基于低秩矩阵近似的鲁棒DOA估计方法

针对非均匀噪声背景下传统非离散化方法在少快拍条件下波达方向（DOA）估计性能恶化的问题, 提出基于原子范数最小化和零化滤波器的非离散化参数估计方法. 该方法利用参数空间连续性构建基于原子集合的阵列信号稀疏表示模型, 将信号协方差矩阵的恢复问题转化为原子${\ell _0}$范数最小化问题. 基于信号协方差矩阵的厄米特托普利兹结构和低秩特性, 将原子${\ell _0}$范数最小化问题转化为实际可解的基于低秩矩阵近似的半定规划问题, 从而恢复信号协方差矩阵. 根据零化滤波理论通过求解零化滤波器系数获取DOA参数估计. 仿真结果表明, 在非均匀噪声和少快拍同时存在条件下, 该方法比现有同类方法具有更高的估计精度和鲁棒性. 在不同最大噪声功率比条件下，本文方法的均方根误差比现有方法平均减小59.4%. 

Low-Rank Matrix Approximation Based Method for DOA Estimation under Nonuniform Noise Background

To solve the performance degrade problem of DOA estimation with few snapshots under nonuniform noise in the traditional discretization free methods, a discretization free parameter estimation method was proposed based on atomic norm minimization and annihilation filter. Firstly, the continuity of parameter space was exploited to construct a sparse representation model of array signal based on atom gathering situation, converting the signal covariance matrix recovery into the atomic norm minimization problem. Then, making full use of the Hermit Toeplitz structure and low-rank characteristics of the signal covariance matrix, the atomic norm minimization problem was transformed into a low-rank matrix approximation based practically solvable semi-definite programming problem. Thereby, the signal covariance matrix was restored. Finally, the annihilating filter coefficients were solved based on the annihilating filter theory to carry out DOA parameter estimation. Simulation results show that the proposed method can provide higher estimation accuracy and more robustness than existing similar methods under the condition of non-uniform noise and few snapshots. The root mean sguare error of this method was reduced by 59.4% on average compared with existing methods, under different maximum noise power ratio conditions.