基于稀疏恢复的快速高精度DOA估计算法

doi:10.12305/j.issn.1001-506X.2024.11.05

摘要/Abstract

摘要：

传统的基于稀疏恢复的波达方向(direction of arrival，DOA)估计算法使用密集的采样网格，导致计算量显著增加，且对邻近入射信号的估计精度不高。针对这一问题，提出一种快速高精度DOA估计算法。该算法首先使用网格进化方法降低网格点总数。然后, 对噪声方差和信号功率进行二次估计，进而使用离网求根稀疏贝叶斯学习(off-grid root sparse Bayesian learning, OGRSBL)技术来实现入射角的精确估计。仿真表明，相比传统稀疏贝叶斯学习类算法，所提算法计算效率高，同时对紧邻信号有着更好的估计能力。

关键词: 波达方向估计, 离网, 网格进化, 稀疏贝叶斯学习

Abstract:

The conventional direction of arrival (DOA) estimation algorithm based on sparse recovery uses dense sampling grids, resulting in significantly increased computational complexity and low estimation accuracy for adjacent signals. To address this issue, this manuscript proposes a fast and high accuracy DOA estimation algorithm. Firstly, starting from sparse grids, the grid evolution method is used to reduce the total number of grid points. Noise variance and signal power are estimated again, then use off-grid root sparse Bayesian learning (OGRSBL) technique to calculate the accurate estimation of incident angle. Simulation results show that compared to conventional sparse Bayesian learning algorithms, the proposed algorithm has higher computational efficiency with higher accuracy for closely spaced signals.

Key words: direction of arrival (DOA) estimation, off-grid, grid evolution, sparse Bayesian learning (SBL)

中图分类号:

TN911.7

刘鲁涛, 徐国珩, 王振. 基于稀疏恢复的快速高精度DOA估计算法[J]. 系统工程与电子技术, 2024, 46(11): 3631-3638.

Lutao LIU, Guoheng XU, Zhen WANG. Fast and high precision DOA estimation algorithm based on sparse recovery[J]. Systems Engineering and Electronics, 2024, 46(11): 3631-3638.

图/表 4

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算法	计算复杂度
本文算法	第1次迭代: $\begin{gathered}O\left(M N_{\max } L+M N_{\max }^2+M^2 N_{\max }+M^3+L K^2=\right. \\ \left.N_{\max } K^2+M N_{\max } K\right)\end{gathered}$
本文算法	第2次迭代: $\begin{gathered}O\left(M N_{\max } L+M N_{\max }^2+M^2 N_{\max }+M^3+\right. \\ \left.M\left(N_{\max }-1\right) L\right)\end{gathered}$
OGSBI	$\begin{gathered}O\left(M N L+M N^2+M^2 N+M^3+\right. \\ \left.L K^2+N K^2+M N K\right)\end{gathered}$
OGRSBL	$\begin{gathered}O\left(M N L+M N^2+M^2 N+M^3+\right. \\ M(N-1) L)\end{gathered}$
PSBL	$\begin{gathered}O\left(M(N-1) L+M(N-1)^2+M^2(N-1)+\right. \\ \left.M^3+L K^2+(N-1) K^2+M(N-1) K\right)\end{gathered}$
GE-OGSBI	$\begin{gathered}O\left(M N_{\max } L+M N_{\max }^2+M^2 N_{\max }+M^3+L K^2+\right. \\ \left.N_{\max } K^2+M N_{\max } K\right)\end{gathered}$
GI-MSBL	第1次迭代: O(MNL+MN+M²N+M³+LK²)
	第2次迭代: $O\left(\overline{M N L}+\overline{M N}+M^2 \bar{N}+M^3+L K^2\right) $
	计算离网误差: (2M²+2M)N₀K

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