Sparse and Low Rank Recovery Based Robust DOA Estimation Method
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摘要:
该文针对有限次采样导致传统波达方向角(DOA)估计算法存在较大估计误差的问题，提出一种基于稀疏低秩分解(SLRD)的稳健DOA估计方法。首先，基于低秩矩阵分解方法，将接收信号协方差矩阵建模为低秩无噪协方差及稀疏噪声协方差矩阵之和；而后基于低秩恢复理论，构造关于信号和噪声协方差矩阵的凸优化问题；再者构建关于采样协方差矩阵估计误差的凸模型，并将此凸集显式包含进凸优化问题以改善信号协方差矩阵估计性能进而提高DOA估计精度及稳健性；最后基于所得最优无噪声协方差矩阵，利用最小方差无畸变响应(MVDR)方法实现DOA估计。此外，基于采样协方差矩阵估计误差服从渐进正态分布的统计特性，该文推导了一种误差参数因子选取准则以较好重构无噪声协方差矩阵。数值仿真表明，与传统常规波束形成(CBF)、最小方差无畸变响应(MVDR)、传统多重信号分类(MUSIC)及基于稀疏低秩分解的增强拉格朗日乘子(SLD-ALM)算法相比，有限次采样条件下所提算法具有较高DOA估计精度及较好稳健性能。
Abstract:Focusing on the problem of rather large estimation error in the traditional Direction Of Arrival (DOA) estimation algorithm induced by finite subsampling, a robust DOA estimation method based on Sparseand Low Rank Decomposition (SLRD) is proposed in this paper. Following the low-rank matrix decomposition method, the received signal covariance matrix is firstly modeled as the sum of the low-rank noise-free covariance matrix and sparse noise covariance one. After that, the convex optimization problem associated with the signal and noise covariance matrix is constructed on the basis of the low rank recovery theory. Subsequently, a convex model of the estimation error of the sampling covariance matrix can be formulated, and this convex set is explicitly included into the convex optimization problem to improve the estimation performance of signal covariance matrix such that the estimation accuracy and robustness of DOA can be enhanced. Finally, with the obtained optimal noiseless covariance matrix, the DOA estimation can be implemented by employing the Minimum Variance Distortionless Response (MVDR) method. In addition, exploiting the statistical characteristics of the sampling covariance matrix estimation error subjecting to the asymptotic normal distribution, an error parameter factor selection criterion is deduced to reconstruct the noise-free covariance matrix preferably. Compared with the traditional Conventional BeamForming (CBF), Minimum Variance Distortionless Response(MVDR), MUltiple SIgnal Classification (MUSIC) and Sparse and Low-rank Decomposition based Augmented Lagrange Multiplier(SLD-ALM) algorithms, numerical simulations show that the proposed algorithm has higher DOA estimation accuracy and better robustness performance under finite sampling snapshot.
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Key words:
- Direction Of Arrival (DOA) /
- Low rank recovery /
- Sparse /
- Convex optimization
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表 1 误差参数对算法重构性能影响
误差参数($\eta $) 理想${R_{\rm s} }$对角线均值 理想$R$对角线均值 重构${R_{\rm s} }$对角线均值 重构$R$对角线均值 0.1 6.3246 7.4181 6.3110 7.3918 1 6.3246 7.3384 5.9738 7.0775 4 6.3246 7.3271 5.2290 6.2905 8 6.3246 7.3012 4.1855 5.2388 12 6.3246 7.2275 3.0957 4.1583 16 6.3246 7.3268 2.1294 3.1999 19 6.3246 7.3724 1.3133 2.4336 
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