]. 测绘学报, 2020, 49(8): 993-1003. DOI: . doi: 10.11947/j.AGCS.2020.20200002
	LÜ Dong, OU Jikun, YU Shengwen. Prediction of the satellite clock bias based on MEA-BP neural network[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(8): 993-1003. DOI: . doi: 10.11947/j.AGCS.2020.20200002
[21]	ZHU Chonghao, ZHANG Jianjing, LIU Yang, et al. Comparison of GA-BP and PSO-BP neural network models with initial BP model for rainfall-induced landslides risk assessment in regional scale: a case study in Sichuan, China[J]. Natural Hazards, 2020, 100(1): 173-204.
[22]	周凯红, 叶高威, 蒋青谷. 基于SSA-GA-BP神经网络的数显千分表非线性误差补偿[J]. 河南科技大学学报(自然科学版), 2024, 45(3): 1-8, 115.
	ZHOU Kaihong, YE Gaowei, JIANG Qinggu. Nonlinear error compensation of digital dial indicator based on SSA-GA-BP neural network[J]. Journal of Henan University of Science and Technology (Natural Science), 2024, 45(3): 1-8, 115.
[23]	MENG Caixia, WU Di, LEI Yu. Neural network satellite clock bias prediction based on the whale optimization algorithm[C]//Proceedings of 2022 Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. Cham: Springer, 2022: 1152-1160.
[24]	RAO R V, SAVSANI V J, VAKHARIA D P. Teaching-learning-based optimization: an optimization method for continuous non-linear large scale problems[J]. Information Sciences, 2012, 183(1): 1-15.
[25]	CHEN Xu, XU Bin. Teaching-learning-based artificial bee colony[C]//Proceedings of 2018 Advances in Swarm Intelligence. Cham: Springer, 2018: 166-178.
[26]	KAHRAMAN H T, BAKIR H, DUMAN S, et al. Dynamic FDB selection method and its application: modeling and optimizing of directional overcurrent relays coordination[J]. Applied Intelligence, 2022, 52(5): 4873-4908.

类型	PRN
MEO-Rb	C19、C20、C21、C22、C23、C24、C32、C33、C36、C37、C41、C42
MEO-PHM	C25、C26、C27、C28、C29、C30、C34、C35、C43、C44、C45、C46
IGSO-PHM	C38、C39、C40
GEO-PHM	C59、C60

预报时间/h	QP/ns	BP/ns	ABC-BP/ns	I-ABC-BP/ns	相对于基准策略/(%)
1	0.24	0.11	0.08	0.07	12.50
3	0.37	0.23	0.17	0.16	5.88
6	0.63	0.43	0.35	0.33	5.71
12	1.41	0.77	0.72	0.69	4.17

钟类型	QP			BP			ABC-BP			I-ABC-BP
钟类型	RMSE	Range	Mean	RMSE	Range	Mean	RMSE	Range	Mean	RMSE	Range	Mean
MEO-Rb	0.199	0.124	0.193	0.139	0.189	0.123	0.092	0.150	0.078	0.072	0.129	0.058
MEO-PHM	0.271	0.170	0.265	0.100	0.151	0.084	0.073	0.123	0.060	0.070	0.119	0.056
IGSO-PHM	0.107	0.076	0.104	0.079	0.112	0.073	0.071	0.089	0.065	0.071	0.087	0.065
GEO-PHM	0.462	0.284	0.454	0.076	0.133	0.062	0.035	0.097	0.011	0.071	0.154	0.048

钟类型	QP			BP			ABC-BP			I-ABC-BP
钟类型	RMSE	Range	Mean	RMSE	Range	Mean	RMSE	Range	Mean	RMSE	Range	Mean
MEO-Rb	0.276	0.336	0.251	0.292	0.469	0.255	0.205	0.377	0.163	0.200	0.398	0.153
MEO-PHM	0.412	0.529	0.362	0.195	0.352	0.153	0.141	0.364	0.078	0.118	0.319	0.060
IGSO-PHM	0.180	0.268	0.149	0.175	0.286	0.150	0.125	0.201	0.112	0.103	0.161	0.091
GEO-PHM	0.909	1.173	0.837	0.199	0.345	0.175	0.162	0.358	0.116	0.213	0.437	0.144

钟类型	QP			BP			ABC-BP			I-ABC-BP
钟类型	RMSE	Range	Mean	RMSE	Range	Mean	RMSE	Range	Mean	RMSE	Range	Mean
MEO-Rb	0.493	0.812	0.399	0.569	1.070	0.459	0.448	0.903	0.352	0.443	0.880	0.351
MEO-PHM	0.683	1.035	0.593	0.299	0.537	0.246	0.256	0.538	0.173	0.218	0.498	0.134
IGSO-PHM	0.276	0.453	0.238	0.268	0.440	0.239	0.202	0.391	0.147	0.151	0.296	0.118
GEO-PHM	1.628	2.257	1.456	0.555	1.203	0.440	0.538	1.226	0.389	0.557	1.351	0.396

改进ABC算法优化BP神经网络的短期钟差预报及其应用

Improved ABC algorithm for optimizing BP neural network in short-term clock bias prediction and application

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 14

参考文献 26

相关文章 15

编辑推荐

Metrics

本文评价

预报时间/h	QP/ns	BP/ns	ABC-BP/ns	I-ABC-BP/ns
1	3.64	0.24	0.21	0.20
3	3.70	0.56	0.44	0.32
6	3.77	0.72	0.68	0.47
12	3.93	1.06	0.84	0.71

测站	纬度/(°)	经度/(°)	高程/m	E方向			N方向			U方向
测站	纬度/(°)	经度/(°)	高程/m	BP/cm	ABC-BP/cm	I-ABC-BP/cm	BP/cm	ABC-BP/cm	I-ABC-BP/cm	BP/cm	ABC-BP/cm	I-ABC-BP/cm
UFPR	-25.448	-49.231	925.8	13.36	10.23	9.33	5.27	4.81	3.04	10.89	7.93	6.54
ABPO	-19.018	47.229	1 552.9	6.77	4.87	4.36	6.21	2.75	3.27	15.33	13.10	8.49
ZAMB	-15.426	28.311	1 324.9	7.96	7.71	1.77	4.20	4.90	1.32	9.43	13.65	6.87
POL2	42.680	74.694	1 714.2	1.49	6.71	1.05	4.64	5.21	4.14	9.31	6.72	4.23
LICC	51.500	-0.175	88.7	5.85	6.75	5.21	3.25	2.22	2.59	9.73	13.16	5.73
SCOR	70.485	-21.950	128.5	4.36	11.07	5.72	7.23	8.99	2.41	12.06	17.54	4.09

[1]	施闯, 邓辰龙, 范磊, 郑福, 张涛, 田原, 景贵飞, 马杰. 单北斗接收机定位性能分析与评估[J]. 测绘学报, 2025, 54(1): 1-13.
[2]	刘洋, 杨光, 程晓晖, 张啸. 基于城市CORS的快速单点定位增强服务与应用[J]. 测绘学报, 2024, 53(9): 1706-1714.
[3]	林英宗, 罗小敏, 杜俊锋. 高纬度地区PPP接收机跟踪噪声随机模型拟合改进[J]. 测绘学报, 2024, 53(4): 666-676.
[4]	刘天骏, 陈渠森, 姜卫平, 陈华, 夏凤雨, 范曹明. 地影期间卫星姿态四元数产品对北斗精密单点定位的影响分析[J]. 测绘学报, 2023, 52(4): 550-558.
[5]	袁运斌, 刘帅, 潭冰峰. 基于钟差解耦的GNSS精密单点定位模糊度固定模型及效果分析[J]. 测绘学报, 2022, 51(8): 1669-1679.
[6]	刘根友, 高铭, 尹翔飞, 肖恭伟, 吕栋, 王生亮, 王润. 基于GNSS精密单点定位的高精度云平台授时[J]. 测绘学报, 2022, 51(8): 1736-1743.
[7]	周锋, 杨宇泽, 王磊, 徐天河. GNSS载波相位整数等变估计及其PPP性能提升算法[J]. 测绘学报, 2022, 51(8): 1779-1786.
[8]	施闯, 辜声峰, 楼益栋, 郑福, 宋伟, 张东, 毛飞宇. 广域实时精密定位与时间服务系统[J]. 测绘学报, 2022, 51(7): 1206-1214.
[9]	金双根, 汪奇生, 史奇奇. 单频到五频多系统GNSS精密单点定位参数估计与应用[J]. 测绘学报, 2022, 51(7): 1239-1248.
[10]	杨凯淳, 吕志平, 李林阳, 邝英才, 许炜, 郑茜. 附加历元间约束的滑动窗单频实时精密单点定位算法[J]. 测绘学报, 2022, 51(5): 648-657.
[11]	蔡洪亮, 孟轶男, 耿长江, 高为广, 张天桥, 李罡, 邵搏, 辛洁, 卢红洋, 毛悦, 袁海波, 刘成, 胡小工, 楼益栋. 北斗三号全球导航卫星系统服务性能评估:定位导航授时、星基增强、精密单点定位、短报文通信与国际搜救[J]. 测绘学报, 2021, 50(4): 427-435.
[12]	房亚男, 朱俊, 李杰, 王冲, 王家松, 张少愚. 北斗混合星座分层约束下的精密定轨方法[J]. 测绘学报, 2021, 50(4): 466-474.
[13]	张兵兵, 牛继强, 王正涛, 徐丰, 田坤俊. Swarm系列卫星非差运动学厘米级精密定轨[J]. 测绘学报, 2021, 50(1): 27-36.
[14]	周锋, 徐天河. GPS/BDS/Galileo三频精密单点定位模型及性能分析[J]. 测绘学报, 2021, 50(1): 61-70.
[15]	张小红, 胡家欢, 任晓东. PPP/PPP-RTK新进展与北斗/GNSS PPP定位性能比较[J]. 测绘学报, 2020, 49(9): 1084-1100.

钟类型	QP			BP			ABC-BP			I-ABC-BP
钟类型	RMSE	Range	Mean	RMSE	Range	Mean	RMSE	Range	Mean	RMSE	Range	Mean
MEO-Rb	1.166	1.847	0.808	1.074	1.941	0.912	1.051	1.846	0.861	0.998	1.763	0.825
MEO-PHM	1.414	2.385	1.127	0.473	0.858	0.398	0.416	0.909	0.302	0.381	0.820	0.279
IGSO-PHM	0.594	1.117	0.459	0.419	1.039	0.279	0.331	0.761	0.246	0.177	0.596	0.212
GEO-PHM	3.511	6.693	2.951	1.718	3.492	1.322	1.336	2.362	1.063	1.519	2.766	1.188