弹载磁导航中弹体磁化场建模研究

doi:10.12305/j.issn.1001-506X.2025.04.28

摘要/Abstract

摘要：

为实现地磁导航在弹体制导中的高精度应用, 提出一种弹体磁化场解算模型。采用四面体单元对弹体模型进行剖分离散, 通过求和每个离散单元对测量点的磁感应强度, 进而计算弹体周围任何位置的磁感应强度。球壳解析模型计算结果和弹体模型的ANSYS (analysis systems)仿真实验表明, 弹体磁化场解算模型相对误差分别为0.42%和0.55%。弹体缩比模型野外试验结果表明, 测量点的测量值和计算值变化趋势的相对误差为1.09%。通过3种方式验证了弹体磁化场解算模型能够高精度测量弹体周围任何位置的磁感应强度, 表明解算模型的有效性和可行性, 具有较高的工程实际价值。

关键词: 地磁导航, 磁化场模型, ANSYS仿真, 球壳数值解析, 弹体缩比模型实验

Abstract:

To achieve high-precision application of geomagnetic navigation in projectile guidance, a magnetic field calculation model for projectile is proposed. The tetrahedral element is used to discretize the projectile model, and the magnetic induction intensity of each discrete element at the measurement point is calculated by summing up the magnetic induction intensity around the projectile at any position. The calculation results of the spherical shell analytical model and the analysis systems (ANSYS) simulation experiments of the projectile model show that the relative errors of the magnetization field calculation model of the projectile are 0.42% and 0.55%, respectively. The field experiment results of the projectile scaling model show that the relative error between trends in the measured values and the calculated values of the measurement points is 1.09%. The magnetic field calculation model of the projectile is validated in three ways to accurately measure the magnetic induction intensity at any position around the projectile, indicating the effectiveness and feasibility of the calculation model, which has high engineering practical value.

Key words: geomagnetic navigation, magnetization field model, ANSYS simulation, numerical analysis of spherical shell, experiment on projectile scaling model

中图分类号:

TH76

张平安, 高敏, 汪伟, 王毅, 李超旺. 弹载磁导航中弹体磁化场建模研究[J]. 系统工程与电子技术, 2025, 47(4): 1319-1326.

Ping'an ZHANG, Min GAO, Wei WANG, Yi WANG, Chaowang LI. Research on modeling of the magnetization field of projectile in magnetic navigation[J]. Systems Engineering and Electronics, 2025, 47(4): 1319-1326.

图/表 7

图1

表1

图2

图3

图4

图5

图6

参考文献 32

1	CUI F , GAO D , ZHENG J H . Magnetometer-based orbit determination via fast reconstruction of three-dimensional decoupled geomagnetic field model[J]. Journal of Spacecraft and Rockets, 2021, 58 (5): 1374- 1386. doi: 10.2514/1.A34939
2	XU M M , BU X Z , YANG H Q . Dual-band infrared and geomagnetic fusion attitude estimation algorithm based on IMMEKF[J]. IEEE Trans.on Industrial Electronics, 2021, 68 (11): 11286- 11295. doi: 10.1109/TIE.2020.3031532
3	LIU J G , LI X G , YAN S G , et al. A novel linear calibration model for three-axis fluxgate magnetometer[J]. IEEE Sensors Journal, 2021, 21 (21): 23917- 23925. doi: 10.1109/JSEN.2021.3103992
4	ZHANG J Y , ZHANG T , SHIN H S , et al. Geomagnetic gradient-assisted evolutionary algorithm for long-range underwater navigation[J]. IEEE Trans.on Instrumentation and Measurement, 2021, 70, 2503212.
5	CHEN Z , ZHANG Q , PAN M C , et al. A new geomagnetic matching navigation method based on multidimensional vector elements of Earth's magnetic field[J]. IEEE Geoscience and Remote Sensing Letters, 2018, 15 (8): 1289- 1293. doi: 10.1109/LGRS.2018.2836465
6	CHEN Z , LIU Z Y , ZHANG Q , et al. A new geomagnetic vector navigation method based on a two-stage neural network[J]. Electronics, 2023, 12 (9): 1975. doi: 10.3390/electronics12091975
7	SHI H K , TANG R Q , WANG Q M , et al. Application of bioinspired geomagnetic sensor measurements and geomagnetic map modeling based on neural networks in simulated navigation[J]. Measurement Science and Technology, 2024, 35 (4): 1361- 6501.
8	CHEN Z , LIU K J , ZHANG Q , et al. Geomagnetic vector pattern recognition navigation method based on probabilistic neural network[J]. IEEE Geoscience and Remote Sensing Letters, 2023, 61, 5909608.
9	ROUX A , CHANGEY S , WEBER J , et al. LSTM-based projectile trajectory estimation in a GNSS-denied environment[J]. Sensors, 2023, 23 (6): 3025. doi: 10.3390/s23063025
10	ROUX A, CHANGEY S, LAUFFENBURGER J P, et al. Mortar trajectory estimation by a deep error-state Kalman filter in a GNSS-denied environment[C]//Proc. of the IEEE/ION Position Location and Navigation Symposium, 2023.
11	COMBETTES C, CHANGEY S, ADAM R, et al. Attitude and velocity estimation of a projectile using low cost magnetometers and accelerometers[C]//Proc. of the IEEE/ION Position Location and Navigation Symposium, 2018.
12	FAIRFAX L D , FRESCONI F E . Position estimation for projectiles using low-cost sensors and flight dynamics[J]. Journal of Aerospace Engineering, 2014, 27 (3): 611- 620. doi: 10.1061/(ASCE)AS.1943-5525.0000284
13	WU J . Real-time magnetometer disturbance estimation via online nonlinear programming[J]. IEEE Sensors Journal, 2019, 19 (12): 4405- 4411. doi: 10.1109/JSEN.2019.2901925
14	CHEN W R , ZHANG H F , SANG S T , et al. Magnetic field interference correction of high-precision geomagnetic directional technology[J]. Measurement, 2021, 184, 109940. doi: 10.1016/j.measurement.2021.109940
15	WANG Q , ZHENG C , WU P L , et al. Geomagnetic/inertial navigation integrated matching navigation method[J]. Heliyon, 2022, 8 (11): e11249. doi: 10.1016/j.heliyon.2022.e11249
16	CHEN K , LIANG W C , LIU M X , et al. Comparison of geomagnetic aided navigation algorithms for hypersonic vehicles[J]. Journal of Zhejiang University-Science A, 2020, 21 (8): 673- 683. doi: 10.1631/jzus.A1900648
17	XU N H , WANG L H , WU T , et al. An innovative PSO-ICCP matching algorithm for geomagnetic navigation[J]. Measurement, 2022, 193, 110958. doi: 10.1016/j.measurement.2022.110958
18	高东, 朱明慧, 韩鹏. 一种地磁/惯性深度融合导航方法[J]. 中国惯性技术学报, 2022, 30 (4): 437- 444.
	GAO D , ZHU M H , HAN P . A geomagnetic/inertial deep fusion navigation method[J]. Chinese Journal of Inertial Technology, 2022, 30 (4): 437- 444.
19	ZHAI H Q , WANG L H , LIU Q Y , et al. Geomagnetic signal de-noising method based on improved empirical mode decomposition and morphological filtering[J]. Proceedings of The Institution of Mechanical Engineers Part G-Journal of Aerospace Engineering, 2021, 235 (5): 578- 588. doi: 10.1177/0954410020951022
20	ZHANG P A , GAO M , WANG W , et al. Application of IMMF-IHHT algorithm to suppressing random interference of geomagnetic sensors[J]. EURASIP Journal on Advances in Signal Processing, 2023, 2023, 23. doi: 10.1186/s13634-023-00985-5
21	WANG W L , LI K Y , YANG Z H , et al. An adaptive alternating magnetic interference suppression (AAIS) algorithm for geomagnetic vector measurement[J]. Sensors, 2022, 22 (10): 3642. doi: 10.3390/s22103642
22	刁云云, 高金耀, 吴国超, 等. 基于形态学-HHT算法的船载地磁三分量信号分析与预处理[J]. 海洋学研究, 2021, 39 (3): 44- 52.
	DIAO Y Y , GAO J Y , WU G C , et al. Analysis and preprocessing of ship borne geomagnetic three component signals based on morphological HHT algorithm[J]. Journal of Marine Sciences, 2021, 39 (3): 44- 52.
23	ZHOU Y K , HUANG G , ZHANG X Y . Geomagnetic sensor noise reduction for improving calibration compensation accuracy based on improved HHT algorithm[J]. IEEE Sensors Journal, 2019, 19 (24): 12096- 12104.
24	QIAO N , WANG L H , LIU Q Y , et al. Multi-scale eigenvalues empirical mode decomposition for geomagnetic signal filtering[J]. Measurement, 2019, 146, 885- 891.
25	ZHOU Y K , ZHANG X Y , XIAO W . Calibration and compensation method of three-axis geomagnetic sensor based on pre-processing total least square iteration[J]. Journal of Instrumentation, 2018, 13, 04006.
26	PANG H F , WAN C B , MOU S F , et al. Integrated calibration of strap-down geomagnetic vector measurement system[J]. IEEE Sensors Journal, 2022, 22 (11): 10476- 10484.
27	ZHANG Q , PANG H F , WAN C B . Magnetic interference compensation method for geomagnetic field vector measurement[J]. Measurement, 2016, 91, 628- 633.
28	LIU Z Y , ZHANG Q , PAN M C , et al. Compensation of geomagnetic vector measurement system with differential magnetic field method[J]. IEEE Sensors Journal, 2016, 16 (24): 9006- 9013.
29	ZHANG Q , LIU Z Y , XU Y J , et al. A geomagnetic vector evolutionary compensation method using Woodbury equation[J]. Measurement Science and Technology, 2024, 35 (2) doi: 10.1088/1361-6501/ad0ca8
30	JI C J , SONG C Y , LI S , et al. An online combined compensation method of geomagnetic measurement error[J]. IEEE Sensors Journal, 2022, 22 (14): 14026- 14037.
31	LIU Z Y , YAN Z X , ZHANG Q , et al. Improved component compensation of magnetic interferential field for geomagnetic vector measurement system using 3-D Helmholtz coil[J]. IEEE Sensors Journal, 2022, 22 (23): 23137- 23144.
32	何保委, 周国华, 刘胜道, 等. 标量磁位积分方程法计算舰艇三维静磁场[J]. 兵工学报, 2024, 45 (3): 948- 956.
	HE B W , ZHOU G H , LIU S D , et al. Ship's 3D magnetostatic field computation utilizing integral equation method of scalar magnetic potential[J]. Acta Armamentarii, 2024, 45 (3): 948- 956.

编号	单元数量	计算时间/s	内存消耗/MB	相对误差/%
1	696	243.8	24	1.2
2	867	366.9	35	0.89
3	1 255	625.4	48	0.63
4	1 590	947.7	72	0.54
5	1 921	1 368.9	103	0.42
6	2 451	1 951.2	187	0.37

[1]	吕志峰, 张金生, 王仕成, 李婷. 基于RBF神经网络的磁屏蔽性能计算方法[J]. 系统工程与电子技术, 2018, 40(8): 1832-1838.
[2]	刘明雍, 刘坤, 李红, 彭星光. 基于探索与开发权衡的地磁仿生导航搜索方法[J]. 系统工程与电子技术, 2016, 38(7): 1644-1648.
[3]	李红, 刘明雍, 刘坤. 基于信息熵的AUV地磁仿生导航方法[J]. 系统工程与电子技术, 2016, 38(6): 1390-1394.