Vector Magnetometer Calibration in Unknown Environment of Strong Noise

doi:10.3969/j.issn.1009-086x.2025.03.011

Abstract

Abstract:

According to the TAM （Three Axis Magnetometer） calibration problem in the unknown noisy environment， a novel unknown measurement noise compensation method is proposed to adaptively calibrate vector magnetic sensors. On the basis of a more complete modeling of the calibration， several shortcomings of the traditional calibration method are pointed out when the error parameter is large. The measurement data matrix and the noise matrix in the unbiased cost function are separated using the convolution formula.The unknown noise amplitude in the noise matrix is obtained by constructing a first-order Schur complement approximation after blocking. Through this method， the unknown noise in the measurement data is completely removed.Both simulation and physical experiments demonstrate that the accuracy of the calibrated vector magnetic sensor is significantly improved after noise compensation compared to before compensation， with the advantage becoming more pronounced as noise increases.

Key words: unknown environment, noise compensation, Shur repair, vector magnetic sensor, off line calibration, convolution

摘要：

针对实验室校正的矢量磁传感器难以适应实际工作环境的问题，提出一种新型未知测量噪声补偿方法以自适应地校正矢量磁传感器。在较完整建立校正模型的基础上，指出传统校正方法在误差参数较大时的几种缺陷；利用卷积公式分离无偏代价函数中的测量数据矩阵与噪声矩阵；通过建立分块后的一阶舒拉补近似求得噪声矩阵中的未知噪声幅值。通过上述方法，完全地将测量数据中的未知噪声去除掉。仿真与实物实验均表明，校正的矢量磁传感器在噪声补偿后较补偿前，精度有了很大提高，并随着噪声的加大，优势更明显。

关键词: 未知环境, 噪声补偿, 舒拉补, 矢量磁传感器, 线下校正, 卷积

CLC Number:

Jingli HUANG, Yuliang ZHAO, Weijie FAN, Qiang XU. Vector Magnetometer Calibration in Unknown Environment of Strong Noise[J]. Modern Defense Technology, 2025, 53(3): 95-102.

黄婧丽, 赵育良, 樊伟杰, 许强. 大噪声未知环境下的矢量磁传感器校正[J]. 现代防御技术, 2025, 53(3): 95-102.

Figures/Tables 11

Table 1 Error parameters

误差源	零偏	尺度因素误差	非正交误差	硬磁干扰
$x$ 轴	1.5	0.2	1°（ $ρ x$ ）	-1.2
$y$ 轴	0.4	-0.2	0.5°（ $ρ y$ ）	0.2
$z$ 轴	2.7	0.3	1°（ $ρ z$ ）	-0.8

Table 1 Error parameters

误差源	零偏	尺度因素误差	非正交误差	硬磁干扰
$x$ 轴	1.5	0.2	1°（ $ρ x$ ）	-1.2
$y$ 轴	0.4	-0.2	0.5°（ $ρ y$ ）	0.2
$z$ 轴	2.7	0.3	1°（ $ρ z$ ）	-0.8

Table 2 Soft iron parameters

误差	$α i x$	$α i y$	$α i z$
$x$	0.58	-0.73	0.36
$y$	1.32	0.46	-0.12
$z$	-0.26	0.44	0.53

Table 2 Soft iron parameters

误差	$α i x$	$α i y$	$α i z$
$x$	0.58	-0.73	0.36
$y$	1.32	0.46	-0.12
$z$	-0.26	0.44	0.53

Fig. 1 Measurements of TAM

Fig. 2 Output of uncalibrated TAM and the fitted ellipsoid

Fig. 3 Magnetic intensity in different cases

Fig. 4 Errors of TAM measurements in different cases

Fig. 5 Magnetic field measurement accuracy in different noise variances magnitude

Table 3 Magnetometer technical index

技术条目	技术指标
轴数	3
量程/μT	$±$ 100
带宽	DC~1 kHz（0.5 dB）
正交度/（°）	$≤ ± 0.5$
线性度	$≤ 0.02 % F s$
时域噪声/nT	$≤ 1$
功耗/W	$≤ 0.4$
工作温度/（℃）	-20℃~+50

Table 3 Magnetometer technical index

技术条目	技术指标
轴数	3
量程/μT	$±$ 100
带宽	DC~1 kHz（0.5 dB）
正交度/（°）	$≤ ± 0.5$
线性度	$≤ 0.02 % F s$
时域噪声/nT	$≤ 1$
功耗/W	$≤ 0.4$
工作温度/（℃）	-20℃~+50

Fig. 6 Calibration experimental system of TAM

Fig. 7 Measurements of magnetic field

Fig. 8 Magnetic intensity

References 18

1	YUE Liangguang， CHENG Defu， WANG Yi， et al. Fast Error Calibration for Three-Axis SQUID Magnetometers Based on Full-Space Rotational and Frequency-controllable Magnetic Field［J］. IEEE Sensors Journal， 2023， 23（7）： 6706-6716.
2	WU Peilin， ZHANG Qunying， CHEN Luzhao， et al. Analysis on Systematic Errors of Aeromagnetic Compensation Caused by Measurement Uncertainties of Three-Axis Magnetometers［J］. IEEE Sensors Journal， 2019， 19（1）： 361-369.
3	LI Jianjun， DENG Yicheng， WANG Xuefeng， et al. Miniature Wide-Range Three-Axis Vector Atomic Magnetometer［J］. IEEE Sensors Journal， 2021， 21（21）： 23943-23948.
4	LI Siran， LU Jixi， MA Danyue， et al. In Situ Measurement of Nonorthogonal Angles of a Three-Axis Vector Optically Pumped Magnetometer［J］. IEEE Transactions on Instrumentation and Measurement， 2022， 71： 1-9.
5	YANG Zhicheng， YAN Shenggang， LI Bin. Hybrid Calibration Method for Three-Axis Gradiometer［J］. IEEE Magnetics Letters， 2017， 8： 1-5.
6	ZHAO Binbin， GUO Hao， ZHAO Rui， et al. High-Sensitivity Three-Axis Vector Magnetometry Using Electron Spin Ensembles in Single-Crystal Diamond［J］. IEEE Magnetics Letters， 2019， 10： 1-4.
7	GHEORGHE M V， BODEA M C. Calibration Optimization Study for Tilt-Compensated Compasses［J］. IEEE Transactions on Instrumentation and Measurement， 2018， 67（6）： 1486-1494.
8	PAPAFOTIS K， SOTIRIADIS P P. MAG.I.C.AL.-A Unified Methodology for Magnetic and Inertial Sensors Calibration and Alignment［J］. IEEE Sensors Journal， 2019， 19（18）： 8241-8251.
9	BATISTA D S， GRANZIERA F， TOSIN M C， et al. Attitude-Independent Magnetometer Calibration Using Nonlinear Least Squares［J］. IEEE Sensors Journal， 2023， 23（13）： 14002-14016.
10	LIU Zhongyan， PANG Hongfeng， PAN Mengchun， et al. Calibration and Compensation of Geomagnetic Vector Measurement System and Improvement of Magnetic Anomaly Detection［J］. IEEE Geoscience and Remote Sensing Letters， 2016， 13（3）： 447-451.
11	REIS J， BATISTA P， OLIVEIRA P， et al. Calibration of High-Grade Inertial Measurement Units Using a Rate Table［J］. IEEE Sensors Letters， 2019， 3（4）： 1-4.
12	HONG J H， KANG D， KIM I J. Robust Autocalibration of Triaxial Magnetometers［J］. IEEE Transactions on Instrumentation and Measurement， 2021， 70： 1-12.
13	LI Qingzhu， LI Zhining， ZHANG Yingtang， et al. Integrated Compensation and Rotation Alignment for Three-Axis Magnetic Sensors Array［J］. IEEE Transactions on Magnetics， 2018， 54（10）： 1-11.
14	YAN Youyu， YAN Shenggang， LIU Jianguo， et al. A Compensation Method in Magnetic Distortion Through Regularized Inverse Problems［J］. IEEE Transactions on Instrumentation and Measurement， 2023， 72： 1-8.
15	KESÄNIEMI M， VIRTANEN K. Direct Least Square Fitting of Hyperellipsoids［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence， 2018， 40（1）： 63-76.
16	HAN Min， KAN Jiangming， YANG Gongping， et al. Robust Ellipsoid Fitting Using Combination of Axial and Sampson Distances［J］. IEEE Transactions on Instrumentation and Measurement， 2023， 72： 1-14.
17	CHANG H T， CHANG J Y. Iterative Robust Ellipsoid Fitting Based on M-Estimator with Geometry Radius Constraint［J］. IEEE Sensors Journal， 2023， 23（2）： 1397-1407.
18	HEMERLY E M， COELHO F A A. Explicit Solution for Magnetometer Calibration［J］. IEEE Transactions on Instrumentation and Measurement， 2014， 63（8）： 2093-2095.

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