Magnetic source single-point positioning by tensor derivative invariant relations

Qing-zhu LI; Zhi-ning LI; Ying-tang ZHANG; Hong-bo FAN

doi:10.3788/OPE.20192708.1880

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Magnetic source single-point positioning by tensor derivative invariant relations

Information Sciences | 更新时间：2020-08-13

- Magnetic source single-point positioning by tensor derivative invariant relations
- Optics and Precision Engineering Vol. 27, Issue 8, Pages: 1880-1893(2019)
- 作者机构：
  
  陆军工程大学车辆与电气工程系，河北石家庄 050003
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20192708.1880
  CLC： TP212.9; TH762
- Received：06 September 2018，
  
  Accepted：27 November 2018，
  
  Published：15 August 2019
- 稿件说明：
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Qing-zhu LI, Zhi-ning LI, Ying-tang ZHANG, et al. Magnetic source single-point positioning by tensor derivative invariant relations[J]. Optics and precision engineering, 2019, 27(8): 1880-1893.
DOI：

Qing-zhu LI, Zhi-ning LI, Ying-tang ZHANG, et al. Magnetic source single-point positioning by tensor derivative invariant relations[J]. Optics and precision engineering, 2019, 27(8): 1880-1893. DOI： 10.3788/OPE.20192708.1880.

摘要

为避免在利用欧拉反演方法进行磁性目标单点定位时，二阶张量数据对误差和噪声的较敏感性导致定位精度低的缺点，提出一种利用张量衍生不变关系、仅需一阶张量数据实现磁源单点定位的方法。在磁偶极子场源张量不变量和特征值分析基础上，推导了两个张量衍生不变关系：磁矩与位置矢量夹角是恒定的，且能用张量特征值表示；绝对值最小特征值的特征向量垂直于磁矩、位置矢量，其余特征值的特征向量共面于磁矩、位置矢量。据此，可计算出位置矢量关于过磁源中心某平面四象限对称的4个可能解，根据实际方位和磁测数据确定唯一解。实验结果表明，实测中经磁梯度张量系统误差校正后，对小尺度磁铁(直径5 cm、厚度0.5 cm)的定位精度控制在1 cm均方根误差范围内。相比欧拉反演方法，提出的方法在同噪声工况下探测距离更远，定位结果更可靠。

Abstract

It is desirable to avoid the error and noise sensitivity of second-order tensor data leading to the disadvantages of low positioning accuracy with the Euler inversion method of magnetic object single-point positioning. For single-point positioning with only first-order tensor data

a method based on tensor derivative invariant relations is proposed. For the analysis of the magnetic dipole source tensor invariant and eigenvalue

two tensor derivative invariant relations were derived. The angle between the magnetic moment and position vector is constant and related to the tensor eigenvalue. The eigenvector of the absolute-minimum eigenvalue is perpendicular to the magnetic moment and position vector

and the eigenvectors of the remaining eigenvalues are coplanar with them. Thus

four possible solutions with respect to the quadrants of a plane above the magnetic source center were obtained

and the unique solution can be determined by the actual orientation and measured data. The results show that after error correction of the magnetic gradient tensor system

the positioning accuracy of a small-scale magnet (diameter of 5 cm

thickness of 0.5 cm) can be controlled within a root mean square error of 5 cm. Compared with the Euler inversion method

the proposed method has a greater detection distance with the same noise and exhibits a more reliable result.

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references

CHMIDT P W, CLARK D A. The magnetic gradient tensor: Its properties and uses in source characterization[J]. The Leading Edge , 2006, 25(1): 75-78.

张昌达.航空磁力梯度张量测量——航空磁测技术的最新进展[J].工程地球物理学报, 2006, 3(5): 354-361.

ZHANG CH D. Airborne tensor magnetic gradiometry——the latest progess of airborne magnetometric technology[J]. Chinese Journal of Engineering Geophysics , 2006, 3(5): 354-361. (in Chinese)

LI Q Z, LI Z N, ZHANG Y T, et al .. Artificial vector calibration method for differencing magnetic gradient tensor systems[J]. Sensors , 2018, 18(2):361.

尹刚, 张英堂, 米松林, 等.基于倾斜角和Helbig方法的多磁源目标反演技术[J].上海交通大学学报, 2017, 51(5): 577-584.

YIN G, ZHANG Y T, MI S L, et al .. Multiple magnetic targets inversion technique based on tilt angle and Helbig method[J]. Journal of Shanghai Jiaotong University , 2017, 51(5): 577-584. (in Chinese)

LEE K M, LI M. Magnetic tensor sensor for gradient-ba-sed localization of ferrous object in geomagnetic field[J]. IEEE Transactions on Magnetics , 2016, 52 (8):1-10.

张朝阳, 肖昌汉, 高俊吉, 等.磁性物体磁偶极子模型适用性的试验研究[J].应用基础与工程科学学报, 2010, 18(5): 862-868.

ZHANG ZH Y, XIAO CH, GAO J J, et al .. Experiment research of magnetic dipole model applicability for a magnetic object[J]. Journal of Basic Science and Engineering , 2010, 18(5): 862-868. (in Chinese)

NARA T, SUZUKI S, ANDO S. A closed-form formula for magnetic dipole localization by measurement of its magnetic field and spatial gradients[J]. IEEE Transactions on Magnetics , 2006, 42(10): 3291-3293.

孙昂, 郭华, 田明阳, 等.基于欧拉反褶积方法的航磁三分量应用研究[J].地球物理学报, 2017, 60(11):4491-4505.

SUN A, GUO H, TIAN M Y, et al .. Application of aeromagnetic three-component survey based on the Euler deconvolution method[J]. Chinese Journal of Geophysics , 2017, 60(11): 4491-4505. (in Chinese)

YIN G, ZHANG Y T, FAN H B, et al .. Magnetic dipole localization based on magnetic gradient tensor data at a single point[J]. Journal of Applied Remote Sensing , 2014, 8(1):083596.

李青竹, 李志宁, 张英堂, 等.磁梯度张量系统传感器阵列的快速旋转校准[J].光学精密工程, 2018, 26(7):1813-1826.

LI Q ZH, LI ZH N, ZHANG Y T, et al .. Fast rotation calibration of sensor array in magnetic gradient tensor system[J]. Opt. Precision Eng., 2018, 26(7): 1813-1826. (in Chinese)

李青竹, 李志宁, 张英堂, 等.基于椭球拟合的磁梯度张量系统集成校正[J].中国惯性技术学报, 2018, 26(2): 187-195.

LI Q ZH, LI ZH N, ZHANG Y T, et al .. Integrated calibration of magnetic gradient tensor system based on ellipsoid fitting[J]. Journal of Chinese Inertial Technology , 2018, 26(2): 187-195. (in Chinese)

尹刚, 张林, 谢艳, 等.磁梯度张量系统的非线性校正方法[J].仪器仪表学报, 2018, 39(4):35-43.

YIN G, ZHANG L, XIE Y, et al .. Nonlinear calibration method of magnetic gradient tensor system[J]. Chinese Journal of Scientific Instrument , 2018, 39(4):35-43. (in Chinese)

SALAM M A. Static Magnetic Field [M]. Electromagnetic Field Theories for Engineering. Singapore: Springer, 2014: 141-185.

吕俊伟, 迟铖, 于振涛, 等.磁梯度张量不变量的椭圆误差消除方法研究[J].物理学报, 2015, 64(19):60-67.

LV J W, CHI CH, YU ZH T, et al .. Research on the asphericity error elimination of the invariant of magnetic gradient tensor[J]. Acta Physica Sinica , 2015, 64(19): 60-67. (in Chinese)

王明, 骆遥, 罗锋, 等.欧拉反褶积在重磁位场中应用与发展[J].物探与化探, 2012, 36(5):834-841.

WANG M, LUO Y, LUO F, et al .. The application and development of Euler deconvolution in gravity and magnetic field[J]. Geophysical & Geochemical Exploration , 2012, 36(5): 834-841. (in Chinese)

CHAI T, DRAXLER R R. Root mean square error (RMSE) or mean absolute error (MAE)?—Arguments against avoiding RMSE in the literature[J]. Geoscientific Model Development , 2014, 7(3): 1247-1250.

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中国科学院国家天文台/南京天文光学技术研究所

Optical Engineering Department of Beijing Institute of Technology

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