| Citation: | Hongyan WANG, Ruonan YU. Sparse and Low Rank Recovery Based Robust DOA Estimation Method[J]. Journal of Electronics & Information Technology, 2020, 42(3): 589-596. doi: 10.11999/JEIT190263
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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.
|
GUO Muran, ZHANG Y D, and CHEN Tao. DOA estimation using compressed sparse array[J]. IEEE Transactions on Signal Processing, 2018, 66(15): 4133–4146. doi: 10.1109/TSP.2018.2847645
|
|
ZHENG Guimei. DOA estimation in MIMO radar with non-perfectly orthogonal waveforms[J]. IEEE Communications Letters, 2017, 21(2): 414–417. doi: 10.1109/LCOMM.2016.2622691
|
|
CAPON J. High-resolution frequency-wavenumber spectrum analysis[J]. Proceedings of the IEEE, 1969, 57(8): 1408–1418. doi: 10.1109/PROC.1969.7278
|
|
ZHU Shaohao, YANG Kunde, MA Yuanliang, et al. Robust minimum variance distortionless response beamforming using subarray multistage processing for circular hydrophone arrays[C]. 2016 Techno-Ocean, Kobe, Japan, 2016: 692–696. doi: 10.1109/Techno-Ocean.2016.7890744.
|
|
李立欣, 白童童, 张会生, 等. 改进的双约束稳健Capon波束形成算法[J]. 电子与信息学报, 2016, 38(8): 2014–2019. doi: 10.11999/JEIT151213
LI Lixin, BAI Tongtong, ZHANG Huisheng, et al. Improved double constraint robust capon beamforming algorithm[J]. Journal of Electronics &Information Technology, 2016, 38(8): 2014–2019. doi: 10.11999/JEIT151213
|
|
VAN TREES H L. Optimum Array Processing: Part IV of Detection, Estimation and Modulation Theory[M]. New York: Wiley-Interscience, 2002.
|
|
LIAO Bin, GUO Chongtao, HUANG Lei, et al. Matrix completion based direction-of-arrival estimation in nonuniform noise[C]. 2016 IEEE International Conference on Digital Signal Processing, Beijing, China, 2016: 66–69.
|
|
SCHMIDT R. Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas and Propagation, 1986, 34(3): 276–280. doi: 10.1109/TAP.1986.1143830
|
|
HE Shun, YANG Zhiwei, and LIAO Guisheng. DOA estimation of wideband signals based on iterative spectral reconstruction[J]. Journal of Systems Engineering and Electronics, 2017, 28(6): 1039–1045. doi: 10.21629/JSEE.2017.06.01
|
|
GU Yujie and LESHEM A. Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation[J]. IEEE Transactions on Signal Processing, 2012, 60(7): 3881–3885. doi: 10.1109/TSP.2012.2194289
|
|
陈沛, 赵拥军, 刘成城. 基于稀疏重构的共形阵列稳健自适应波束形成算法[J]. 电子与信息学报, 2017, 39(2): 301–308. doi: 10.11999/JEIT160436
CHEN Pei, ZHAO Yongjun, and LIU Chengcheng. Robust adaptive beamforming algorithm for conformal arrays based on sparse reconstruction[J]. Journal of Electronics &Information Technology, 2017, 39(2): 301–308. doi: 10.11999/JEIT160436
|
|
HU Rui, FU Yuli, CHEN Zhen, 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
|
|
HUANG Weibin and LI Hui. An improved DOA estimation algorithm based on sparse reconstruction[C]. The 11th International Symposium on Antennas, Propagation and EM Theory, Guilin, China, 2016: 621–625.
|
|
GU Yujie, GOODMAN N A, HONG Shaohua, et al. Robust adaptive beamforming based on interference covariance matrix sparse reconstruction[J]. Signal Processing, 2014, 96: 375–381. doi: 10.1016/j.sigpro.2013.10.009
|
|
HUANG Lei, ZHANG Jing, XU Xu, et al. Robust adaptive beamforming with a novel interference-plus-noise covariance matrix reconstruction method[J]. IEEE Transactions on Signal Processing, 2015, 63(7): 1643–1650. doi: 10.1109/tsp.2015.2396002
|
|
韦娟, 计永祥, 牛俊儒. 一种新的稀疏重构的DOA估计算法[J]. 西安电子科技大学学报: 自然科学版, 2018, 45(5): 13–18. doi: 10.3969/j.issn.1001-2400.2018.05.003
WEI Juan, JI Yongxiang, and NIU Junru. Novel algorithm for DOA estimation based on the sparse reconstruction[J]. Journal of Xidian University:Natural Science, 2018, 45(5): 13–18. doi: 10.3969/j.issn.1001-2400.2018.05.003
|
|
CHEN Yong, WANG Fang, WAN Jianwei, et al. Sparse and low-rank decomposition of covariance matrix for efficient DOA estimation[C]. The 9th IEEE International Conference on Communication Software and Networks, Guangzhou, China, 2017: 957–961.
|
|
WANG Xianpeng, ZHU Yanghui, HUANG Mengxing, et al. Unitary matrix completion-based DOA estimation of noncircular signals in nonuniform noise[J]. IEEE Access, 2019, 7: 73719–73728. doi: 10.1109/ACCESS.2019.2920707
|
|
CANDES E J and PLAN Y. Matrix completion with noise[J]. Proceedings of the IEEE, 2010, 98(6): 925–936. doi: 10.1109/jproc.2009.2035722
|
|
HE Zhenqing, SHI Zhiping, and HUANG Lei. Covariance sparsity-aware DOA estimation for nonuniform noise[J]. Digital Signal Processing, 2014, 28: 75–81. doi: 10.1016/j.dsp.2014.02.013
|
|
BLANCHARD P and BRÜNING E. Constrained Minimization Problems (Method of Lagrange Multipliers)[M]. BLANCHARD P and BRÜNING E. Mathematical Methods in Physics. Cham: Birkhäuser, 2015: 537–546.
|
|
LEE S, YOON Y J, LEE J E, et al. Two-stage DOA estimation method for low SNR signals in automotive radars[J]. IET Radar, Sonar & Navigation, 2017, 11(11): 1613–1619. doi: 10.1049/iet-rsn.2017.0221
|
|
TIAN Ye, SUN Xiaoying, and ZHAO Shishun. DOA and power estimation using a sparse representation of second-order statistics vector and
|
|
HU Yao, ZHANG Debing, YE Jieping, et al. Fast and accurate matrix completion via truncated nuclear norm regularization[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(9): 2117–2130. doi: 10.1109/tpami.2012.271
|
|
MALIOUTOV D, ÇETIN 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
|
|
WRIGHT J, GANESH A, RAO S, et al. Robust principal component analysis: Exact recovery of corrupted low-rank matrices[J]. arXiv: 0905.0233, 2009.
|
|
HAN Le and LIU Xiaolan. Convex relaxation algorithm for a structured simultaneous low-rank and sparse recovery problem[J]. Journal of the Operations Research Society of China, 2015, 3(3): 363–379. doi: 10.1007/s40305-015-0089-8
|
|
WANG Xianpeng, WANG Luyun, LI Xiumei, et al. Nuclear norm minimization framework for DOA estimation in MIMO radar[J]. Signal Processing, 2017, 135: 147–152. doi: 10.1016/j.sigpro.2016.12.031
|
|
LUO Xiaoyu, FEI Xiaochao, GAN Lu, et al. Direction-of-arrival estimation using an array covariance vector and a reweighted norm[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2015, E98.A(9): 1964–1967. doi: 10.1587/transfun.E98.A.1964
|
|
LIAO Bin, GUO Chongtao, and SO H. Direction-of-arrival estimation in nonuniform noise via low-rank matrix decomposition[C]. The 22nd International Conference on Digital Signal Processing, London, UK, 2017: 1–4.
|
|
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
|
|
HORN R A and JOHNSON C R. Matrix Analysis[M]. Cambridge, UK: Cambridge University Press, 1985: 1-162.
|
|
ARLOT S and CELISSE A. A survey of cross-validation procedures for model selection[J]. Statistics Surveys, 2010, 4: 40–79. doi: 10.1214/09-SS054
|
|
DAS A. Theoretical and experimental comparison of off-grid sparse Bayesian direction-of-arrival estimation algorithms[J]. IEEE Access, 2017, 5: 18075–18087. doi: 10.1109/ACCESS.2017.2747153
|
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