阵列信号处理是现代声纳设备的核心功能之一。通过接收阵列的信号处理，可以获取空间指向性增益，提高空间分辨和干扰抑制能力，实现对目标的检测与跟踪、方位与距离估计；通过发射阵列的信号处理，可以获取具有一定时延差或相位差的阵元信号，从而形成指向性发射波束，提高声源级；通过空-时自适应处理，可以提高对弱目标的检测能力。近年来，声纳技术不断发展，出现了多线列阵声纳、连续波声纳、MIMO声纳等新体制声纳以及自适应盲处理、时反处理、矢量信号处理、鲁棒性波束形成、模基信号处理等新型处理算法，这些都是声纳阵列信号处理的发展与丰富。本书深入、系统地介绍了可应用于实际声纳设备的阵列信号处理技术，在简单的原理接收基础上又大量的计算机模拟仿真及湖、海试实际数据的处理结果。另外本书有较大篇幅的声纳阵列信号处理领域的新技术介绍。

阵列信号处理是现代声纳设备的核心功能之一。通过对接收阵列的信号处理，可以获 取空间指向性增益，提高声纳作用距离，实现对目标的检测与跟踪、方位与距离估计；通 过发射阵列的信号处理，可以获取具有一定时延差或相位差的阵元信号，从而形成指向性 发射波束，提高声源级；通过空—时自适应处理，可以提高对弱目标的检测能力。近年来， 声纳技术不断发展，出现了多线列阵声纳、连续波主动声纳、MIMO 声纳等新体制声纳及 自适应盲处理、时反处理、矢量信号处理、鲁棒性波束形成、模基信号处理等新型处理算 法，这些都是声纳阵列信号处理的发展与丰富。 本书作者一直从事水声及水声对抗技术研究和装备研制工作，在长期工作和学习中积 累了较丰富的理论知识和工程经验，现将多年来在阵列信号处理方面的研究成果进行提炼 和总结，形成本书。本书分为基础理论、阵列应用和新技术研究三个部分。基础理论部分 （第1～3 章）介绍了海洋信道中的声场模型、基阵理论基础和阵列信号模型，是各种阵列 信号处理技术研究的理论基础。阵列应用部分（第4～8 章）分别介绍了矢量水听器及阵处 理、自适应波束形成与噪声抵消、声纳被动定位、目标运动分析、空时自适应处理技术和方 法，是阵列信号处理的具体应用和实践。第9 章新技术研究部分介绍了模基信号处理、MIMO 声纳处理、连续波主动声纳处理技术的原理和方法，是阵列信号处理的重要发展方向。 本书试图将阵列信号处理的理论模型和工程应用结合起来，侧重于实用。希望对从事 水声及水声对抗技术研究和装备研制的科研人员有所帮助。本书可作为水声工程、信号处 理等专业研究生教材，也可作为声纳设备设计人员开展相关研究工作的参考。 本书在撰写过程中，得到了姚蓝教授、惠俊英教授、王广恩研究员等老一辈水声行业专家的 指导，并提出十分关键的修改意见，在此向他们表示崇高的敬意和衷心的感谢。本书的研究 工作得到水声对抗技术重点实验室孟昭文主任的大力支持，刘本奇、蒋小勇、潘谢帆、谭君 红等参与了有关章节的研究工作，在此一并表示感谢。 由于作者水平有限，书中难免有不妥之处，敬请读者批评指正。 作者 2017 年4 月

第1 章 声场概述············································································································1 1.1 引言···························································································································· 1 1.2 声波的基本概念········································································································ 1 1.3 声学基本物理量········································································································ 1 1.4 理想流体介质中小振幅波传播的基本规律······························································ 2 1.4.1 理想流体介质······································································································· 2 1.4.2 连续性方程·········································································································· 3 1.4.3 状态方程············································································································· 3 1.4.4 运动方程············································································································· 4 1.4.5 波动方程············································································································· 4 1.4.6 速度势函数·········································································································· 4 1.4.7 亥姆霍兹方程······································································································· 5 1.4.8 三种不同坐标系下亥姆霍兹方程求解····································································· 5 1.4.9 线性滤波器理论框架下波动方程求解····································································· 9 1.4.10 介质特性阻抗··································································································· 11 1.5 分层介质中的波传播······························································································· 11 1.5.1 平行平面层中波传播的一般关系·········································································· 11 1.5.2 边界条件··········································································································· 12 1.5.3 硬底均匀浅海声场······························································································ 12 1.5.4 液态海底均匀浅海声场······················································································· 14 1.6 声场传播基本模型··································································································· 15 1.7 声学工具·················································································································· 16 1.8 本章小结·················································································································· 17 参考文献······························································································································17 第2 章 基阵理论基础···································································································18 2.1 引言·························································································································· 18 2.2 基阵的主要性能参数······························································································· 18 2.2.1 常见的基阵类型································································································· 18 2.2.2 主要性能参数····································································································· 18 2.3 均匀线列阵·············································································································· 21 2.3.1 基阵响应（指向性函数） ···················································································· 22 2.3.2 乘积定理··········································································································· 24 2.3.3 幅度加权··········································································································· 25 2.3.4 波束扫描··········································································································· 25 2.3.5 离散空间傅里叶变换··························································································· 27 2.3.6 宽带声源··········································································································· 29 2.4 均匀平面阵·············································································································· 29 2.5 圆形阵······················································································································ 30 2.6 双线列阵·················································································································· 31 2.7 三元组线列阵·········································································································· 33 2.8 四元组线列阵·········································································································· 35 2.9 本章小结·················································································································· 36 参考文献··························································································································· 37 第3 章 阵列信号模型···································································································38 3.1 引言·························································································································· 38 3.2 基阵信号与噪声······································································································ 38 3.2.1 空间信号··········································································································· 38 3.2.2 基本假设条件····································································································· 39 3.2.3 信号的窄带假设和解析表示················································································· 42 3.2.4 基阵噪声假设····································································································· 45 3.3 阵列信号模型·········································································································· 46 3.3.1 基阵的阵列流形与模糊······················································································· 46 3.3.2 基阵的离散时间信号模型···················································································· 48 3.3.3 信号的空间采样································································································· 49 3.3.4 采样数据··········································································································· 50 3.4 波束形成·················································································································· 52 3.4.1 波束响应··········································································································· 52 3.4.2 输出信噪比········································································································ 54 3.5 空间匹配滤波器······································································································ 55 3.5.1 空间匹配滤波器································································································· 55 3.5.2 阵元间距··········································································································· 56 3.5.3 阵列孔径和角度分辨率······················································································· 58 3.6 本章小结·················································································································· 59 参考文献··························································································································· 59 第4 章 矢量水听器及阵处理技术·················································································60 4.1 声场中的振速信息··································································································· 60 4.1.1 平面波声场声学欧姆定律···················································································· 60 4.1.2 各向同性噪声场中矢量水听器测量模型································································ 61 4.2 矢量水听器的种类··································································································· 62 4.2.1 声场振速的测量方法··························································································· 62 4.2.2 矢量水听器的种类······························································································ 62 4.2.3 几种矢量水听器································································································· 63 4.3 单矢量水听器探测技术··························································································· 67 4.3.1 单矢量水听器的自然指向性················································································· 67 4.3.2 矢量水听器指向性的电子旋转············································································· 67 4.3.3 单个矢量水听器的测向方法················································································· 68 4.4 矢量水听器线列阵技术··························································································· 68 4.4.1 矢量波束形成····································································································· 68 4.4.2 矢量线列阵测向研究··························································································· 70 4.4.3 目标跟踪算法研究······························································································ 71 4.4.4 矢量线列阵的增益······························································································ 71 4.4.5 矢量水听器线列阵校正······················································································· 78 4.5 矢量拖线列阵技术··································································································· 82 4.5.1 拖曳用矢量水听器······························································································ 82 4.5.2 矢量水听器的姿态稳定技术················································································· 84 4.5.3 矢量拖线列阵拖曳噪声研究················································································· 84 4.5.4 拖曳试验数据处理······························································································ 88 4.6 矢量时间反转镜······································································································ 91 4.6.1 时反聚焦原理····································································································· 91 4.6.2 声压时反镜聚焦理论··························································································· 92 4.6.3 矢量时反聚焦理论······························································································ 92 4.6.4 时反镜的聚焦稳健性··························································································· 93 4.7 本章小结·················································································································· 93 参考文献······························································································································93 第5 章 自适应波束形成与噪声抵消技术······································································95 5.1 引言·························································································································· 95 5.2 常规波束形成技术··································································································· 95 5.2.1 窄带相移波束形成······························································································ 95 5.2.2 宽带波束形成····································································································· 96 5.3 分裂阵波束形成技术······························································································· 97 5.3.1 分裂阵参考阵元选取··························································································· 98 5.3.2 分裂阵互相关检测······························································································ 99 5.3.3 半波束相位单元化处理····················································································· 101 5.4 自适应波束形成技术····························································································· 108 5.4.1 MVDR 波束形成技术························································································ 108 5.4.2 MUSIC 算法····································································································· 109 5.4.3 计算机仿真······································································································ 110 5.4.4 快速收敛MVDR 算法······················································································· 112 5.4.5 海试数据处理结果···························································································· 115 5.4.6 自适应波束形成改进研究的方向········································································ 115 5.5 自适应噪声抵消技术····························································································· 116 5.5.1 自适应噪声抵消技术的基本原理········································································ 116 5.5.2 基于LMS 算法的自适应噪声抵消······································································ 117 5.5.3 AIC 技术在拖船噪声抵消中的应用····································································· 118 5.5.4 逆波束形成拖船干扰抵消·················································································· 121 5.6 本章小结················································································································ 124 参考文献························································································································· 124 第6 章 声纳被动定位技术·························································································· 127 6.1 引言························································································································ 127 6.2 三角定位法············································································································ 127 6.2.1 基本原理········································································································· 127 6.2.2 误差分析········································································································· 128 6.2.3 实现方法········································································································· 129 6.3 三点/四点测距······································································································· 130 6.3.1 基本原理········································································································· 131 6.3.2 误差分析········································································································· 132 6.3.3 实现方法········································································································· 133 6.4 聚焦波束形成定位································································································· 134 6.4.1 基本原理········································································································· 134 6.4.2 理论计算········································································································· 135 6.4.3 实现方法········································································································· 136 6.4.4 高分辨聚焦波束形成方法·················································································· 137 6.4.5 工程应用考虑··································································································· 139 6.5 匹配场处理············································································································ 140 6.5.1 概述················································································································ 140 6.5.2 匹配场处理技术简介························································································· 141 6.5.3 匹配场处理发展······························································································· 142 6.5.4 匹配场数据模型······························································································· 143 6.5.5 匹配场处理仿真······························································································· 145 6.5.6 匹配场处理存在问题························································································· 148 6.6 基于波导不变量的被动定位················································································· 148 6.6.1 问题的提出······································································································ 150 6.6.2 干涉现象的产生机理························································································· 151 6.6.3 波导不变量β ···································································································· 153 6.6.4 仿真实验········································································································· 154 6.6.5 基于波导不变量的快速被动估距技术································································· 156 6.7 多途定位················································································································ 159 6.7.1 多途定位基本原理···························································································· 159 6.7.2 计算机仿真······································································································ 160 6.8 本章小结················································································································ 163 参考文献························································································································· 163 第7 章 目标运动分析································································································· 165 7.1 引言························································································································ 165 7.2 多基阵联合的被动纯方位目标运动分析······························································ 166 7.2.1 常规单基阵纯方位TMA···················································································· 166 7.2.2 双基阵被动纯方位TMA 的数据融合模型···························································· 168 7.2.3 仿真计算········································································································· 171 7.3 利用多维信息的被动目标跟踪性能研究······························································ 174 7.3.1 基本概念········································································································· 174 7.3.2 方位—频率TMA 及多阵纯方位TMA 的最大似然估计········································· 177 7.3.3 仿真计算········································································································· 180 7.4 本章小结················································································································ 183 参考文献························································································································· 184 第8 章 空时自适应处理····························································································· 186 8.1 引言························································································································ 186 8.2 混响空时分布特性································································································· 186 8.2.1 主动拖曳线列阵声纳························································································· 187 8.2.2 海试混响空时分布特性····················································································· 188 8.2.3 主动声纳检测背景分析····················································································· 189 8.3 STAP 原理介绍······································································································ 191 8.3.1 空时数据结构··································································································· 191 8.3.2 全维STAP 处理方法························································································· 194 8.3.3 降维STAP 处理方法························································································· 195 8.4 STAP 数据处理结果验证······················································································ 201 8.5 STAP 在被动声纳中应用······················································································ 205 8.5.1 空—频二维自适应处理····················································································· 205 8.5.2 仿真处理········································································································· 206 8.6 本章小结················································································································ 207 参考文献························································································································· 208 第9 章 新型声纳信号处理技术·················································································· 209 9.1 引言························································································································ 209 9.2 模基信号处理········································································································ 209 9.2.1 卡尔曼滤波技术······························································································· 210 9.2.2 MBSP 在水声信号处理中的应用方向·································································· 211 9.2.3 模基信号处理小结···························································································· 214 9.3 多输入多输出声纳处理························································································· 214 9.3.1 MIMO 声纳原理······························································································· 215 9.3.2 MIMO 声纳数学模型························································································ 215 9.3.3 MIMO 声纳特点······························································································· 217 9.3.4 MIMO 声纳正交波形························································································ 219 9.3.5 MIMO 声纳等效虚拟阵····················································································· 227 9.3.6 MIMO 声纳指向性···························································································· 229 9.3.7 MIMO 声纳波束形成························································································ 233 9.3.8 MIMO 声纳信号处理小结·················································································· 233 9.4 连续波主动声纳处理····························································································· 234 9.4.1 研究现状········································································································· 235 9.4.2 直达波干扰抑制······························································································· 236 9.4.3 CAS 发射信号·································································································· 237 9.4.4 基于差拍—分数阶傅里叶变换的CAS 回波检测算法············································ 242 9.4.5 小结················································································································ 247 9.5 本章小结················································································································ 247 参考文献························································································································· 247

杜选民，1970年9月出生，研究员/博士生导师，毕业于哈尔滨工程大学，获水声工程专业博士学位。现担任中国船舶重工集团公司第七二六研究所副所长、水声对抗技术重点实验室副主任、水声对抗技术重点实验室学术委员会副主任委员、水声对抗国防科技创新团队带头人、上海市声学学会理事、《声学学报》《声学技术》《舰船科学技术》编委会委员。__eol__从事水声及水声对抗技术研究工作20余年，主持研制了舰用鱼雷报警声纳、舰水声对抗系统、港口近程水下警戒探测系统等装备，均填补国内空白，获国防科技进步一等奖2项、二等奖2项、三等奖2项。在国内首次解决了拖线阵左右舷分辨、高速运动目标自适应检测与识别、非线性声纳工程应用等关键技术。__eol__入选国家新世纪百千万人才工程、国防科技工业511人才工程、国防科技工业有突出贡献中青年专家、上海市领军人才。__eol__