基于平行四阶稀疏线阵的二维波达方向求根闭式估计-“多域协同与智能目标状态感知关键技术”专刊

悦亚星; 贺雄鹏; 周杭; 高大伟; 陈毓锋; 廖桂生

doi:10.7527/S1000-6893.2025.32194

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DOI: https://doi.org/10.7527/S1000-6893.2025.32194

基于平行四阶稀疏线阵的二维波达方向求根闭式估计-“多域协同与智能目标状态感知关键技术”专刊

悦亚星 ,
贺雄鹏 ,
周杭 ,
高大伟 ,
陈毓锋 ,
廖桂生

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西安电子科技大学

收稿日期: 2025-05-07

修回日期: 2025-07-16

网络出版日期: 2025-07-18

基金资助

资源受限平台的雷达多维域联合降采样理论与方法

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Closed-form root-finding-based two-dimensional direction-of-arrival estimation using a parallel fourth-order sparse linear array

YUE Ya-Xing ,
HE Xiong-Peng ,
ZHOU Hang ,
GAO Da-Wei ,
CHEN Yu-Feng ,
LIAO Gui-Sheng

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Received date: 2025-05-07

Revised date: 2025-07-16

Online published: 2025-07-18

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摘要

针对传统二维波达方向估计中阵列自由度受限与噪声敏感性等问题，本文提出了一种基于平行四阶稀疏线阵的求根闭式估计算法。首先，构建平行四阶稀疏线阵下的信号模型，并基于此推导四阶标准累积量矩阵。接着，提出一种新的矩阵数据变换方法，将原四阶标准累积量矩阵转换为虚拟阵元下的四阶累积量矩阵，从而构造出虚拟的高自由度阵列结构。随后，利用该虚拟阵列对应的噪声子空间，推导出一种基于多项式求根的波达方向估计算法，以实现高效的二维角度估计。此外，分析了计算复杂度，并给出了信号可辨识个数的比较。相比于已有方法，该方法能够大幅增加虚拟阵元个数，有效提升可分辨信源数，并可抑制高斯色噪声。仿真结果验证了所提方法在信号可辨识性、二维波达方向估计精度及信号分辨概率方面的更优性能。

关键词： 二维波达方向; 四阶累积量; 多项式求根; 平行线阵; 闭式估计

本文引用格式

悦亚星 , 贺雄鹏 , 周杭 , 高大伟 , 陈毓锋 , 廖桂生 . 基于平行四阶稀疏线阵的二维波达方向求根闭式估计-“多域协同与智能目标状态感知关键技术”专刊[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2025.32194

Abstract

To address the challenges of limited array degrees-of-freedom and noise sensitivity in traditional two-dimensional direction-of-arrival (DOA) estimation, this paper proposes a root-finding closed-form estimation algorithm based on a parallel fourth-order sparse linear array (PFOSLA). First, the signal model for the considered PFOSLA is constructed, and the corresponding fourth-order standard cumulant matrix is analytically derived. Next, a novel matrix transformation method is proposed to convert the original fourth-order standard cumulant matrix into a virtual-element-based fourth-order cumulant matrix, thereby constructing a virtual high-degree-of-freedom array structure. Subsequently, leveraging the noise subspace of this trans-formed matrix, a polynomial root-finding-based DOA estimation algorithm is developed to achieve efficient two-dimensional angular estimation. Additionally, the computational complexity and the maximum number of resolvable sources are analyzed. Compared with existing methods, the proposed approach significantly increases the number of virtual elements, effectively enhances the number of resolvable sources, and suppresses colored Gaussian noise. Simulation results validate the superior performance of the proposed method in terms of signal identifiability, two-dimensional direction-of-arrival estimation accura-cy, and source resolution probability.

Key words： Two-dimensional direction-of-arrival; Fourth-order cumulant; Polynomial roots finding; Parallel liner array; Closed-form estimation

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