基于正交基函数-编辑距离的低信噪比下磁异常信号相似性度量方法

邱景; 欧津东; 谢冬; 王铮; 杜杰卓

doi:10.11999/JEIT210029

基于正交基函数-编辑距离的低信噪比下磁异常信号相似性度量方法

doi: 10.11999/JEIT210029

重庆大学光电工程学院光电技术及系统教育部重点实验室重庆 400044

基金项目: 国家自然科学基金(51775070)，中央高校基本科研业务费专项基金(2019CDJGFGD002)

详细信息

作者简介:
邱景：男，1982年生，教授，研究方向为微弱磁场探测技术、可穿戴柔性传感技术、环境能量采集及自供电传感技术、雷达隐身技术

欧津东：男，1995年生，硕士生，研究方向为微弱磁场探测技术

谢冬：男，1995年生，硕士生，研究方向为微弱磁场探测技术

王铮：女，1996年生，硕士生，研究方向为微弱磁场探测技术

杜杰卓：男，1996年生，硕士生，研究方向为微弱磁场探测技术、可穿戴柔性传感技术

通讯作者:
邱景　jingqiu@cqu.edu.com

中图分类号: TN911.7; O441
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出版历程
- 收稿日期: 2021-01-08
- 修回日期: 2021-06-24
- 网络出版日期: 2021-07-07
- 刊出日期: 2022-02-25

A Similarity Measurement Method for Magnetic Anomaly Signal under Low Signal-to-Noise Based on Orthogonal Basis Function–Edit Distance

Key Laboratory of Optoelectronic Technology and System of Ministry of Education, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China

Funds: The National Natural Science Foundation of China (51775070), The Fundamental Research Funds for the Central Universities (2019CDJGFGD002)

摘要

摘要: 针对低信噪比下磁异常信号相似性难以度量的问题，该文提出基于正交基函数(OBF)分解和编辑距离法(EDR)相结合的OBF-EDR磁异常信号相似性度量方法。该方法通过对磁异常信号进行正交基函数分解得到离散基函数系数，根据背景噪声与基函数不相关的特性提高离散基函数系数信噪比，利用编辑距离法对离散基函数系数进行相似性计算从而间接实现对磁异常信号的相似性度量。仿真测试表明OBF-EDR方法相较于EDR算法可在更低信噪比情况下对磁异常信号进行相似性度量。
- 正交基函数 /
- 编辑距离 /
- 磁场曲线 /
- 相似性度量 /
- 低信噪比
Abstract: Considering the problem that the similarity of magnetic anomaly signals is difficult to measure under low signal-to-noise ratio, a similarity measurement method OBF-EDR based on the combination of Orthogonal Basis Function (OBF) decomposition and Edit Distance on Real sequence (EDR) is proposed. This method obtains discrete basis function coefficients by decomposing the magnetic anomaly signals with orthogonal basis functions method. The signal-to-Noise Ratio (SNR) of discrete basis function coefficients is improved due to the uncorrelated characteristics of background noise and basis functions. EDR is used to measure the discrete coefficients of the basis function so as to measure indirectly the similarity of the magnetic anomaly signals. The simulation test shows that the OBF-EDR method can measure the similarity of magnetic anomaly signals at a lower SNR than the EDR algorithm.
- Orthogonal Basis Function(OBF) /
- Edit distance /
- Magnetic signature waveform /
- Similarity measurement /
- Low Signal-to-Noise Rate (SNR)

HTML全文

图 1 磁异常探测模型图

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图 2 原始磁异常信号

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图 3 含噪磁异常信号

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图 4 X轴方向磁异常信号离散基函数系数

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图 5 Y轴方向磁异常信号离散基函数系数

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图 6 Z轴方向磁异常信号离散基函数系数

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图 7 序列A转换为序列B的编辑距离计算过程

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图 8 X轴方向磁异常测试信号

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图 9 Y 轴方向磁异常测试信号

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图 10 Z轴方向磁异常测试信号

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图 11 FAR随SNR变化情况

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图 12 FRR随SNR变化情况

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表 1 EDR算法伪代码

输入：两个实数序列A和B
输出：序列A与B的相似度
第1步：计算序列A,B的长度以及阈值e
L_A=LENGTH(A); L_B=LENGTH(B); e=0.1× (max(A)–min(A))
第2步：创建编辑距离矩阵E [L_A+1, L_B+1]并进行初始化
E [0,0]=0
for each row i from 1 to L_A do
E [i, 0] ← E [i–1, 0]+deleteCost(A [i], B [0])
for each column j from 1 to L_B do
E [0, j] ← E [0, j–1]+insertCost(A [0], B [j])
第3步：循环执行
for each row i from 1 to L_A do
for each column j from 1 to L_B do
E [i, j] ← min(E [i–1, j]+deleteCost(A [i], B [j]),
E [i, j–1]+insertCost(A [i], B [j]),
E [i–1, j–1]+substituteCost(A [i], B [j]))
end
end
第4步：返回1–E [L_A, L_B]/max(L_A, L_B)

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表 2 OBF-EDR计算磁异常信号相似度结果

计算对象	${{S} }{ {\rm{\alpha} } _1}$	${W_1}$	${{S} }{ {\rm{\alpha} } _2}$	${W_2}$	${{S} }{ {\rm{\alpha} } _3}$	${W_3}$	${\rm{sLines}}$
${B_x}$和${{\rm{Br}}_x}$	1.000	0.700	0.768	0.145	0.816	0.155	0.938
${B_y}$和${{\rm{Br}}_y}$	1.000	0.718	0.794	0.138	0.829	0.143	0.946
${B_z}$和${{\rm{Br}}_z}$	0.961	0.782	0.724	0.086	0.754	0.132	0.913

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表 3 EDR计算磁异常信号相似度结果

	计算对象
	${B_x}$和${\rm{B}}{{\rm{r}}_x}$	${B_y}$和${\rm{B}}{{\rm{r}}_y}$	${B_z}$和${\rm{B}}{{\rm{r}}_z}$
相似度	0.75	0.767	0.741

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