传统的无网格压缩感知在进行波达方向（Direction of Arrival，DOA）估计时，使用凸优化工具箱（如CVX）来求解半正定规划问题（Semi-Definite Programming，SDP），所消耗的时间会随着矢量水听器阵列规模的增加，逐渐增大。为了提高算法的收敛速度，将交替方向乘子法（Alternative Direction Method of Multiplier，ADMM）应用到矢量水听器阵列的DOA估计中，考虑到海洋环境噪声，使用原子范数去噪方法（Atomic Norm Soft Thresholding，AST）来估计线谱参数，将原子范数最小化问题（Atomic Norm Minimization，ANM）转化为SDP问题，使用ADMM对SDP问题进行求解，最后使用对偶多项式估计角度。为了验证ADMM算法的性能，在不同信噪比和矢量阵元数条件下，与快速求根多重信号分类（Root-Multiple Signal Classification，ROOTMUSIC）算法和CVX进行对比仿真实验。结果表明，ADMM在保证DOA估计模型收敛性的同时，提高了算法效率。
The time required by the traditional grid-less compressive sensing approach for Direction of Arrival estimation, which utilizes a convex optimization toolbox (e.g. CVX) to solve the Semi-Definite Programming problem, gradually increases with the vector hydrophone array size grows. To improve the convergence speed of the algorithm, the Alternative Direction Method of Multiplier is applied to the DOA estimation of vector hydrophone arrays. Taking ocean environmental noise into account, the Atomic Norm Soft Thresholding is used to estimate the line spectral parameters, transform the Atomic Norm Minimization problem into a SDP problem, solve the SDP problem using the ADMM algorithm, and finally estimate the angle using dyadic polynomials. In order to verify the performance of the ADMM algorithm, comparative simulation experiments are conducted with the Root-Multiple Signal Classification(ROOTMUSIC) algorithm and the CVX algorithm under different signal-to-noise ratios and number of vector array elements, and the results show that the ADMM algorithm enhances the computational efficiency of the algorithm while ensuring convergence of the DOA estimation model.
2024,46(12): 140-143 收稿日期：2023-08-25
DOI：10.3404/j.issn.1672-7649.2024.12.024
分类号：TN911.7
基金项目：国家自然科学基金资助项目（62172269）；中国博士后科学基金资助项目（2014M561512）
作者简介：刘永豪(1999-),男,硕士研究生,研究方向为水声信号处理
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