张量衍生不变关系下的磁源单点定位

李青竹; 李志宁; 张英堂; 范红波

doi:10.3788/OPE.20192708.1880

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张量衍生不变关系下的磁源单点定位

信息科学 | 更新时间：2020-08-13

- 张量衍生不变关系下的磁源单点定位
- Magnetic source single-point positioning by tensor derivative invariant relations
- 光学精密工程 2019年27卷第8期页码：1880-1893
- 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：
  
  [ "李青竹(1993-)，男，四川绵阳人，2016年于西南交通大学获得学士学位，2018年于陆军工程大学获得硕士学位，主要从事磁异常探测，磁梯度张量系统设计与误差校正等方面的研究。E-mail：laznlqz666@qq.com" ]
  [ "李志宁(1972-)，男，河北石家庄人，副教授，1999年于军械工程学院获硕士学位，2007年于清华大学获博士学位，主要从事弱磁测试技术研究。E-mail：lizn03@hotmail.com" ]
- 基金信息：
  
  军内科研项目资助；装备试验技术项目资助
- DOI：10.3788/OPE.20192708.1880
  中图分类号： TP212.9; TH762
- 收稿日期：2018-09-06，
  
  录用日期：2018-11-27，
  
  纸质出版日期：2019-08-15
- 稿件说明：
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李青竹, 李志宁, 张英堂, 等. 张量衍生不变关系下的磁源单点定位[J]. 光学精密工程, 2019,27(8):1880-1893.

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.
李青竹, 李志宁, 张英堂, 等. 张量衍生不变关系下的磁源单点定位[J]. 光学精密工程, 2019,27(8):1880-1893. DOI： 10.3788/OPE.20192708.1880.

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

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