基于协方差拟合旋转不变子空间信号参数
估计算法的高分辨到达角估计

doi:10.16183/j.cnki.jsjtu.2017.09.019

摘要/Abstract

摘要： 为进行高分辨到达角(DOA)估计的同时避免稀疏类算法的不足，提出了协方差拟合旋转不变子空间信号参数估计(ESPRIT)算法.首先将协方差拟合准则转换成半正定规划问题，利用凸优化进行求解，得到更接近理论值的信号协方差矩阵；然后对估计的信号协方差矩阵进行特征分解，利用信号子空间和噪声子空间特征值的差异估计信源个数；最后利用子空间旋转不变性反解出未知DOA.仿真实验从DOA估计精度、分辨率等方面验证了该算法的有效性，较传统ESPRIT算法具有更高的DOA估计分辨率并且受相干信源影响小；与稀疏类算法相比，不依赖先验信息以及避免了网格失配问题.

关键词: , 到达角估计, 协方差拟合, 高分辨, 旋转不变子空间信号参数估计算法

Abstract: Spare representation based direction of arrival (DOA) estimation algorithms have the merits of high resolution and good adaptability to coherent signals, while they suffer from the shortages of depending on prior information and offgrid problem. In order to get high DOA estimation resolution and avoid the shortcomings of spare representation algorithms, covariance fitting estimation of signal parameters by rotational invariance technique (ESPRIT) algorithm is proposed in this paper. Firstly, covariance fitting criterion is converted into a semidefinite programming problem solved by convex optimization. As a result, a signal covariance matrix which is closer to theoretical value is obtained. Then, eigen decomposition of the estimated signal covariance matrix is conducted and the number of signals is estimated through the differences between eigenvalues of signal subspace and noise subspace. Finally, rotational invariance technique of signal subspace is used to estimate DOA. Simulation experiments have proved the validity of the method. Compared with traditional ESPRIT algorithm, the proposed algorithm has higher DOA estimation resolution and is slightly affected by coherent signals. It is also superior to spare representation algorithms for independence of prior information and avoidance of the offgrid problem.

Key words: direction of arrival (DOA) estimation, covariance fitting, high resolution, estimation of signal parameters by rotational invariance technique (ESPRIT)

中图分类号:

TN 911.7

冯明月，何明浩，韩俊，郁春来. 基于协方差拟合旋转不变子空间信号参数
估计算法的高分辨到达角估计[J]. 上海交通大学学报（自然版）, 2017, 51(9): 1145-.

FENG Mingyue，HE Minghao，HAN Jun，YU Chunlai. High Resolution Direction of Arrival Estimation Based on
Covariance Fitting Estimation of Signal Parameters by
Rotational Invariance Technique Algorithm[J]. Journal of Shanghai Jiaotong University, 2017, 51(9): 1145-.

参考文献

［1］STOICA P, BABU P, LI J. New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data［J］. IEEE Transactions on Signal Processing, 2011, 59(1): 3547.
［2］毛琳琳，张群飞，黄建国，等. 基于互相关协方差矩阵的改进多重信号分类高分辨波达方位估计方法［J］. 电子与信息学报，2015, 37(8): 18861891.
MAO Linlin, ZHANG Qunfei, HUANG Jianguo, et al. Improved multiple signal classification algorithm for direction of arrival estimation based on covariance matrix of crosscorrelation［J］. Journal of Electronics & Information Technology, 2015, 37(8): 18861891.
［3］CAO R, WANG C, ZHANG X. Twodimensional direction of arrival estimation using generalized ESPRIT algorithm with nonuniform Lshaped array［J］. Wireless Personal Communications， 2015, 84(1): 321339.
［4］LI Y, CHI Y. OfftheGrid line spectrum denoising and estimation with multiple measurement vectors［J］. IEEE Transactions on Signal Processing， 2015, 64(5): 12571269.
［5］CHI Y, SCHARF L L, PEZESHKI A, et al. Sensitivity to basis mismatch in compressed sensing［J］. IEEE Transactions on Signal Processing, 2011, 59(5): 21822196.
［6］ZHANG Y, YE Z, XU X, et al. Offgrid DOA estimation using array covariance matrix and blocksparse Bayesian learning［J］. Signal Processing, 2014, 98(13): 197201.
［7］YANG Z, XIE L, ZHANG C. OffGrid direction of arrival estimation using sparse Bayesian inference［J］. IEEE Transactions on Signal Processing, 2013, 61(1): 3843.
［8］YANG Z, XIE L. Enhancing sparsity and resolution via reweighted atomic norm minimization［J］. IEEE Transactions on Signal Processing, 2015, 64(4): 9951006.
［9］BHASKAR B N, TANG G, RECHT B. Atomic norm denoising with applications to line spectral estimation［J］. IEEE Transactions on Signal Processing, 2013, 61(23): 59875999.
［10］BLU T, DRAGOTTI P L, VETTERLI M, et al. Sparse sampling of signal innovations［J］. IEEE Signal Processing Magazine, 2008, 25(2): 3140.
［11］YANG Z, XIE L. On gridless sparse methods for line spectral estimation from complete and incomplete data［J］. IEEE Transactions on Signal Processing, 2015, 63(12): 31393153.
［12］YANG Z, XIE L, ZHANG C. A discretizationfree sparse and parametric approach for linear array signal processing［J］. IEEE Transactions on Signal Processing, 2014, 62(19): 49594973.
［13］OTTERSTEN B, STOICA P, ROY R. Covariance matching estimation techniques for array signal processing applications［J］. Digital Signal Processing, 1988, 8(3): 185210.
［14］STOICA P, BABU P, LI J. SPICE: A sparse covariancebased estimation method for array processing［J］. IEEE Transactions on Signal Processing, 2011, 59(2): 629639.
［15］RAO B D, HARI K V S. Performance analysis of ESPRIT and TAM in determining the direction of arrival of plane waves in noise［J］. IEEE Transactions on Signal Processing, 1989, 37(12): 19901995.
［16］HE Z, CICHOCKI A, XIE S, et al. Detecting the number of clusters in nway probabilistic clustering［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(11): 20062021.
［17］SAHOO S K, MAKUR A. Signal recovery from random measurements via extended orthogonal matching pursuit［J］. IEEE Transactions on Signal Processing, 2015, 63(10): 25722582.
［18］JING Y, FENG N, SHEN Y. Modified MUSIC estimation for correlated signals with compressive sampling arrays［J］. Journal of Systems Engineering and Electronics, 2014, 25(5): 755759.

[1]	张晏合, 臧月进, 陈渤, 徐铭晟. 基于解耦表征变分自编码机的雷达目标识别算法[J]. 空天防御, 2022, 5(2): 87-93.
[2]	王聚团, 戚晓宁, 黄志明. 水下生产管汇测试技术及其改进研究[J]. 海洋工程装备与技术, 2022, 9(2): 43-49.
[3]	袁振钦, 邹科, 孙亚峰, 刘刚, 屈衍, 李居跃. 基于时域分析法的动态电缆疲劳分析[J]. 海洋工程装备与技术, 2022, 9(2): 50-55.
[4]	王娟, 杨明旺, 郑茂尧, 刘凌云, 赵立君. 高强钢在大型半潜式平台组块建造中的应用[J]. 海洋工程装备与技术, 2022, 9(1): 27-31.
[5]	陈欣, 赵晓磊, 王立坤, 肖德明, 张腾月. 深水大型吸力锚建造技术研究[J]. 海洋工程装备与技术, 2022, 9(1): 32-36.
[6]	尹彦坤, 易涤非. 半潜式生产平台船体结构关键节点工程临界评估[J]. 海洋工程装备与技术, 2022, 9(1): 52-57.
[7]	陈春红, 顾村锋, 胡俊, 杨建超, 吴文. 空中目标分布式ISAR成像仿真技术研究[J]. 空天防御, 2022, 5(1): 12-19.
[8]	MA Qunsheng (马群圣), CEN Xingxing (岑星星), YUAN Junyi (袁骏毅), HOU Xumin (侯旭敏). Word Embedding Bootstrapped Deep Active Learning Method to Information Extraction on Chinese Electronic Medical Record[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(4): 494-502.
[9]	ZHANG Shengfa (张胜发), TANG Na (唐纳), SHEN Guofeng (沈国峰), WANG Han (王悍), QIAO Shan (乔杉). Universal Software Architecture of Magnetic Resonance-Guided Focused Ultrasound Surgery System and Experimental Study[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(4): 471-481.
[10]	安庆升, 孙立东, 武秋生. 碳纤维增强复合材料发射筒设计研究[J]. 空天防御, 2021, 4(2): 13-.
[11]	KONG Xiangqiang (孔祥强), MENG Xiangxi (孟祥熙), LI Jianbo (李见波), SHANG Yanping (尚燕平), CUI Fulin (崔福林) . Comparative Study on Two-Stage Absorption Refrigeration Systems with Different Working Pairs[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(2): 155-162.
[12]	ZHUANG Weimin (庄蔚敏), WANG Pengyue (王鹏跃), AO Wenhong (熬文宏), CHEN Gang (陈刚) . Experiment and Simulation of Impact Response of Woven CFRP Laminates with Different Stacking Angles[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(2): 218-230.
[13]	ZHOU Xuhui (周旭辉), ZHANG Wenguang (张文光), XIE Jie (谢颉). Effects of Micro-Milling and Laser Engraving on Processing Quality and Implantation Mechanics of PEG-Dexamethasone Coated Neural Probe[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(1): 1-9.
[14]	HUANG Ningning (黄宁宁), MA Yixin (马艺馨), ZHANG Mingzhu (张明珠), GE Hao (葛浩), WU Huawei (吴华伟). Finite Element Modeling of Human Thorax Based on MRI Images for EIT Image Reconstruction[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(1): 33-39.
[15]	WANG Xianjin, GAO Xu, YU Kuigang . Fixture Locating Modelling and Optimization Research of Aluminum Alloy Sidewall in a High-Speed Train Body[J]. J Shanghai Jiaotong Univ Sci, 2020, 25(6): 706-713.