﻿ 基于稠密连接网络的单矢量水听器目标方位估计
 舰船科学技术  2024, Vol. 46 Issue (12): 132-139    DOI: 10.3404/j.issn.1672-7649.2024.12.023 PDF

Single vector hydrophone target direction estimation based on densenet
KE Kailei, SUN Delong
Shanghai Marine Electronic Equipment Research Institute, Shanghai 201108, China
Abstract: Consider the problem of bearing estimation as a multi label classification problem, apply dense connected networks to single vector hydrophone target bearing estimation, use second-order statistics widely concerned in classical methods as input to the neural network, and train the neural network using the method of continuously generating training sets. The simulation and lake trial results show that using DenseNet has narrower main lobes and higher azimuth resolution compared to classical methods; When the signal-to-noise ratio of two targets differs by 6 dB or more, the DenseNet has the ability to simultaneously detect two targets that classical methods do not have, and still has excellent azimuth resolution; When the signal-to-noise ratio difference between two targets exceeds 18 dB, the DenseNet gradually losses its ability to detect weak targets.
Key words: densenet     single-vector hydrophone     direction of arrival     azimuth resolution     signal-to-noise ratio
0 引　言

1 经典方法 1.1 单矢量水听器信号模型

 $\left\{\begin{array}{l}p\left(t\right)=\displaystyle \sum _{i=1}^{N}{s}_{i}\left(t\right)+{n}_{p}\left(t\right)，\\ {v}_{x}\left(t\right)=\displaystyle \sum _{i=1}^{N}{s}_{i}\left(t\right)\mathrm{cos}{\theta }_{i}\mathrm{cos}{\phi }_{i}+{n}_{x}\left(t\right)，\\ {v}_{y}\left(t\right)=\displaystyle \sum _{i=1}^{N}{s}_{i}\left(t\right)\mathrm{sin}{\theta }_{i}\mathrm{cos}{\phi }_{i}+{n}_{y}\left(t\right)，\\ {v}_{z}\left(t\right)=\displaystyle \sum _{i=1}^{N}{s}_{i}\left(t\right)\mathrm{sin}{\phi }_{i}+{n}_{z}\left(t\right)。\end{array}\right.$ (1)

 $\left\{\begin{array}{l}p\left(t\right)=\displaystyle \sum _{i=1}^{N}{s}_{i}\left(t\right)+{n}_{p}\left(t\right)，\\ {v}_{x}\left(t\right)=\displaystyle \sum _{i=1}^{N}{s}_{i}\left(t\right)\mathrm{cos}{\theta }_{i}+{n}_{x}\left(t\right)，\\ {v}_{y}\left(t\right)=\displaystyle \sum _{i=1}^{N}{s}_{i}\left(t\right)\mathrm{sin}{\theta }_{i}+{n}_{y}\left(t\right)。\end{array}\right.$ (2)

 $\boldsymbol{x}\left(t\right)=\boldsymbol{A}\cdot \boldsymbol{s}\left(t\right)+\boldsymbol{n}，$ (3)
 $\boldsymbol{x}\left(t\right)={\left[\begin{array}{ccc}p\left(t\right)& {v}_{x}\left(t\right)& {v}_{y}\left(t\right)\end{array}\right]}^{\mathrm{T}}，$ (4)
 $\boldsymbol{A}=\left[\begin{array}{cc}1& 1\\ \mathrm{cos}{\theta }_{1}& \mathrm{cos}{\theta }_{2}\\ \mathrm{sin}{\theta }_{1}& \mathrm{sin}{\theta }_{2}\end{array}\cdots \begin{array}{c}1\\ \mathrm{cos}{\theta }_{i}\\ \mathrm{sin}{\theta }_{i}\end{array}\cdots \begin{array}{c}1\\ \mathrm{cos}{\theta }_{N}\\ \mathrm{sin}{\theta }_{N}\end{array}\right] ，$ (5)
 $\boldsymbol{s}\left(t\right)={\left[\begin{array}{cc}{s}_{1}\left(t\right)& {s}_{2}\left(t\right)\end{array}\cdots {s}_{i}\left(t\right)\cdots {s}_{N}\left(t\right)\right]}^{\mathrm{T}}，$ (6)
 $\boldsymbol{n}={\left[\begin{array}{ccc}{n}_{p}\left(t\right)& {n}_{x}\left(t\right)& {n}_{y}\left(t\right)\end{array}\right]}^{\mathrm{T}} 。$ (7)
1.2 基于声强的单矢量水听器方位估计

 $\boldsymbol{I}\left(t\right)=p\left(t\right)\boldsymbol{v}\left(t\right)。$ (8)

 $\left\{\begin{array}{c}{I}_{x}=\overline {p\left(t\right){v}_{x}\left(t\right)}=\displaystyle \sum _{i=1}^{N}{I}_{i}\left(t\right)\mathrm{cos}{\theta }_{i}，\\ {I}_{y}=\overline {p\left(t\right){v}_{y}\left(t\right)}=\displaystyle \sum _{i=1}^{N}{I}_{i}\left(t\right)\mathrm{sin}{\theta }_{i}。\end{array}\right.$ (9)

 $\left\{\begin{array}{c}{I}_{x}\left(f\right)=p\left(f\right){v}_{x}^{*}\left(f\right)=\displaystyle \sum _{i=1}^{N}{I}_{i}\left(f\right)\mathrm{cos}{\theta }_{i}，\\ {I}_{y}\left(f\right)=p\left(f\right){v}_{y}^{*}\left(f\right)=\displaystyle \sum _{i=1}^{N}{I}_{i}\left(f\right)\mathrm{sin}{\theta }_{i}。\end{array}\right.$ (10)

 $\widehat{\theta }=\text{arctan}\frac{{I}_{y}}{{I}_{x}}。$ (11)

 $\widehat{\theta }\left(f\right)=\text{arctan}\frac{Re\left[{I}_{y}\left(f\right)\right]}{Re\left[{I}_{x}\left(f\right)\right]}。$ (12)

 $\left\{\begin{array}{l}{I}_{p}=\overline{p\left(t\right)p\left(t\right)}=\displaystyle \sum _{i=1}^{N}{I}_{i}\left(t\right)，\\ {I}_{xx}=\overline{{v}_{x}\left(t\right){v}_{x}\left(t\right)}=\displaystyle \sum _{i=1}^{N}{I}_{i}\left(t\right)\mathrm{cos}{\theta }_{i}\mathrm{cos}{\theta }_{i}，\\ {I}_{xy}=\overline{{v}_{x}\left(t\right){v}_{y}\left(t\right)}=\displaystyle \sum _{i=1}^{N}{I}_{i}\left(t\right)\mathrm{cos}{\theta }_{i}\mathrm{sin}{\theta }_{i}，\\ {I}_{yy}=\overline{{v}_{y}\left(t\right){v}_{y}\left(t\right)}=\displaystyle \sum _{i=1}^{N}{I}_{i}\left(t\right)\mathrm{sin}{\theta }_{i}\mathrm{sin}{\theta }_{i}。\end{array}\right.$ (13)

1.3 基于波束形成的单矢量水听器方位估计

 ${P}_{CBF}={a}^{\mathrm{H}}Ra，$ (14)
 ${P}_{MVDR}=\frac{1}{{a}^{\mathrm{H}}{R}^{-1}a} 。$ (15)

 $a\left(\theta \right)={\left[\begin{array}{ccc}1& \mathrm{cos}\theta & \mathrm{sin}\theta \end{array}\right]}^{\mathrm{T}}，$ (16)
 ${\boldsymbol{R}}=\overline {\boldsymbol{x}\left(t\right){\boldsymbol{x}}^{\mathrm{T}}\left(t\right)}=\left[\begin{array}{ccc}{I}_{p}& {I}_{x}& {I}_{y}\\ {I}_{x}& {I}_{xx}& {I}_{xy}\\ {I}_{y}& {I}_{xy}& {I}_{yy}\end{array}\right]。$ (17)

2 基于稠密连接网络的单矢量水听器目标方位估计 2.1 稠密连接网络

 图 1 稠密连接网络结构图 Fig. 1 DenseNet structure diagram
2.2 训练集生成及数据预处理

2.3 训练过程

 图 2 训练损失变化情况 Fig. 2 Changes in train loss
3 仿真及湖试数据结果分析 3.1 仿真数据分析 3.1.1 单目标仿真

 图 3 仿真信号方位估计随信噪比变化历程图 Fig. 3 Diagram of the variation of simulated signal azimuth estimation with signal-to-noise ratio

 图 4 仿真信号方位估计均方根误差随信噪比变化 Fig. 4 The root mean square error of simulated signal direction estimation varies with signal-to-noise ratio
3.1.2 等强度双目标仿真

2个目标信噪比相同，一个目标位于179°，另一个目标随时间变化从0°运动到359°，目标信号种类、矢量水听器采样频率、信号处理时长与单目标仿真时相同。分别用CBF、MVDR、复声强直方图、稠密连接网络这4种方法计算2个等强度目标信噪比为−5 dB、5 dB、15 dB时的时间方位历程图。

 图 5 信噪比为−5 dB的等强度双目标方位估计时间历程图 Fig. 5 Time history of equal intensity dual target direction estimation with a signal-to-noise ratio of -5 dB

 图 6 信噪比为5 dB的等强度双目标方位估计时间历程图 Fig. 6 Time history of equal intensity dual target direction estimation with a signal-to-noise ratio of 5 dB

 图 7 信噪比为15 dB的等强度双目标方位估计时间历程图 Fig. 7 Time history of equal intensity dual target direction estimation with a signal-to-noise ratio of 15 dB

 图 8 使用稠密连接网络估计等强度双目标方位随信噪比变化历程图 Fig. 8 Using DenseNet to estimate the change history of equal strength dual target azimuth with signal-to-noise ratio
3.1.3 不等强度双目标仿真

 图 9 信噪比分别为3 dB和6 dB的双目标方位估计 Fig. 9 Dual target bearing estimation with signal-to-noise ratios of 3 dB and 6 dB

 图 10 信噪比分别为3 dB和9 dB的双目标方位估计 Fig. 10 Dual target bearing estimation with signal-to-noise ratios of 3 dB and 9 dB

 图 11 信噪比分别为3 dB和12 dB的双目标方位估计 Fig. 11 Dual target bearing estimation with signal-to-noise ratios of 3 dB and 12 dB

 图 12 不等强度双目标方位估计单帧结果对比 Fig. 12 Comparison of single frame results for unequal intensity dual target direction estimation

 图 13 弱目标信噪比为0 dB时的不等强度双目标方位估计 Fig. 13 Unequal intensity dual target direction estimation when the signal-to-noise ratio of week targets is 0 dB

 图 14 强目标信噪比为20 dB时的不等强度双目标方位估计 Fig. 14 Unequal intensity dual target direction estimation when the signal-to-noise ratio of strong targets is 20 dB

 图 15 稠密连接网络不等强度双目标方位估计单帧结果对比 Fig. 15 Comparison of single frame results for unequal intensity dual target direction estimation in DenseNet
3.2 湖试数据分析

2020年8月，于莫干山进行了一次矢量水听器目标方位估计试验，目标为电瓶船，未携带声源，先低速航行，后高速机动。信号处理带宽0.8～4 kHz，矢量水听器采样频率12 kHz，每8129个采样点估计一次目标方位。

 图 16 湖试目标方位估计时间历程图 Fig. 16 The history chart of lakes trial target bearing estimation
4 结　语

1）稠密连接网络在低信噪比下，相较经典方法具有更窄的主瓣宽度和较高的估计精度，在高信噪比的情况下，主瓣宽度更窄但估计精度不如经典方法；

2） 在2个等强度目标信噪比6 dB以上的情况下，稠密连接网络的双目标分辨力能达到20°，相较经典方法中方位分辨能力最强的MVDR减小79°以上；

3）在2个目标信噪比相差小于等于6 dB的情况下，稠密连接网络和经典方法均能分辨2个目标，当2个目标信噪比相差大于6 dB后，只有稠密连接网络可发现弱目标，当2个目标信噪比相差大于18 dB后，稠密连接网络才逐渐丧失了对弱目标的检测能力。

 [1] 惠俊英, 刘宏, 余华兵, 等. 声压振速联合信息处理及其物理基础初探[J]. 声学学报, 2000(4): 303-307. HUI Junying LIU Hong, YU Huabing, et al. Preliminary study on the joint information processing of sound pressure and vibration velocity and its physical basis[J]. Acta Acustica, 2000(4): 303-307. [2] 惠俊英, 惠娟. 矢量声信号处理基础[M]. 北京: 国防工业出版社, 2009: 10−17. [3] HOCHWALD B, NEHORAI A. Identifiability in array processing models with vector-sensor applications[J]. IEEE Transactions on signal processing, 1996, 44(1): 83-95. DOI:10.1109/78.482014 [4] 杨士莪. 单矢量传感器多目标分辨的一种方法[J]. 哈尔滨工程大学学报, 2003(6): 591-595. YANG Shie. A method for multi target resolution of single vector sensor[J]. Journal of Harbin Engineering University, 2003(6): 591-595. [5] AGARWAL A, AGRAWAL M, KUMAR A. Higher-order-statistics-based direction-of-arrival estimation of multiple wideband sources with single acoustic vector sensor[J]. IEEE Oceanic Engineering., 2020, 45(4): 1439-1449.. DOI:10.1109/JOE.2019.2934211 [6] 张维, 尚玲. 单矢量水听器水中多目标方位跟踪方法[J]. 国防科技大学学报, 2017, 39(2): 114-119. ZHANG Wei, SHANG Ling. A method for azimuth tracking of multiple targets in water using a single vector hydrophone[J]. Journal of National University of Defense Technology, 2017, 39(2): 114-119. DOI:10.11887/j.cn.201702017 [7] 孟春霞, 李秀坤, 杨士莪. 单矢量水听器多目标方位估计的算法研究[J]. 舰船科学技术, 2007(2): 123-126. MENG Chunxia, LI Xiukun, YANG Shie. Direction estmation of multi-sources received by a single vector sensor[J]. Ship Science and Technology, 2007(2): 123-126. [8] TICHAVSKY P, WONG K T, ZOLTOWSKI M D. Near-field/far-field azimuth and elevation angle estimation using a single vector hydrophone[J]. IEEE Transactions on Signal Processing, 2001, 49(11): 2498-2510. DOI:10.1109/78.960397 [9] 梁国龙, 张锴, 付进, 等. 单矢量水听器的高分辨方位估计应用研究[J]. 兵工学报, 2011, 32(8): 986-990. LING Guolong, ZHANG Kai, FU Jin, et al. Research on high-resolution direction-of-arrival estimation based on an acoustic vector-hydrophone[J]. Acta Armamentarii, 2011, 32(8): 986-990. [10] 曾雄飞, 孙贵青, 李宇, 等. 单矢量水听器的几种DOA估计方法[J]. 仪器仪表学报, 2012, 33(3): 499-507. ZENG Xiongfei, SUN Guiqing, LI Yu, et al. Several approaches of DOA estimation for single vector hydrophone[J]. Chinese Journal of Scientifie Instrument, 2012, 33(3): 499-507. [11] 王超, 笪良龙, 韩梅, 等. 单矢量水听器稀疏近似最小方差方位估计算法[J]. 声学学报, 2021, 46(6): 1050-1058. WANG Chao, DA Lianglong, HAN Mei, et al. Signal vector hydrophone sparse asymptotic minimum variance hearing estimation algorithm[J]. Acta Acustica, 2021, 46(6): 1050-1058. [12] 王宇杰, 李子高, 迟骋, 等. 单矢量水听器的组合二阶统计量解卷积方位估计[J]. 声学学报, 2023, 48(4): 656−667. WANG Yujie, LI Zigao, CHI Pin, et al. Single vector hydrophone time-domain deconvolution bearing estimation method based on combined second-order statistics[J]. Acta Acustica, 2023, 48(4): 656−667. [13] ZHANG M, PAN X, SHEN Y N, et al. Deep learning-based direction-of-arrival estimation for multiple speech sources using a small scale array[J]. The Journal of the Acoustical Society of America, 2021, 149(6): 3841. DOI:10.1121/10.0005127 [14] LIU Y J, CHEN H X, WANG B. DOA estimation based on CNN for underwater acoustic array[J]. Applied Acoustics, 2021, 172: 107594. DOI:10.1016/j.apacoust.2020.107594 [15] 余春祥, 王彪, 朱雨男, 等. 胶囊网络矢量水听器DOA估计[J]. 舰船科学技术, 2023, 45(4): 128−132. YU Chunxiang, WANG Biao, ZHU Yunan, et al. DOA estimation of vector hydrophone based on capsules network[J]. Ship Science and Technology, 2023, 45(4): 128−132. [16] 曹怀刚, 任群言, 郭圣明, 等. 卷积神经网络单矢量水听器方位估计[J]. 哈尔滨工程大学学报, 2020, 41(10): 1524-1529. CAO Huaigang, REN Qunyan, GUO Shengming, et al. Source azimuth estimation with single vector sensor based on convolutional neural network[J]. Journal of Harbin Engineering University, 2020, 41(10): 1524-1529. [17] 杨德森, B. A. Γордиенко, 洪连进,. 水下矢量声场理论与应用等[J]. 声学学报, 2015, 40(1): 124-125. YANG Desen, B. A. Γордиенко, HONG Lian-jin, et al. Underwater vector sound field theory and its applications[J]. Acta Acustica, 2015, 40(1): 124-125. [18] HUANG G, LIU Z, VAN DER MAATEN L, et al. Densely connected convolutional networks[C]//Proceedings of the IEEE conference on computer vision and pattern recognition. 2017: 4700−4708. [19] TSOUMAKAS G, KATAKIS I. Multi-label classification: an overview[J]. International Journal of Data Ware- housing and Mining, 2007, 3(3): 1-13. DOI:10.4018/jdwm.2007070101