Jensen-Bregman LogDet散度在正定矩阵流形上的水声传感器阵列DOA估计

doi:10.12382/bgxb.2024.0225

摘要/Abstract

摘要：

由于传统的欧式空间方法无法有效反映协方差矩阵之间的差异,而导致信息损失,为了解决这一问题,提出了一种基于詹森-布雷格曼洛格德特散度(Jensen-Bregman LogDet divergence)的阵列波达方向(Direction of Arrival, DOA)估计方法,将目标方位估计问题转化为矩阵流形上两点间的几何距离问题,揭示了方位估计与黎曼空间矩阵流形的映射规律,从而得到了几何距离最小值处对应的角度即为目标入射角度的结论,并通过构建两个强鲁棒性的矩阵流形,完成了矩阵信息几何DOA估计理论模型的建立。通过模拟仿真与实测数据对所新方法进行了验证。验证结果表明:与现有的最小方差无失真响应算法和多信号分类算法相比,新方法在低信噪比环境下拥有更好的估计精度;新方法的应用具有一定的实际意义和应用前景,可以为海洋防御及民用领域中的水下目标方位估计等提供坚实的技术支持。

关键词: 海洋, 阵列波达方向估计, 詹森-布雷格曼洛格德特散度, 矩阵流形, 矩阵信息几何

Abstract:

Because the covariance matrix is a nonlinear space,the traditional method using Euclidean space does not reflect the difference between covariance matrices,resulting in information loss.To address this issue,a DOA estimation method based on Jensen-Bregman LogDet divergence (JBLD) is proposed,which transforms the target orientation estimation problem into the geometric distance problem between two points on the matrix manifold.It is concluded that the angle corresponding to the minimum geometric distance is the incidence angle of target,and two robust matrix manifolds are constructed to complete the establishment of matrix information DOA estimation theory model.The proposed method is verified by simulation and measured data.The results show that the proposed method has better estimation accuracy in low SNR environment than the existing MVDR and MUSIC algorithms.The proposed method has specific practical significance and application prospects,and can provide a solid technical support for underwater target positioning in marine defence and the civil field.

Key words: ocean, direction of arrival estimation, Jensen-Bregman LogDet divergence, matrix manifold, matrix information geometry

中图分类号:

TN911

王柱颖, 闫永胜, 张红伟, 锁健, 何轲, 王海燕. Jensen-Bregman LogDet散度在正定矩阵流形上的水声传感器阵列DOA估计[J]. 兵工学报, 2025, 46(2): 240225-.

WANG Zhuying, YAN Yongsheng, ZHANG Hongwei, SUO Jian, HE Ke, WANG Haiyan. DOA Estimation for Underwater Acoustic Sensor Arrays Using Jensen-Bregman LogDet Divergence on Positive Definite Matrix Manifolds[J]. Acta Armamentarii, 2025, 46(2): 240225-.

图/表 9

图1 不同角度对应的几何距离

Fig.1 Geometric distances corresponding to different angles

图2 多个入射源对应的几何距离

Fig.2 Geometric distance corresponding to multiple incident sources

图3 不同信噪比时各算法的DOA估计均方根误差

Fig.3 RMSEs of DOA estimation using different algorithms versus SNR

图4 不同快拍数时各算法的DOA估计均方根误差

Fig.4 RMSEs of DOA estimation using different algorithms versus the number of snapshots

图5 不同阵元数时各算法的DOA估计均方根误差

Fig.5 RMSEs of DOA estimation of different algorithms versus the number of array elements

图6 消声水池试验示意图

Fig.6 Schematic diagram of anechoic pool experiment

图7 水池试验设备

Fig.7 Pool experimental equipment

图8 单阵元接收数据的时域和频域分析

Fig.8 Time domain and frequency domain analysis of single array element received data

图9 均匀线列阵接收数据的DOA估计

Fig.9 DOA estimation of received data from ULA

参考文献 25

[1]	SUN S B, QIN S S, HAO Y, et al. Underwater acoustic localization of the black box based on generalized second-order time difference of arrival (GSTDOA)[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 59(9):7245-7255.
[2]	ZHOU A L, LI X Y, ZHANG W, et al. A novel cross-attention fusion-based joint training framework for robust underwater acoustic signal recognition[J]. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61:1-16.
[3]	高晓峰, 栗苹, 李国林, 等. 基于互协方差的L型嵌套阵列二维波达方向估计[J]. 兵工学报, 2019, 40(6):1207-1215. doi: 10.3969/j.issn.1000-1093.2019.06.011
	GAO X F, LI P, LI G L, et al. L-type nested array two-dimensional direction of reach estimation based on cross-covariance[J]. Acta Armamentarii, 2019, 40(6):1207-1215. (in Chinese)
[4]	LIU A F, SHI S G, WANG X Y, et al. Robust DOA estimation method for underwater acoustic vector sensor array in presence of ambient noise[J]. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61:1-14.
[5]	单泽彪, 常立民, 刘小松, 等. 基于自然对数复合函数近似l₀范数的DOA估计[J]. 兵工学报, 2023, 44(5):1521-1528.
	SHAN Z B, CHANG L M, LIU X S, et al. DOA estimation based on approximate l0 norm of natural logarithm composite function[J]. Acta Armamentarii, 2023, 44(5):1521-1528. (in Chinese)
[6]	LI W J, XU X, HUANG X Y, et al. Direction-of-arrival estimation for coherent signals exploiting moving co-prime array[J]. IEEE Signal Processing Letters, 2023, 30:304-308.
[7]	ZHU F Y, CHAI S R, ZOU Y F, et al. An efficient and accurate RCS reconstruction technique using adaptive TLS-ESPRIT algorithm[J]. IEEE Antennas and Wireless Propagation Letters, 2024, 23(1):49-53.
[8]	YANG Z. Nonasymptotic performance analysis of ESPRIT and spatial-smoothing ESPRIT[J]. IEEE Transactions on Information Theory, 2022, 69(1):666-681.
[9]	YANG Z, CHEN X Y, WU X M. A robust and statistically efficient maximum-likelihood method for DOA estimation using sparse linear arrays[J]. IEEE Transactions on Aerospace and Electronic Systems, 2023, 59(5):6798-6812.
[10]	MENG D D, WANG X P, HUANG M X, et al. Robust weighted subspace fitting for DOA estimation via block sparse recovery[J]. IEEE Communications Letters, 2019, 24(3):563-567.
[11]	TUCKER D, ZHAO S, POTTER C. Maximum likelihood estimation in mixed integer linear models[J]. IEEE Signal Processing Letters, 2023, 30:1557-1561. doi: 10.1109/lsp.2023.3324833 pmid: 37981947
[12]	SCHENCK D, LUBBE K, TRINH-HOANG M, et al. Partially relaxed orthogonal least squares weighted subspace fitting direction-of-arrival estimation[C]// Proceedings of IEEE International Conference on Acoustics,Speech and Signal Processing. Singapore:IEEE, 2022:5028-5032.
[13]	ZHAO J W, LIU J, GAO F F, et al. Gridless compressed sensing based channel estimation for UAV wideband communications with beam squint[J]. IEEE Transactions on Vehicular Technology, 2021, 70(10):10265-10277.
[14]	HUANG Z K, WANG W, ZHANG B, et al. Measurement matrix design based on compressed sensing for DOA estimation[C]// Proceedings of 2018 14th IEEE International Conference on Signal Processing. Beijing,China: IEEE, 2018:167-171.
[15]	MALIOUTOV D, CETIN M, WILLSKY S. A sparse signal reconstruction perspective for source localization with sensor arrays[J]. IEEE Transactions on Signal Processing, 2005, 53(8):3010-3022.
[16]	COUTINO M, PRIBIC R, LEUS G. Direction of arrival estimation based on information geometry[C]// Proceedings of 2016 IEEE International Conference on Acoustics,Speech and Signal Processing. Shanghai,China: IEEE, 2016:066-3070.
[17]	DONG Y Y, DONG C X, LIU W, et al. Scaling transform based information geometry method for DOA estimation[J]. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(6):3640-3650.
[18]	WU H, CHENG Y Q, CHEN X X, et al. Power spectrum information geometry-based radar target detection in heterogeneous clutter[J]. IEEE Transactions on Geoscience and Remote Sensing, 2024, 62:1-16.
[19]	ARNAUDON M, BARBARESCO F, YANG L. Riemannian medians and means with applications to radar signal processing[J]. IEEE Journal of Selected Topics in Signal Processing, 2013, 7(4):595-604.
[20]	WANG J L, ZHANG C X, AHN C K, et al. Continuous-discrete cubature Kalman filter with Log-Euclidean metric-based covariance integration[J]. IEEE Transactions on Circuits and Systems II:Express Briefs, 2023, 70(11):4281-4285.
[21]	ZHANG F F, ZHANG T Z, MAO Q R, et al. Geometry guided pose-invariant facial expression recognition[J]. IEEE Transactions on Image Processing, 2020, 29:4445-4460.
[22]	YE S, ZHANG F, GAO F, et al. Fault diagnosis for multilevel converters based on an affine-invariant Riemannian metric autoencoder[J]. IEEE Transactions on Industrial Informatics, 2022, 19(3):2619-2628.
[23]	LIU, Q G, SHAO G G, WANG Y H, et al. Log-euclidean metrics for contrast preserving decolorization[J]. IEEE Transactions on Image Processing, 2017, 26(12):5772-5783. doi: 10.1109/TIP.2017.2745104 pmid: 28858795
[24]	CHERAIAN A, SRA S, BANERJEE A, et al. Jensen-Bregman LogDet divergence with application to efficient similarity search for covariance matrices[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 35(9):2161-2174.
[25]	ZHANG J, ZHANG G H, DAI L R. Frequency-invariant sensor selection for MVDR beamforming in wireless acoustic sensor networks[J]. IEEE Transactions on Wireless Communications, 2022, 21(12):10648-10661.