复杂环境下基于变换协方差矩阵的无网格稀疏DOA估计

Gridless Sparse Methods, which operate directly in the continuous domain and therefore can completely resolve the grid mismatch problem for sparse DOA estimation, is a major problem in array signal processing. Considering the current needs of radar system of high resolution, high resistance, anti-stealth, Gridless Sparse Methods for parameter estimation under the scenes of low SNR, unknown source number, unknown nonuniform noise\spatial colored noise, noncircular and coherent sources are facing new challenges..This project introduces the sparse representation of covariance transform into the Gridless Sparse Methods to improve the performance of parameter estimation. First, we research the Gridless Sparse Representation theory based on trace norm, and propose Gridless Sparse Methods with high precision based on matrix rank minimization. Then, based on the analysis of the covariance matrix of the observed signals, we design covariance matrix transformations and establish sparse representation models. Finally, the residual energy constraint and the structural characteristic constraint schemes independent of the noise statistical characteristics are studied and Gridless Sparse Methods based on transformed covariance matrix is introduced. This project improves the estimation accuracy, resolution, efficiency and stability of Gridless Sparse Methods under Complex Scenes and has important theoretical significance and application prospect to enhance the capability of remote detection of China's early warning system and the combat capability under condition of conflict circumstance in information warfare.

无网格稀疏算法将信号参数空间直接描述为连续域，对于解决基于稀疏方法DOA估计中基不匹配问题具有重要意义，已成为阵列信号处理重要方向。基于当前雷达系统高分辨率、高对抗性、反隐身等需求，在低信噪比、目标数未知、非均匀\色噪声分布、非圆信源、相干目标等复杂环境下，无网格稀疏方法参数估计面临新的挑战。.本申请提出将协方差变换稀疏表示引入无网格稀疏方法以提高复杂环境下参数估计性能。研究基于迹范数无网格稀疏表示理论，提出基于矩阵秩最小化无网格稀疏参数估计方法；分析信号协方差矩阵特性，设计协方差矩阵变换，建立基于变换协方差矩阵的稀疏表示模型；研究独立于噪声特性的残差能量约束和结构特性约束方案，提出基于变换协方差矩阵的稳健多约束无网格稀疏重构算法。提高复杂环境下无网格稀疏方法DOA估计精度、分辨率，以及算法的效率和稳定性，对提升我国远程预警系统探测能力和信息化战争对抗能力，具有重要的理论意义和应用前景。

在低信噪比、非均匀\色噪声分布、非圆信源、相干目标等复杂环境下，无网格稀疏方法参数估计面临重大挑战。本项目基于现有无网格压缩感知框架，将协方差变换稀疏表示引入无网格稀疏方法以提高上述复杂环境下DOA估计精度。.研究了非理想噪声环境下的四种无网格DOA估计方法，设计了基于ULA和SLA的信号模型。从一阶时域到二阶协方差域再到高阶四阶累积量域的层级递进，完善了非理想噪环境下无网格压缩感知理论。并在此基础上进一步考虑低信噪比、有限快拍等影响，设计针对非均匀\色噪声抑制及稀疏表示的矩阵变换，确保在多种复杂环境混合下算法的鲁棒性和实用性。.为提高阵列\信源非理想条件下的DOA估计精度，基于无网格压缩感知技术，研究了ULA和SLA下的相参信源角度估计问题，分别提出计算有效的向量化ANM和简化DPM的解相干角度估计方法；针对压缩采样场景下非圆信号的DOA估计问题，联合利用协方差和伪协方差矩阵结构信息，扩展现有的低秩结构协方差重构理论，提出低秩Toeplitze-Hankel协方差重构方法；研究了任意阵下的一维DOA估计问题，提出了基于Jacobi-Angle近似的流行分离技术，是的现有ANM和地址结构协方差重构理论技术可以被推广到任意阵列场景。仿真验证所提方法在复杂环境下能实现高精度DOA估计。.为拓展无网格压缩感知技术在二维DOA估计中的应用，充分考虑加性噪声、有限快拍和维度提升所致计算成本剧增的影响，通过充分利用二阶统计量的结构信息，提出去冗余度变换以挖掘矩阵内在具有结构特性的特征，并将其分别应用到L型阵列和双基地MIMO体制以提出计算有效的无网格DOA估计方法。.研究了色噪声条件下离网格DOA估计方法，实现离网格压缩感知理论在色噪声条件下的拓展。从高斯\空间色噪声和高效计算速率角度考虑，构建离网格稀疏表示模型，采用分布交替迭代优化算法求解已划分网格角度及其修正角度。所提三种离网格DOA估计方法在粗网格划分下实现了精细角度的修正，较在网格DOA估计精度有所提升。