舰船尾迹是真实海场景中不可缺失的部分，是识别舰船目标的类型、位置、航速和航向信息等特征的重要途径。 本书共8 章，详细阐述了Kelvin 尾迹、含湍流远场综合尾迹、泡沫流尾迹、近场尾迹、内波尾迹和水下运动目标尾迹的几何建模、电磁散射建模和合成孔径雷达（SAR）成像仿真技术；结合计算流体力学（CFD）仿真技术和电磁散射的调制谱优化面元模型，将仿真模型应用于舰船尾迹的SAR 图像特征检测、基于尾迹的舰船目标参数反演和浮标目标隐蔽优化设计工程中。本书构建了一套基于舰船尾迹流场的电磁散射特性分析和雷达图像仿真的系统理论和应用方法，使读者能够通过本书的学习掌握运动舰船尾迹的电磁散射机理和成像仿真方法，灵活解决实际工程问题。 本书适合从事雷达设计与评估、微波遥感、雷达目标与环境特性、电磁成像算法与图像理解的相关科研工作人员阅读，也可作为高等学校相关专业研究生的教学参考用书。

前言 海面上除了风驱海面自然产生的海浪之外，舰船的运动也会带来特定形态的波浪，统称为舰船尾迹。尾迹是真实海上运动舰船场景中不可缺失的部分，海面舰船尾迹在合成孔径雷达（Synthetic Aperture Radar，SAR）图像中往往表现出特别显著的散射特征，而且不同舰船在不同运动状态时所具有尾迹的电磁散射和成像特征也有所不同，使得尾迹成为识别舰船目标的类型、位置、航速和航向信息等特征的重要途径。开展舰船尾迹的雷达成像机理和特征提取技术研究，可以为海洋目标遥感、舰船目标特征提取和环境监测，特别是为海面目标高分辨率观测技术提供重要的理论基础和新方法。 1978 年在SeaSat 的SAR 图像上，人们第一次发现海洋表面延伸20km 长的舰船尾迹。自此，科学家们逐渐开始关注SAR 图像中的舰船尾迹并进行研究。1986 年在IGARSS’86 会议上，美国科学家Lyden 发表了关于SAR 图像舰船尾迹类别和产生机理的研究论文。1989 年在苏格兰林纳湖（Loch Linnhe）所做的SAR 图像相关实验充分显示了内波尾迹的显著特征。2000年在加拿大由海洋遥感联盟召集，专门召开了世界上第一次关于海岸水域舰船检测的专题讨论会“Ship Detection in Coastal Waters Workshop 2000”，研究了不同尾迹对SAR 图像的调制机理。近十几年来，SAR 系统已经能获得令人较为满意的海洋图像，通过实验观测，科学家对舰船尾迹和海洋内波成像进行了系统研究，建立了多种基于SAR 图像的舰船目标监视系统。同时，随着计算机技术的快速发展，逐渐出现了尾迹SAR 图像仿真及其应用的研究。Zilman 等人依据双尺度模型和速度聚束积分对Kelvin 尾迹的SAR 图像进行了仿真分析，利用快速离散Radon 变换对Kelvin 尾迹边界进行检测，同时估计了检测方法的失检率和虚警率。Graziano 等人根据SAR 图像中典型尾迹的纹理特征，利用Radon 变换实现了舰船目标的检测和航迹估计，并且进一步结合X 波段TerraSAR-X 和COSMO/SkyMed 的SAR 图像数据开展了尾迹探测识别算法在不同极化和入射方位角下舰船目标航迹和船速预估方面的应用研究。然而，现有研究多是通过对实际SAR 图像的分析来研究尾迹及舰船检测方法的，由于实验条件复杂，难以很好地解释所观测的结果，缺乏对SAR 图像中尾迹纹理特征的完备分析。而且，不同SAR 平台的测试参 数（信号的入射方位角、极化、带宽运动速度等）和不同船速的舰船尾迹的几何形态和电磁散射特征是不同的，对应的Kelvin 尾迹、湍流尾迹、内波尾迹，特别是水下运动目标的内波尾迹的电磁成像机理和SAR 图像仿真方法仍然缺失。因此，必须通过舰船尾迹的电磁散射特性研究，更好地理解SAR成像机理，开展SAR 图像仿真，进而促进舰船目标特征识别技术的研究。 鉴于此，形成一套系统而完整的舰船尾迹电磁成像仿真方法和应用技术无疑是必要且紧迫的。本书立足于舰船尾迹电磁成像机理问题，结合海洋计算流体力学和舰船运动特征，建立了Kelvin 尾迹、湍流尾迹和内波尾迹的非线性流场几何模型， 重点通过著者团队建立的调制谱面元散射模型（Modulated Facet Scattering Model，MFSM），结合实测数据，力求实现对Kelvin 尾迹、湍流尾迹、内波尾迹的电磁散射机理的准确描述，在获取包含不同舰船尾迹的大场景海面的电磁散射模型和尾迹SAR 图像仿真算法的基础上，完成舰船尾迹的SAR 图像仿真和基于尾迹的目标特征识别技术研究。 全书共8 章。其中，第1 章对海面舰船尾迹电磁散射的基本概念和理论进行介绍；第2 章给出传统线性叠加Kelvin 尾迹的SAR 图像仿真方法；第3 章针对远场湍流尾迹与背景波耦合难题，提出一种调制谱面元散射模型，并结合计算流体力学仿真，对包含Kelvin 尾迹、湍流尾迹以及背景海浪的SAR 图像进行仿真与特征分析；第4 章探讨辐射输运理论及其在泡沫流尾迹电磁计算中的应用；第5 章主要对包含波浪破碎的舰船近场尾迹的电磁散射特性进行建模与特性分析；第6 章主要介绍分层海洋条件下内波尾迹的电磁散射计算和成像方法；第7 章主要探讨和分析不同分层条件下水下运动目标尾迹的电磁散射和雷达图像特征变化；第8 章围绕舰船尾迹的各类工程应用展开讨论，主要包括基于神经网络的尾迹SAR 图像检测、基于尾迹的舰船参数反演，以及利用尾迹特征进行浮标目标隐身优化设计的方法。 本书是西安电子科技大学复杂地海环境目标雷达散射成像与特征控制团队老师和研究生长期科研工作的积累和辛勤劳动的结晶，也是著者及所在团队近年来在海面舰船尾迹的雷达特性研究工作的总结。这里要特别感谢团队中的罗伟博士、赵言伟博士、聂丁博士、陈珲博士、孙荣庆博士、罗根博士、魏鹏博博士、王佳坤博士、陈俊龙博士和李金星博士和团队中各届博士研究生和硕士研究生。同时，本书得到了国家自然科学基金（62171351、61771355、61372004、41306188、60871070）、航空科学基金（20200001081006）、中央高校基本科研业务费专项资金和目标与环境电磁散射辐射重点实验室基金的资助，在此表示诚挚的谢意。此外，中国航天科工集团第二研究院207 所（北 京环境特性研究所）、北京控制与电子技术研究所、中国航天科工集团第三研究院三部对本书的相关研究也给予了大力支持，在此深表感谢。 由于著者水平有限，书中难免有不足之处，恳请读者批评指正。 著者 2023 年1 月

第1 章 舰船尾迹电磁散射的理论基础·········································001 1.1 海浪和舰船尾迹的基本概念········································002 1.1.1 海浪仿真·······················································002 1.1.2 典型海谱函数·················································005 1.1.3 舰船尾迹的基本类型·······································.011 1.2 海面与舰船尾迹电磁散射的计算基础····························017 1.2.1 Bragg 散射理论···············································018 1.2.2 半确定面元散射模型········································020 1.2.3 海面散射场分析··············································023 1.3 本章小结································································026 参考文献······································································027 第2 章 Kelvin 尾迹······························································031 2.1 Kelvin 尾迹流场模型·················································032 2.1.1 船行波基本特征··············································032 2.1.2 Kelvin 尾迹波高场···········································033 2.1.3 Kelvin 尾迹仿真结果········································035 2.2 海面调制理论··························································037 2.2.1 海浪波的流体力学描述·····································037 2.2.2 倾斜调制·······················································038 2.2.3 流体力学调制·················································039 2.2.4 速度聚束调制·················································040 2.2.5 三种调制作用对比···········································041 2.3 速度聚束成像模型与尾迹成像仿真·······························043 2.3.1 实孔径雷达和合成孔径雷达·······························043 2.3.2 Kelvin 尾迹SAR 成像仿真·································045 2.3.3 Kelvin 尾迹SAR 图像特性分析···························048 2.3.4 Kelvin 尾迹中的窄尾迹分量·······························057 2.4 本章小结································································061 参考文献······································································062 第3 章 湍流远场综合尾迹·······················································063 3.1 远场湍流尾迹的流场仿真···········································064 3.1.1 CFD 理论基础·················································065 3.1.2 基于CFD 理论的远场尾迹仿真···························068 3.2 调制谱面元散射模型·················································069 3.2.1 调制谱方程····················································070 3.2.2 调制谱源项····················································071 3.2.3 调制谱的求解·················································075 3.2.4 基于调制谱的海面散射·····································078 3.3 湍流尾迹散射场分析·················································079 3.3.1 尾迹的背景波调制作用·····································079 3.3.2 远场综合尾迹SAR 成像····································083 3.4 本章小结································································087 参考文献······································································087 第4 章 泡沫流尾迹·······························································090 4.1 泡沫流尾迹的理论基础··············································090 4.1.1 泡沫层反射率·················································090 4.1.2 泡沫覆盖率····················································093 4.2 泡沫海面的体散射统计模型········································095 4.2.1 球形气泡的电磁散射特性··································095 4.2.2 散射矩阵·······················································099 4.2.3 泡沫海面体散射的VRT 模型······························104 4.3 泡沫流尾迹的相干散射场模型····································.110 4.3.1 泡沫层的相干散射场模型·································.110 4.3.2 仿真结果与分析·············································.115 4.4 本章小结································································120 参考文献······································································121 第5 章 近场尾迹··································································123 5.1 近场尾迹的几何建模·················································124 5.1.1 尾迹流场仿真设置···········································125 5.1.2 近场尾迹仿真结果···········································126 5.2 近场尾迹电磁散射的算法···········································129 5.2.1 网格转换和消隐处理········································129 5.2.2 迭代物理光学法（IPO）····································131 5.2.3 迭代优化技术·················································133 5.3 近场尾迹的电磁散射特性分析·····································134 5.3.1 FBIPO 算法验证与分析·····································134 5.3.2 近场尾迹电磁散射总场分析·······························136 5.3.3 近场尾迹电磁散射场分布··································139 5.4 本章小结································································143 参考文献······································································143 第6 章 内波尾迹··································································146 6.1 内波尾迹流场特性····················································146 6.1.1 内波尾迹仿真方法···········································146 6.1.2 离散内波层的波动···········································147 6.1.3 扩散内波层的波动···········································151 6.1.4 内波尾迹波高反演···········································156 6.1.5 内波尾迹仿真结果···········································158 6.2 内波尾迹电磁散射计算··············································160 6.2.1 小斜率近似模型··············································160 6.2.2 内波尾迹对海面电磁散射系数的影响····················163 6.2.3 内波尾迹的电磁散射分布与SAR 成像··················172 6.3 本章小节································································182 参考文献······································································183 第7 章 水下运动目标尾迹·······················································185 7.1 水下运动目标尾迹流场仿真········································186 7.1.1 均匀流下的水下运动目标尾迹····························186 7.1.2 内波尾迹与海水密度分层··································193 7.1.3 任意分层条件下的水下运动目标尾迹····················196 7.2 水下运动目标尾迹SAR 成像仿真·································198 7.2.1 水下运动目标尾迹散射场分布····························198 7.2.2 水下运动目标尾迹SAR 成像······························200 7.3 本章小结································································209 参考文献······································································209 第8 章 舰船尾迹检测与特征提取··············································212 8.1 舰船尾迹检测基础····················································212 8.1.1 Radon 变换····················································212 8.1.2 尾迹线性特征增强···········································215 8.1.3 尾迹线性特征检测···········································219 8.2 基于神经网络的尾迹SAR 图像检测······························222 8.2.1 Faster R-CNN··················································222 8.2.2 样本数据处理·················································224 8.2.3 检测结果与分析··············································225 8.3 基于尾迹的舰船参数反演···········································227 8.3.1 基于波幅函数的舰船尺寸反演····························227 8.3.2 基于尾迹图像的舰船航速估计····························229 8.3.3 舰船尾迹空间频谱分量分析·······························231 8.4 基于尾迹的浮标目标隐蔽优化方法·······························235 8.4.1 流场仿真与参数设定········································235 8.4.2 浮标目标的电磁散射特性与SAR 图像··················237 8.4.3 目标尾迹的可探测性评判标准····························241 8.4.4 浮标目标的隐蔽优化方法探讨····························243 8.5 本章小结································································245 参考文献······································································245