大阵列下基于稀疏相位恢复和大维随机矩阵理论的稳健波达方向估计

Existing direction of arrival estimation methods mostly assume that the sensor number is fixed, while the snapshot number tends to infinity. In contrast, the sensor number is large, but the snapshot number is limited in actual detecting systems. In this situation, the performance of the classical statistical theory based methods will be decreased or even failure, caused by the inaccurate estimation of covariance matrix, eigenvalue and eigenvector. Meanwhile, the increase of the number of sensors further exacerbates the probability of generating array phase synchronization error. As a result, the robustness of the existing methods is difficult to be guaranteed. The project will use sparse phase retrieval and large dimensional random matrix theory as the mathematical processing tools to research robust direction of arrival estimation method under large arrays. The research contents include: (1) robust direction of arrival estimation method utilizing sparse phase retrieval in the presence of phase synchronization error; (2) robust subspace-based direction of arrival estimation method utilizing large dimensional random matrix theory under large arrays; (3) high-performance direction of arrival estimation method jointly utilizing sparse phase retrieval and large dimensional random matrix theory under large arrays. Sparse phase retrieval has good robustness to the phase synchronization error, and large dimensional random matrix theory can effectively solve the common problem of inaccurate parameter estimation, which is caused by using classical statistical theory in high-dimensional data. The research of this project has important significance and value for enhancing the actual detection performance of radar system, sonar system, et al.

现有波达方向估计方法大多假定阵元数固定而快拍数趋于无穷，实际探测系统中的阵元数往往较大，而采样快拍数有限。在这种条件下，基于经典统计理论的波达方向估计方法会因协方差矩阵、特征值及特征向量估计不准确而使性能下降甚至失效。同时，阵元数的增大加剧了阵列相位同步误差的产生，导致已有方法的稳健性亦难以保证。本项目以稀疏相位恢复和大维随机矩阵理论为数学处理手段，研究大阵列下的稳健波达方向估计问题。研究内容包括：（1）相位同步误差下基于稀疏相位恢复的稳健波达方向估计方法；（2）大阵列下基于大维随机矩阵理论的特征子空间类稳健波达方向估计方法；（3）大阵列下基于稀疏相位恢复和大维随机矩阵理论联合的高性能波达方向估计方法。稀疏相位恢复对相位同步误差具有较好的鲁棒性，大维随机矩阵理论能有效解决经典统计理论在高维数据下参量估计不准确的共性问题。本项目的研究对提升雷达、声呐等系统的实际探测性能具有重要的意义和价值。

稳健的波达方向估计是阵列信号处理领域中的关键问题之一，对提高雷达、声呐等实际探测系统的性能具有重要的意义和价值。本项目基于特征子空间理论、稀疏重构与稀疏相位恢复理论以及大维随机矩阵理论对稳健波达方向估计问题进行了深入研究。主要成果如下：（1）提出了相位误差下基于稀疏相位恢复和非线性稀疏重构的稳健波达方向估计新方法，高效提高了算法的波达方向估计性能；（2）提出了复杂噪声、复杂源等背景下基于稀疏重构和特征子空间理论的稳健波达方向估计新方法，分析了相关算法的自由度数和理论估计误差界；（3）提出了大阵列下基于稀疏重构和大维随机矩阵理论的高性能波达方向估计新方法。本项目开发出的新算法/技术可以作为支撑技术应用于室内导航、应急疏散、灾后救援、雷达和声呐探测等关系国计民生的诸多领域，并对相关产业发展具有重要的推动作用。本项目共发表论文15篇，其中通信和信号处理领域SCI二区及以上期刊论文7篇，申请发明专利3项。