基于稀疏和低秩恢復(fù)的穩(wěn)健DOA估計(jì)方法
doi: 10.11999/JEIT190263
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大連大學(xué)信息工程學(xué)院 大連 116622
Sparse and Low Rank Recovery Based Robust DOA Estimation Method
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College of Information Engineering, Dalian University, Dalian 116622, China
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摘要:
該文針對(duì)有限次采樣導(dǎo)致傳統(tǒng)波達(dá)方向角(DOA)估計(jì)算法存在較大估計(jì)誤差的問題，提出一種基于稀疏低秩分解(SLRD)的穩(wěn)健DOA估計(jì)方法。首先，基于低秩矩陣分解方法，將接收信號(hào)協(xié)方差矩陣建模為低秩無噪?yún)f(xié)方差及稀疏噪聲協(xié)方差矩陣之和；而后基于低秩恢復(fù)理論，構(gòu)造關(guān)于信號(hào)和噪聲協(xié)方差矩陣的凸優(yōu)化問題；再者構(gòu)建關(guān)于采樣協(xié)方差矩陣估計(jì)誤差的凸模型，并將此凸集顯式包含進(jìn)凸優(yōu)化問題以改善信號(hào)協(xié)方差矩陣估計(jì)性能進(jìn)而提高DOA估計(jì)精度及穩(wěn)健性；最后基于所得最優(yōu)無噪聲協(xié)方差矩陣，利用最小方差無畸變響應(yīng)(MVDR)方法實(shí)現(xiàn)DOA估計(jì)。此外，基于采樣協(xié)方差矩陣估計(jì)誤差服從漸進(jìn)正態(tài)分布的統(tǒng)計(jì)特性，該文推導(dǎo)了一種誤差參數(shù)因子選取準(zhǔn)則以較好重構(gòu)無噪聲協(xié)方差矩陣。數(shù)值仿真表明，與傳統(tǒng)常規(guī)波束形成(CBF)、最小方差無畸變響應(yīng)(MVDR)、傳統(tǒng)多重信號(hào)分類(MUSIC)及基于稀疏低秩分解的增強(qiáng)拉格朗日乘子(SLD-ALM)算法相比，有限次采樣條件下所提算法具有較高DOA估計(jì)精度及較好穩(wěn)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 誤差參數(shù)對(duì)算法重構(gòu)性能影響
誤差參數(shù)($\eta $) 理想${R_{\rm s} }$對(duì)角線均值 理想$R$對(duì)角線均值 重構(gòu)${R_{\rm s} }$對(duì)角線均值 重構(gòu)$R$對(duì)角線均值 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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