基于矩阵补全的二阶统计量重构DOA估计方法

王洪雁; 房云飞; 裴炳南

doi:10.11999/JEIT170826

基于矩阵补全的二阶统计量重构DOA估计方法

doi: 10.11999/JEIT170826

基金项目:

国家自然科学基金(61301258, 61271379)，中国博士后科学基金(2016M590218)

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- 被引次数: 0
出版历程
- 收稿日期: 2017-08-23
- 修回日期: 2018-01-08
- 刊出日期: 2018-06-19

Matrix Completion Based Second Order Statistic Reconstruction DOA Estimation Method

Funds:

The National Natural Science Foundation of China (61301258, 61271379), China Postdoctoral Science Foundation (2016M590218)

摘要

摘要: 该文针对传统波达方向角(DOA)估计算法在非均匀噪声下角度估计精度差及分辨率低的问题，基于矩阵补全理论，提出一种二阶统计量域下加权L1(MC-WLOSRSS)稀疏重构DOA估计算法。首先，基于矩阵补全方法，引入弹性正则化因子将接收信号协方差矩阵重构为无噪声协方差矩阵；而后在二阶统计量域下通过矩阵求和平均将无噪声协方差矩阵多矢量问题转化为单矢量问题；最后利用稀疏重构加权L1范数实现DOA参数估计。数值仿真表明，与传统MUSIC, IL1-SRACV, L1-SVD子空间算法及稀疏重构加权L1算法相比，所提算法能显著抑制非均匀噪声影响，具有较好DOA估计性能，且在低信噪比条件下，亦具有较高估计精度和分辨力。
- 波达方向 /
- 非均匀噪声 /
- 矩阵补全 /
- 二阶统计量 /
- 加权L1范数
Abstract: Focusing on the problem of poor accuracy and low resolution of traditional Direction Of Arrival (DOA) estimation algorithm in the presence of non-uniform noise, based on the Matrix Complement theory, a Weighted L1 Sparse Reconstruction DOA estimation algorithm is developed under the Second-order Statistical domain (MC-WLOSRSS) in this paper. Following the matrix completion approach, the regularization factor is firstly introduced to reconstruct the signal covariance matrix reconstruction as a noise-free covariance matrix. After that, the multi-vector problem of the noise-free covariance matrix can be transformed into a single vector one by exploiting sum-average operation for matrix in the second-order statistical domain. Finally, the DOA can be complemented by employing the sparse reconstruction weighted L1 norm. Numerical simulations show that the proposed algorithm outperforms the traditional DOA algorithms such as MUltiple SIgnal Classification (MUSIC), Improved L1-SRACV (IL1-SRACV), L1-norm-Singular Value Decomposition (L1-SVD) subspace and sparse reconstruction weighted L1 methods in the following respects: suppressing the influence of the non-uniform noise significantly, bettering DOA estimation performance, as well as improving estimation accuracy and resolution with low Signal-Noise Ratio (SNR).
- Direction Of Arrival (DOA) /
- Non-uniform noise /
- Matrix Completion (MC) /
- Second-order statistics /
- Weighted L1 norm

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参考文献(26)

SCHMIDT R. Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas Propagation, 1986, 34(3): 276-280. doi: 10.1109/TAP.1986. 1143830.

VAN TREES H L. Optimum Array Processing: Part IV of Detection, Estimation and Modulation Theory[M]. New York, NY, USA: John Wiley Sons, 2002: 917-1317.

LIAO B, HUANG L, GUO C, et al. New approaches to direction-of-arrival estimation with sensor arrays in unknown nonuniform noise[J]. IEEE Sensors Journal, 2016, 16(24): 8982-8989. doi: 10.1109/JSEN.2016.2621057.

TIAN Y, SHI H, and XU H. DOA estimation in the presence of unknown nonuniform noise with coprime array[J]. Electronics Letters, 2016, 53(2): 113-115. doi: 10.1049/ el.2016.3944.

HU R, FU Y, CHEN Z, et al. Robust DOA estimation via sparse signal reconstruction with impulsive noise[J]. IEEE Communications Letters, 2017, 21(6): 1333-1336. doi: 10.1109/LCOMM.2017.2675407.

MALIOUTOV D, CETIN M, and WILLSKY A S. A sparse signal reconstruction perspective for source localization with sensor arrays[J]. IEEE Transactions on Signal Processing, 2005, 53(8): 3010-3022. doi: 10.1109/TSP.2005.850882.

PAL P and VAIDYANATHAN P P. A grid-less approach to underdetermined direction of arrival estimation via low rank matrix denoising[J]. IEEE Signal Processing Letters, 2014, 21(6): 737-741. doi: 10.1109/LSP.2014.2314175.

PESAVENTO M and GERSHMAN A B. Maximum- likelihood direction-of-arrival estimation in the presence of unknown nonuniform noise[J]. IEEE Transactions on Signal Processing, 2002, 49(7): 1310-1324. doi: 10.1109/78.928686.

HE Z Q, SHI Z P, and HUANG L. Covariance sparsity-aware DOA estimation for nonuniform noise[J]. Digital Signal Processing, 2014, 28(1): 75-81. doi: 10.1016/j.dsp.2014.02. 013.

YIN J H and CHEN T Q. Direction-of-arrival estimation using a sparse representation of array covariance vectors[J]. IEEE Transactions on Signal Processing, 2011, 59(9): 4489-4493. doi: 10.1109/TSP.2011.2158425.

LIAO B, GUO C, HUANG L, et al. Matrix completion based direction-of-arrival estimation in nonuniform noise[C]. IEEE International Conference on Digital Signal Processing, Beijing, China, 2017: 66-69. doi: 10.1109/ICDSP.2016. 7868517.

CANDES E J and RECHT B. Exact matrix completion via convex optimization[J]. Foundations of Computational Mathematics, 2009, 9(6): 717-772. doi: 10.1007/s10208-009- 9045-5.

CANDES E J and PLAN Y. Matrix completion with noise[J]. Proceedings of the IEEE, 2009, 98(6): 925-936. doi: 10.1109 /JPROC.2009.2035722.

JIANG X, ZHONG Z, LIU X, et al. Robust matrix completion via alternating projection[J]. IEEE Signal Processing Letters, 2017, 24(5): 579-583. doi: 10.1109/LSP. 2017.2685518.

CANDES E J, WAKIN M B, and BOYD S P. Enhancing sparsity by reweighted L1 minimization[J]. Journal of Fourier Analysis Applications, 2008, 14(5): 877-905. doi: 10.1007/ s00041-008-9045-x.

方庆园, 韩勇, 金铭, 等. 基于噪声子空间特征值重构的DOA估计算法[J]. 电子与信息学报, 2014, 36(12): 2876-2881. doi: 10.3724/SP.J.1146.2013.02014.

FANG Qingyuan, HAN Yong, JIN Ming, et al. DOA estimation based on eigenvalue reconstruction of noise subspace[J]. Journal of Electronics Information Technology, 2014, 36(12): 2876-2881. doi: 10.3724/SP.J.1146.2013.02014.

SUN S and PETROPULU A P. Waveform design for MIMO radars with matrix completion[J]. IEEE Journal of Selected Topics in Signal Processing, 2015, 9(8): 1400-1414. doi: 10.1109/JSTSP.2015.2469641.

CAI J F, CANDES E J, and SHEN Z. A singular value thresholding algorithm for matrix completion[J]. SIAM Journal on Optimization, 2010, 20(4): 1956-1982. doi: 10.1137/080738970.

HOR R A and JOHNSON C R. Matrix Analysis[M]. Cambridge, U.K: Cambridge University Press, 1985: 1-162.

冯明月, 何明浩, 徐璟, 等. 低信噪比条件下宽带欠定信号高精度DOA估计[J]. 电子与信息学报, 2017, 39(6): 1340-1347. doi: 10.11999/JEIT160921.

FENG Mingyue, HE Minghao, XU Jing, et al. High accuracy DOA estimation under low SNR condition for wideband underdetermined signals[J]. Journal of Electronics Information Technology, 2017, 39(6): 1340-1347. doi: 10.11999/JEIT160921.

OTTERSTEN B, STOICA P, and ROY R. Covariance matching estimation techniques for array signal processing applications[J]. Digital Signal Processing, 1998, 8(3): 185-210. doi: 10.1006/dspr.1998.0316.

TIAN Y, SUN X, and ZHAO S. DOA and power estimation using a sparse representation of second-order statistics vector and l0-norm approximation[J]. Signal Processing, 2014, 105(12): 98-108. doi: 10.1016/j.sigpro.2014.05.014.

LOBO M, VANDENBERGHE L, BOYD S, et al. Application of second-order cone programming[J]. Linear Algebra and its Applications, 1998, 284(1/3): 193-228. doi: 10.1016/S0024- 3795(98)10032-0.

LIAO B, CHAN S C, HUANG L, et al. Iterative methods for subspace and DOA estimation in nonuniform noise[J]. IEEE Transactions on Signal Processing, 2016, 64(12): 3008-3020. doi: 10.1109/TSP.2016.2537265.

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