基于几何代数的电磁矢量传感器阵列抗强干扰参数估计算法

王通; 刘尚合; 陈东伟; 金梦哲; 方庆园

doi:10.12263/DZXB.20250490

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基于几何代数的电磁矢量传感器阵列抗强干扰参数估计算法

学术论文 | 更新时间：2026-02-05

- 基于几何代数的电磁矢量传感器阵列抗强干扰参数估计算法
- Joint DOA and Polarization Estimation of Unequal Power Sources for Electromagnetic Vector-Sensor Array Based on Geometric Algebra
- 电子学报 2025年53卷第10期页码：3529-3539
- 作者机构：
  
  1.石家庄铁道大学河北省电磁环境效应与信息处理重点实验室，河北石家庄 050043
  2.陆军工程大学石家庄校区电磁环境效应国家重点实验室，河北石家庄 050050
- 作者简介：
  
  [ "王通男，1996年出生于河北省沧州市.现为石家庄铁道大学在读博士生.主要研究方向为矢量传感器阵列信号处理.E-mail: 2202206018@student.stdu.edu.cn" ]
  [ "方庆园女，1987年出生于山东省威海市.现为石家庄铁道大学副教授、硕士生导师.主要研究方向为信号与信息处理、天线设计等.E-mail: fangqingyuan@stdu.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(61801309);国家重点实验室开放课题(JCKYS2022DC07)
- DOI：10.12263/DZXB.20250490
  中图分类号： TN911.7
- 收稿：2025-06-06，
  
  录用：2025-09-25，
  
  纸质出版：2025-10-25
- 稿件说明：
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王通, 刘尚合, 陈东伟, 等. 基于几何代数的电磁矢量传感器阵列抗强干扰参数估计算法[J]. 电子学报, 2025, 53(10): 3529-3539.

WANG Tong, LIU Shang-he, CHEN Dong-wei, et al. Joint DOA and Polarization Estimation of Unequal Power Sources for Electromagnetic Vector-Sensor Array Based on Geometric Algebra[J]. Acta Electronica Sinica, 2025, 53(10): 3529-3539.
王通, 刘尚合, 陈东伟, 等. 基于几何代数的电磁矢量传感器阵列抗强干扰参数估计算法[J]. 电子学报, 2025, 53(10): 3529-3539. DOI：10.12263/DZXB.20250490

WANG Tong, LIU Shang-he, CHEN Dong-wei, et al. Joint DOA and Polarization Estimation of Unequal Power Sources for Electromagnetic Vector-Sensor Array Based on Geometric Algebra[J]. Acta Electronica Sinica, 2025, 53(10): 3529-3539. DOI：10.12263/DZXB.20250490

摘要

随着无人机蜂群在民用领域的广泛应用，掌握其所在位置空间角度、信号极化等关键状态参数，对其有效监管至关重要，利用电磁矢量传感器阵列进行波达方向与极化联合估计可获取无人机的空域角度与极化参数.然而在复杂电磁环境中非合作无人机蜂群中的多无人机目标同时探测场景下，尤其环境中存在功率较强的干扰信号时，传统基于电磁矢量传感器阵列的参数估计算法对功率较弱的真实目标信号的参数估计性能下降.因此本文提出一种基于三维几何代数（Geometric algebra of Euclidean 3-space，G3）模型的不变噪声子空间空域与极化域参数联合估计算法.首先基于G3模型下的MUSIC算法的期望谱研究强弱信号共存对基于G3的传统子空间算法参数估计性能的影响，然后理论证明了在G3模型下接收信号阵列协方差矩阵具有噪声子空间不变性.本文算法基于G3的噪声子空间不变性进行空域-极化域联合参数估计，利用入射信号功率提升时噪声空间特征值保持不变这一特性，提高了算法对功率较弱的真实目标信号的波达方向与极化联合参数估计性能.通过理论推导虚拟信源极化参数变化对基于G3的阵列协方差矩阵噪声子空间不变性的影响，证明了算法无需4维谱峰搜索，仅通过2维谱峰搜索即可实现空域与极化域参数联合估计，提高了算法的计算效率.仿真结果表明，随着强干扰信号功率的提升，传统算法无法分辨功率较弱的入射信号.而本文所提出的算法在不同信噪比、强弱功率比和噪声相关性条件下，对弱信号的参数估计性能均优于传统算法，相较于传统算法，本文算法对弱信号可测向的信噪比门限可降低3 dB以上，空域与极化域参数联合估计精度可提高88.7%，且与传统基于不变噪声子空间类算法相比，计算量可减小97.11%以上.本文所提出算法可用于复杂环境中尤其存在强功率干扰时，对非合作无人机蜂群中的多无人机同时获取其所在位置空间角度与其发射信号的极化参数，在基于无人机平台的移动无线通信抗干扰等场景中亦有潜在应用价值.

Abstract

With the widespread application of drone swarms in civilian fields

it is crucial for drones effective regulation to obtain some key state parameters of drone swarms such as spatial angles and signal polarization which are acquired by utilizing joint direction of arrival (DOA) and polarization estimation based on electromagnetic vector sensor arrays (EMVA). However

in simultaneous detection of non-cooperative multi unmanned aerial vehicles (UAVs) of drone swarms in a complex electromagnetic environment

the joint DOA and polarization estimation performance of traditional methods on real UAVs signal sources with weak power usually deteriorates when interference signal with high power impinge on an EMVA. Therefore

a joint DOA and polarization estimation method with invariant property of noise subspace (IPNS) based on geometric algebra of Euclidean 3-space (G3) model is proposed. Firstly

the impact of the coexistence of strong and weak signals on the performance of parameter estimation of traditional subspace methods based on G3 is studied by using expected spectrum of multiple signal classification method based on geometric algebra of Euclidean 3-space framework (G3-MUSIC). Then the invariant property of G3 noise subspace of array covariance matrix is theoretically proved. The performance of joint DOA and polarization estimation on real targets with weak power is improved by utilizing the characteristic of the method that the eigenvalues of G3 noise subspace remain unchanged when the incident signal power is increased. Simultaneously

by theoretically deriving the impact of changes in virtual source polarization parameters on the invariance of the noise subspace of the array covariance matrix based on G3

it is proved that 4-dimensional spectral peak search is not required by the proposed method which realizes joint DOA and polarization estimation only by 2-dimensional spectral peak search. It is verified by simulation that the weak signals cannot be distinguished by the traditional methods as the power of strong interference signals increases. At the same time

simulation verified that when high power signals impinge on an EMVA

the proposed method outperforms the traditional methods in terms of different signal-to-noise ratios

power ratios between strong and weak signals

and noise correlations. Compared with the traditional methods based on invariant noise subspace

the signal to noise ratio threshold of direction finding of the weak source was reduced by more than 3 dB

the accuracy of joint DOA and polarization estimation was enhanced by 88.7%

and the calculation amount was reduced by more than 97.11%. The proposed method can be used for obtaining locations of multiple UAVs and polarization parameters of signals emitted by multiple UAVs in non-cooperative drone swarms in complex electromagnetic environments

especially in circumstance of interference with high power

and has potential application value in scenarios such as anti-interference for mobile wireless communication based on UAVs platforms.

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references

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