基于模型数据混合驱动的干扰磁场补偿方法

张德慧; 张金生; 李婷; 马啸宇; 廖守亿; 倪静; 魏豪

doi:10.13700/j.bh.1001-5965.2025.0141

基于模型数据混合驱动的干扰磁场补偿方法

doi: 10.13700/j.bh.1001-5965.2025.0141

1.
火箭军工程大学导弹工程学院，西安 710025
2.
飞行器数字敏捷设计全国重点实验室，成都 610000

基金项目:

国家自然科学基金(62473377)；陕西省自然科学基础研究计划(2024JC-YBQN-0657)；飞行器数字敏捷设计全国重点实验室基金(KFJJ-2024-I-03-05)

详细信息

通讯作者:
E-mail：772108312@qq.com

中图分类号: V249.32；TP183；P318
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出版历程
- 收稿日期: 2025-03-20
- 录用日期: 2025-05-27
- 网络出版日期: 2025-07-01
- 整期出版日期: 2026-09-01

An interference magnetic field compensation method based on a model-data hybrid drive

1.
College of Missile Engineering，Rocket Force University of Engineering，Xi’an 710025，China
2.
The National Key Laboratory of Digital and Agile Aircraft Design，Chengdu 610000，China

Funds:

National Natural Science Foundation of China (62473377); Natural Science Basic Research Program of Shaanxi (2024JC-YBQN-0657); The National Key Laboratory of Digital and Agile Aircraft Design (KFJJ-2024-I-03-05)

More Information

Corresponding author: E-mail：772108312@qq.com

摘要

摘要:
载体自身干扰磁场的精确补偿是提升地磁导航精度的关键挑战。针对传统补偿方法受限于线性假设和难以适应复杂场景的泛化需求等问题，提出2种基于模型数据混合驱动的磁干扰协同补偿方案。在预处理阶段，采用主成分分析方法对数据进行降维处理，并利用物理模型所求补偿参数对神经网络进行初始化处理；方案一通过分析传统补偿模型的缺陷，利用神经网络求解补偿参数，打破传统模型求解范式并预防可能存在的复共线问题，同时，在干扰磁场中引入随机因子项模拟非线性较强的随机干扰磁场；方案二通过构造损失函数联动数据驱动与模型驱动，将磁场特征的高效提取与干扰场的物理约束深度耦合。实验结果表明：所提方法较纯模型和纯数据补偿方法具有补偿精度高、泛化能力强等优点，在不同高度、不同地域进行泛化能力测试的最高补偿精度分别提高了69.64%和69.39%，验证了所提方法的有效性。
- 地磁导航 /
- 干扰磁场 /
- 航磁补偿 /
- 物理模型约束 /
- BP神经网络 /
- 混合驱动
Abstract:
The precise compensation of the carrier’s self-interference magnetic field is a key challenge in improving the accuracy of geomagnetic navigation. Two model-data hybrid-driven magnetic interference collaborative compensation strategies are presented in response to the drawbacks of conventional compensation techniques, including the linear assumption and the challenge of responding to complex settings. In the preprocessing stage, principal component analysis is used to reduce the dimensionality of the data, and the compensation parameters obtained from the physical model are used to initialize the neural network. In scheme one, the shortcomings of the conventional compensation model are analyzed, the compensation parameters are solved using a neural network, the traditional model-solving paradigm is broken and potential multicollinearity issues are avoided, and a random factor term is introduced in the interference magnetic field to simulate the random interference magnetic field with strong nonlinearity. Scheme two constructs a loss function to link data-driven and model-driven, deeply coupling the efficient extraction of magnetic field features with the physical constraints of the interference field. Experimental results show that the proposed methods have the advantages of high compensation accuracy and strong generalization ability compared with pure model and pure data compensation methods. The highest compensation accuracy in generalization ability tests at different heights and different regions has increased by 69.64% and 69.39%, respectively, verifying the effectiveness of the proposed methods.
- geomagnetic navigation /
- interference magnetic field /
- aeromagnetic compensation /
- physical model constraint /
- BP neural network /
- hybrid drive

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图 1 载体坐标系

Figure 1. Carrier coordinate system

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图 2 BP神经网络

Figure 2. BP neural network

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图 3 方案一训练过程

Figure 3. Training process of scheme one

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图 4 方案二训练过程

Figure 4. Training process of scheme two

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图 5 神经网络的训练过程

Figure 5. The training process of neural networks

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图 6 不同激活函数的对比曲线

Figure 6. Comparative curves of different activation functions

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图 7 不同方案的补偿效果

Figure 7. The compensatory effects of different schemes

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图 8 不同航线泛化能力测试结果

Figure 8. Test results of generalization ability for different routes

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表 1 2种方案的共同网络参数设置

Table 1. Common network parameter settings for the two schemes

模型输入	学习率	批量大小	迭代次数	L1正则化系数	L2正则化系数	激活函数	优化器
45个特征	0.000 1	128	300	0.000 01	0.000 001	Swish（·）函数	Adam

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表 2 不同航线数据解读

Table 2. Interpretation of data for different routes

航线编号	描述
1003.02	安大略省东部400 m高度自由飞行
1003.04	安大略省东部800 m高度自由飞行
1003.08	伦弗鲁省400 m高度自由飞行

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表 3 神经网络的输入、标签信息描述

Table 3. Description of input and label information for neural networks

特征量	描述
mag_4_iuc	4号标量磁力计未经补偿的磁异常数据
flux_b_x	磁通门B的X轴方向的磁场大小
flux_b_y	磁通门B的Y轴方向的磁场大小
flux_b_z	磁通门B的Z轴方向的磁场大小
cur_strb	频闪灯的电流传感器
cur_ac_hi	空调风扇高速的电流传感器
cur_heat	惯性导航系统加热器的电流传感器
vol_bat_1	电池1的电压传感器
vol_block	模块的电压传感器
mag_1_ic	1号标量磁力计经补偿后的磁异常数据

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表 4 不同方案的补偿能力对比

Table 4. Comparison of compensation capabilities of different schemes

方案	RMSE/nT	R²
岭回归	33.944	0.985 83
神经网络	9.301	0.998 82
方案一	6.871	0.999 36
方案二	7.313	0.999 27

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表 5 不同方案的泛化能力对比

Table 5. Comparison of generalization capabilities of different schemes

方案	RMSE/nT			R²
方案	1003.02航线	1003.04航线	1003.08航线	1003.02航线	1003.04航线	1003.08航线
岭回归	86.490	73.191	133.078	0.834 9	0.811 4	−0.836 4
神经网络未初始化	14.561	31.465	31.153	0.995 7	0.963 4	0.895 3
神经网络初始化	10.849	13.302	16.574	0.997 6	0.993 5	0.970 4
方案一	9.796	9.552	9.536	0.998 0	0.996 6	0.990 2
方案二	9.746	9.761	10.304	0.998 3	0.996 5	0.988 5

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参考文献(22)

[1]	何康辉, 董朝阳, 王青. 一种考虑GPS信号中断的导航滤波算法[J]. 北京航空航天大学学报, 2019, 45(9): 1874-1881. He K H, Dong C Y, Wang Q. A navigation filtering algorithm considering GPS signal interruption[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(9): 1874-1881(in Chinese).
[2]	陈飞强, 孙一凡, 唐小妹, 等. GNSS信号功率增强对调零抗干扰接收机的性能影响[J]. 国防科技大学学报, 2023, 45(5): 72-77. Chen F Q, Sun Y F, Tang X M, et al. Effect of signal power enhancement on the performance of GNSS null-steering anti-jamming receiver[J]. Journal of National University of Defense Technology, 2023, 45(5): 72-77(in Chinese).
[3]	吴德伟, 苗强, 何思璇, 等. 量子传感的导航应用研究现状与展望[J]. 空军工程大学学报(自然科学版), 2021, 22(6): 67-76. Wu D W, Miao Q, He S X, et al. A study of existing status and prospects for quantum sensor in navigation[J]. Journal of Air Force Engineering University (Natural Science Edition), 2021, 22(6): 67-76(in Chinese).
[4]	朱祥维, 沈丹, 肖凯, 等. 类脑导航的机理、算法、实现与展望[J]. 航空学报, 2023, 44(19): 1-33. Zhu X W, Shen D, Xiao K, et al. Mechanisms, algorithms, implementation and perspectives of brain-inspired navigation[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 1-33(in Chinese).
[5]	李婷, 王仕成, 张金生. 磁场测量误差补偿技术综述[J]. 电光与控制, 2018, 25(6): 66-71. Li T, Wang S C, Zhang J S. A review on geomagnetic measurement error compensation technologies[J]. Electronics Optics & Control, 2018, 25(6): 66-71(in Chinese).
[6]	缪林良, 米洒洒, 王玮琳, 等. 航磁矢量测量的误差分析和补偿算法研究[J]. 电子测量与仪器学报, 2021, 35(12): 15-23. Miao L L, Mi S S, Wang W L, et al. Error analysis and compensation algorithm research of aeromagnetic vector measurement[J]. Journal of Electronic Measurement and Instrumentation, 2021, 35(12): 15-23(in Chinese).
[7]	周斌, 王劲东. 卫星磁部件分布对梯度法消除剩磁的影响分析[J]. 中国空间科学技术, 2013, 33(5): 29-34. Zhou B, Wang J D. Influence of magnetic component distribution of satellite on eliminating remanant magnetic field by gradient method[J]. Chinese Space Science and Technology, 2013, 33(5): 29-34(in Chinese).
[8]	吕禺萱, 雷华明. 磁异常探测中载体干扰磁场RLS补偿方法[J]. 电子测量与仪器学报, 2022, 36(3): 96-104. Lyu Y X, Lei H M. RLS method for carrier interference compensation in magnetic anomaly detection[J]. Journal of Electronic Measurement and Instrumentation, 2022, 36(3): 96-104(in Chinese).
[9]	Ye L W, Yu Z T, Zhang Y X, et al. An aeromagnetic compensation strategy for large UAVs[J]. Sensors, 2024, 24(12): 3775.
[10]	Ma X Y, Zhang J S, Liao S Y, et al. Aeromagnetic compensation method based on recursive least square and elastic weight consolidation[J]. Applied Geophysics, 2025, 22(2): 279-290.
[11]	张宇, 陈正想, 覃涛. 基于BP神经网络的航磁补偿方法研究[J]. 数字海洋与水下攻防, 2023, 6(6): 734-742. Zhang Y, Chen Z X, Qin T. Research on aeromagnetic compensation method based on BP neural network[J]. Digital Ocean & Underwater Warfare, 2023, 6(6): 734-742(in Chinese).
[12]	Wang Y Z, Han Q, Zhan D C, et al. A data-driven OBE magnetic interference compensation method[J]. Sensors, 2022, 22(20): 7732.
[13]	王劲楠, 张晓明, 张鸽, 等. 基于GAN-LSTM改进T-L磁补偿方法[J]. 电子测量技术, 2025, 48(5): 50-56. Wang J N, Zhang X M, Zhang G, et al. Improved T-L magnetic compensation method based on GAN-LSTM[J]. Electronic Measurement Technology, 2025, 48(5): 50-56(in Chinese).
[14]	Xu Y J, Liu Z Y, Zhang Q, et al. Interference model guided neural network for aeromagnetic compensation[J]. IEEE Sensors Journal, 2024, 24(8): 12266-12275.
[15]	王晨阳. PCA和GA-BP结合的地磁导航适配区选择方法[J]. 电光与控制, 2018, 25(6): 110-114. Wang C Y. Geomagnetic navigation matching area selection based on PCA and GA-BP neural network[J]. Electronics Optics & Control, 2018, 25(6): 110-114(in Chinese).
[16]	林沂, 孙晶京, 闫旭. 地磁导航定位技术原理与方法综述[J]. 全球定位系统, 2023, 48(6): 32-41. Lin Y, Sun J J, Yan X. A review of the principles and methods of geomagnetic navigation and positioning technology[J]. GNSS World of China, 2023, 48(6): 32-41(in Chinese).
[17]	李季. 地磁测量中载体干扰磁场特性及补偿方法研究[D]. 长沙: 国防科学技术大学, 2013: 99-100. Li J. Study on the characteristics and compensation method of vehicle interferential magnetic field in geomagnetic measurement[D]. Changsha: National University of Defense Technology, 2013: 99-100(in Chinese).
[18]	Tolles W E, Lawson J D. Magnetic compensation of mad equipped aircraft, 201-1[R]. Mineola: Airborne Instruments Laboratory, 1950: 201-211.
[19]	Leliak P. Identification and evaluation of magnetic-field sources of magnetic airborne detector equipped aircraft[J]. IRE Transactions on Aerospace and Navigational Electronics, 1961, ANE-8(3): 95-105.
[20]	Su Z N, Jiao J, Zhou S, et al. Aeromagnetic compensation method based on ridge regressional gorithm[J]. Global Geology, 2022, 25(1): 41-48.
[21]	戚德虎, 康继昌. BP神经网络的设计[J]. 计算机工程与设计, 1998, 19(2): 48-50. Qi D H, Kang J C. On design of the BP neural network[J]. Computer Engineering and Design, 1998, 19(2): 48-50(in Chinese).
[22]	徐文耀, 白春华, 康国发. 地壳磁异常的全球模型[J]. 地球物理学进展, 2008, 23(3): 641-651. Xu W Y, Bai C H, Kang G F. Global models of earth’s crust magnetic anomalies[J]. Progress in Geophysics, 2008, 23(3): 641-651(in Chinese).