海杂波背景下雷达目标特征检测方法的现状与展望

许述文 白晓惠 郭子薰 水鹏朗

许述文, 白晓惠, 郭子薰, 等. 海杂波背景下雷达目标特征检测方法的现状与展望[J]. 雷达学报, 2020, 9(4): 684–714. doi:  10.12000/JR20084
引用本文: 许述文, 白晓惠, 郭子薰, 等. 海杂波背景下雷达目标特征检测方法的现状与展望[J]. 雷达学报, 2020, 9(4): 684–714. doi:  10.12000/JR20084
XU Shuwen, BAI Xiaohui, GUO Zixun, et al. Status and prospects of feature-based detection methods for floating targets on the sea surface[J]. Journal of Radars, 2020, 9(4): 684–714. doi:  10.12000/JR20084
Citation: XU Shuwen, BAI Xiaohui, GUO Zixun, et al. Status and prospects of feature-based detection methods for floating targets on the sea surface [J]. Journal of Radars, 2020, 9(4): 684–714. doi:  10.12000/JR20084

海杂波背景下雷达目标特征检测方法的现状与展望

(中文/English)

doi: 10.12000/JR20084
基金项目: 国家自然科学基金(61871303),电波环境特性及模化技术重点实验室基金(6142403180204),111引智计划(B18039)
详细信息
    作者简介:

    许述文(1985–),男,安徽黄山人,博士,副教授,博士生导师,加拿大 Mcmaster 大学访问学者,入选陕西省青年人才托举计划。2011 年在西安电子科技大学获得博士学位,现就职于西安电子科技大学电子工程学院雷达信号处理国家重点实验室。主要研究方向为雷达目标检测、机器学习、时频分析和 SAR 图像处理。E-mail: swxu@mail.xidian.edu.cn

    白晓惠(1998–),女,陕西宝鸡人,西安电子科技大学博士生。主要研究方向为雷达目标检测、机器学习和海杂波信号处理。E-mail: xhbai@stu.xidian.edu.cn

    郭子薰(1994–),女,陕西西安人,西安电子科技大学博士生。主要研究方向为雷达目标检测、机器学习和海杂波信号处理。E-mail: zxguo_724@stu.xidian.edu.cn

    水鹏朗(1967–),男,陕西西安人,博士,教授。1999年在西安电子科技大学获得博士学位,现担任西安电子科技大学电子工程学院雷达信号处理国家重点实验室教授、硕导、博导。主要研究方向为海杂波建模、雷达目标检测和图像处理。E-mail: plshui@xidian.edu.cn

    通讯作者:

    许述文 swxu@mail.xidian.edu.cn

  • 责任主编:关键 Corresponding Editor: GUAN Jian
  • 中图分类号: TN95

Status and Prospects of Feature-based Detection Methods for Floating Targets on the Sea Surface (in English)

(English)

Funds: The National Natural Science Foundation of China (61871303), The Foundation of National Key Laboratory of Electromagnetic Environment (6142403180204), The Foreign Scholars in University Research and Teaching Programs (the 111 Project) (B18039)
More Information
    Author Bio:

    XU Shuwen was born in Huangshan city in Anhui, China. He received his B.Eng. and Ph.D. degrees, both in electronic engineering, from Xidian University, Xi’an, China, in 2006 and 2011, respectively. Subsequently, he worked at the National Laboratory of Radar Signal Processing, Xidian University. He worked as a visiting professor in McMaster University, Canada in 2018. He is currently a professor with the National Laboratory of Radar Signal Processing, Xidian University. His research interests are in the fields of radar target detection, statistical learning, and SAR image processing. E-mail: swxu@mail.xidian.edu.cn

    BAI Xiaohui was born in Baoji, Shaanxi province in 1998. She is now a Ph.D. student in Xidian University. Her main research fields are radar target detection, machine learning, and sea clutter signal processing. E-mail: xhbai@stu.xidian.edu.cn

    GUO Zixun was born in Xi’an, Shaanxi province in 1994. She is now a Ph.D. student in Xidian University. Her main research fields are radar target detection, machine learning, and sea clutter signal processing. E-mail: zxguo_724@stu.xidian.edu.cn

    SHUI Penglang was born in Xi’an, Shaanxi province in 1967. He received his Ph.D. degree in electronic engineering from Xidian University, Xi’an, China, in 1999. He is now a professor, PhD supervisor at the Radar Signal Processing National Key Lab of Electronic Engineering from Xidian University. His main research fields are sea clutter modeling, radar target detection, and image processing. E-mail: plshui@xidian.edu.cn

    Corresponding author: XU Shuwen, swxu@mail.xidian.edu.cn
  • 摘要: 海杂波背景下的雷达目标检测对民用和军事都有着重要的意义。随着海面目标的小型化和隐身化,海面慢速、漂浮小目标已经成为了雷达警戒的重点对象。关于此类小目标的检测一直以来都是海杂波背景下目标检测中的难题。通常,漂浮小目标的雷达散射横截面积(RCS)微弱,并且运动速度慢,常常在时域和频域均存在“超杂波检测”的困难。传统目标检测方法对漂浮小目标的检测存在明显的性能瓶颈。对于海面漂浮小目标的检测,采用高多普勒和高距离分辨体制(“双高”体制)是从雷达体制上解决这个问题的有效途径。在双高体制下,雷达接收的目标回波提供了更多的可用信息。然而,如何将这些更加精细化的信息转化为探测性能的提升,一直以来都是雷达届关注的难点,相关科研成果也一直在不断地推陈出新。近些年,在双高雷达体制下,学者们提出了多种基于特征的目标检测方法,作为对海智能检测的人工特征工程阶段,这些方法缓解了仅依靠能量信息较难检测小目标的困难局面,极大程度地改善了对漂浮小目标的检测性能。为了更好地让相关雷达从业者了解该领域这些年的发展和未来的趋势,该文首先总结了对海检测的难点和常用的目标检测方法,然后分析了特征检测的原理和通用框架以及国内外几种典型的基于特征的检测方法,最后对特征检测方法发展趋势进行了展望。
  • 图  1  常见的海面小目标

    Figure  1.  Some common small targets on the sea

    图  2  实测数据功率图及幅度拟合结果

    Figure  2.  Power map of measured data and amplitude fitting results

    图  3  自适应检测方法流程图

    Figure  3.  The flowchart of the adaptive detection methods

    图  4  VV极化、逆风情况下,海况4级时各种不同舰船的信杂比

    Figure  4.  In the case of headwind situation, SCR for various ships at sea state 4 (VV polarization)

    图  5  可实现“双高”体制的雷达工作模式

    Figure  5.  Radar working modes that realize the "double high" system

    图  6  特征检测流程图

    Figure  6.  The flowchart of the feature-based detection methods

    图  7  部署现场平面图[11]

    Figure  7.  A plan overview of the deployment site[11]

    图  8  2006年试验架设位置(OTB)[11]

    Figure  8.  Location of the deployment site in 2006 (OTB)[11]

    图  9  试验合作船只[11]

    Figure  9.  Experimental cooperative boats[11]

    图  10  X波段固态功放监视/导航雷达[51]

    Figure  10.  X-band solid-state power amplifier surveillance/navigation radar[51]

    图  11  组合脉冲发射的3种模式[51]

    Figure  11.  Three modes of combined pulse transmission[51]

    图  12  14个距离单元分形特性分析[30]

    Figure  12.  Analysis of fractal characteristics in 14 range cells[30]

    图  13  14个距离单元H(q)趋势图[30]

    Figure  13.  The trends of H(q) in 14 range cells[30]

    图  14  HH极化下纯杂波单元与含目标单元Hurst频率分布图[30]

    Figure  14.  Hurst frequency distribution of clutter cells and target cells under HH polarization[30]

    图  15  分形特征检测器的原理框图[73]

    Figure  15.  The flowchart of fractal-based detector[73]

    图  16  分形曲线[73]

    Figure  16.  Fractal curves[73]

    图  17  训练样本和待分类样本在二维特征平面的显示图[73]

    Figure  17.  The distribution of training samples and test samples on the two-dimensional feature plane[73]

    图  18  经典CFAR算法检测曲线[73]

    Figure  18.  Classic CFAR algorithm detection curves[73]

    图  19  基于神经网络预测的检测器框图[33]

    Figure  19.  The flowchart of detector based on neural network prediction[33]

    图  20  基于神经网络检测器和传统多普勒CFAR检测器的ROC曲线[33]

    Figure  20.  ROC curves of the detector based on neural network and traditional Doppler CFAR detector[33]

    图  21  基于预测的检测方法流程图

    Figure  21.  The flowchart of detection methods based on prediction

    图  22  海杂波抑制后的微动信号变换域特征(N=256)[41]

    Figure  22.  Micro-motion signal features after sea clutter suppression (N=256)[41]

    图  23  海杂波抑制后基于STFT和GSTFRFT的微动信号检测结果比较(N=512)[41]

    Figure  23.  Comparison of micro-motion target detection results based on STFT and GSTFRFT after sea clutter suppression (N=512)[41]

    图  24  基于ST-SFT的海上微动目标检测结果(起始时间=20 s)[42]

    Figure  24.  ST-SFT-based micro-motion targets detection results (starting time=20 s)[42]

    图  25  基于ST-SFRFT的海上微动目标检测结果(起始时间=20 s)[42]

    Figure  25.  ST-SFRFT-based micro-motion targets detection results (starting time=20 s)[42]

    图  26  基于CNN的检测方法流程图[43]

    Figure  26.  Processing flow diagram of method based on CNN[43]

    图  27  散斑的平均一致性因子检测器的流程图[74]

    Figure  27.  The flowchart of a feature-based detector using the average consistency factor of speckle[74]

    图  28  4种极化下纯杂波和目标杂波的平均一致性因子[74]

    Figure  28.  The average consistency factors of pure clutter and clutter with target under 4 polarization channels[74]

    图  29  L=1024, 4种极化下4种检测器的检测概率[74]

    Figure  29.  L = 1024, the detection probabilities of the four detectors under 4 polarization channels[74]

    图  30  纯杂波与目标在特征空间中的分布情况

    Figure  30.  Distributions of features of clutter-only vectors and vectors with target in 3D feature space

    图  31  原始数据生成的凸包和给定虚警率的凸包

    Figure  31.  Convex hull with the original training data and convex hull with given false alarm rate

    图  32  基于决策树的检测器流程图[78]

    Figure  32.  The flowchart of the decision-tree-based detector[78]

    图  33  极化3特征检测方法与原始3特征检测方法检测概率柱状图[76]

    Figure  33.  Detection probabilities of polarization features-based detector and tri-detector at HH, VV, HV, and VH polarizations for ten data sets[76]

    图  1  Some common small targets on sea

    图  2  Power map of measured data and amplitude fitting results

    图  3  Flowchart of adaptive detection methods

    图  4  SCRs for various ships at sea state 4 (VV polarization), in the case of headwind

    图  5  Radar working modes that realize the “double-high” system

    图  6  Flowchart of the feature-based detection methods

    图  7  A plan overview of the deployment site[11]

    图  8  Location of the deployment site in 2006 (OTB)[11]

    图  9  Experimental cooperative boats[11]

    图  10  X-band solid-state power amplifier surveillance/navigation radar[51]

    图  11  Three modes of combined pulse transmission[51]

    图  12  Analysis of fractal characteristics in 14 range cells[30]

    图  13  Trends of H(q) in 14 range cells[30]

    图  14  Hurst frequency distribution of clutter cells and target cells under HH polarization[30]

    图  15  Flowchart of fractal-based detector[73]

    图  16  Fractal curves[73]

    图  17  Distribution of training samples and test samples on the two-dimensional feature plane[73]

    图  18  Classic CFAR algorithm detection curves[73]

    图  19  Flowchart of detector based on neural network prediction[33]

    图  20  ROC curves of neural network-based detector and traditional Doppler CFAR detector[33]

    图  21  Flowchart of detection methods based on prediction

    图  22  Micro-motion signal features after sea clutter suppression (N = 256)[41]

    图  23  Comparison of micro-motion target detection results based on STFT and GSTFRFT after sea clutter suppression (N = 512)[41]

    图  24  ST-SFT-based micro-motion target detection results (starting time = 20 s)[42]

    图  25  ST-SFRFT-based micro-motion targets detection results (starting time = 20 s)[42]

    图  26  Processing flow diagram of CNN-based method[43]

    图  27  Flowchart of a feature-based detector using the average speckle consistency factor[74]

    图  28  Average consistency factors of pure clutter and clutter with target under four polarization channels[74]

    图  29  The detection probabilities of the four detectors under four polarization channels, L = 1024[74]

    图  30  Distributions of features of clutter-only vectors and vectors with target in 3D feature space

    图  31  Convex hull with the original training data and convex hull with given false alarm rate

    图  32  Flowchart of the decision tree-based detector[78]

    图  33  Detection probabilities of polarization feature-based detector and tri-detector at HH, VV, HV, and VH polarizations for 10 datasets[76]

    表  1  1993年IPIX雷达数据说明[28,50]

    Table  1.   The description of IPIX radar data collected in 1993[28,50]

    数据名称Data name浪高(m) Wave heights (m)风速(km/h) Wind speed (km/h)目标所在单元Primary受影响单元Secondary
    #172.2998, 10, 11
    #261.1976, 8
    #300.91976, 8
    #310.91976, 8, 9
    #401.0975, 6, 8
    #540.72087, 9, 10
    #2801.61087, 10
    #3100.93376, 8, 9
    #3110.93376, 8, 9
    #3200.92876, 8, 9
    下载: 导出CSV

    表  2  1998年IPIX雷达数据说明[28,50]

    Table  2.   The description of IPIX radar data collected in 1998[28,50]

    数据名称Data name距离范围(m) Range(m)目标所在单元Primary受影响单元Secondary雷达照射方向Radar direction
    #2022253201~40112423, 25
    #2025253201~401176, 8
    下载: 导出CSV

    表  3  OTB MS3的主要特性[11]

    Table  3.   Main characteristics of OTB MS3[11]

    参数Parameter数值Value
    纬度Latitude34°36'55.32"S
    经度Longitude20°17'20.11"E
    地面高度Ground height53 m
    天线高度Antenna height56 m
    离海距离Distance to sea1.2 km
    方位角范围Azimuth coverage208°~80° N (SSW-ENE)
    距离Range(CNR > 15 dB) 1.25~4.50 km
    擦地角Grazing angle(< 15 km) 3.00°~0.16°
    擦地角Grazing angle(CNR > 15 dB) 3.0°~0.7°
    下载: 导出CSV

    表  4  Fynmeet系统和性能参数[11]

    Table  4.   Fynmeet system and performance specifications[11]

    系统组成System composition系统参数System parameters参数设置Parameter values
    发射机Transmitter频率范围Frequency range6.5~17.5 GHz
    峰值功率Peak power2 kW
    PRF范围PRF range0~30 kHz
    波形Waveforms固定频率波形,步进频率波形,频率捷变波形Fixed frequency waveform, step frequency waveform, frequency agility waveform
    捷变带宽Agile bandwidth脉冲间500 MHz 500 MHz pulse to pulse
    天线Antenna类型Type双偏移反射器Dual-offset reflector
    增益Gain≥ 30 dB
    波束宽度Beamwidth≤ 2° (3 dB波束宽度) ≤2° (3 dB beamwidth)
    旁瓣Slidelobes≤ –25 dB
    接收机Receiver动态范围Dynamic range60 dB (瞬时) / 120 dB (总计) 60 dB (instantaneous)/120 dB (total)
    灵敏度Sensitivity0.1 m2 @ 10 km
    仪表范围Instrumented range200 m~15 km
    距离门Range gates1~64; ΔR = 100 ns, 300 ns or 400 ns
    采样器类型Sampler type中频采样器(IFS) Intermediate frequency sampler
    编码类型Encoding type正交编码Quadrature
    镜像抑制Image rejection≤ –41 dBc
    下载: 导出CSV

    表  5  X波段试验雷达参数[51]

    Table  5.   X-band radar parameters[51]

    雷达参数Radar parameters参数设置Parameters setting
    工作频段Working bandX
    工作频率范围Frequency range9.3~9.5 GHz
    量程Measuring range0.0625~96 nm
    扫描带宽Scanning bandwidth25 MHz
    距离分辨率Range resolution6 m
    脉冲重复频率Pulse repetition frequency1.6 K, 3 K, 5 K和10 K
    发射峰值功率Transmit peak power50 W
    天线转速Rotating speed of antenna2 rpm, 12 rpm, 24 rpm, 48 rpm
    天线长度Length of antenna1.8 m
    天线工作模式Antenna operation mode凝视、圆周扫描Gaze, circular scanning
    天线极化方式Antenna polarizationHH
    天线水平波束宽度Antenna horizontal beam width1.2°
    天线垂直波束宽度Antenna vertical beam width22°
    下载: 导出CSV

    表  6  现有特征检测方法的特征

    Table  6.   Features introduction of feature-based detection method

    现有特征Existing features
    分形特征Fractal features单分形特征[29,31,67]、多重分形特征[30,68]、分数阶傅里叶变换域的分形特征[69-73] Single fractal features[29,31,67], multifractal features[30,68], fractal features in FRFT[69-73]
    海杂波混沌特征Chaotic characteristics of sea clutter关联维、Lyapunov指数以及Kolmogorov熵 Correlation dimension, Lyapunov exponent, and Kolmogorov entropy[33][33]
    时域特征Features in the time domain相对平均幅度[28]、时域的信息熵[77]、时域的Hurst指数[77]、散斑一致性因子特征[74] Relative average amplitude[28], temporal information entropy[77], temporal Hurst exponent[77], the speckle consistency factor[74]
    频域特征Features in the frequency domain相对多普勒峰高[28]、相对多普勒谱熵[28]、频谱峰值与均值之比[77]、频域Hurst指数[78] Relative Doppler peak height[28], relative vector-entropy[28], frequency peak-to-average ratio[77], Hurst exponent in frequency domain[78]
    时频域特征Features in the time and frequency domains微多普勒特征[41,42]、归一化时频分布的时频累积[75]、由归一化时频分布亮像素构成二值图像中的连通区域数目和最大连通区域的尺寸[75] Micro-Doppler features[41,42], the ridge integration of NTFD[75], the number of connected regions and the maximum size of connected regions in a binary image[75]
    极化特征Polarization features相对体散射机制对应能量[76]、相对二面角散射机制对应能量[76]和相对面散射机制对应能量[76] Relative surface scattering power[76], relative dihedral scattering power[76], and the relative volume scattering power[76]
    下载: 导出CSV

    表  7  不同方法海上微动目标检测性能对比[42]

    Table  7.   Detection performance of different methods of micro-motion model of maritime targets[42]

    参数ParameterMTDFRFTWVDSPWVDST-SFTST-SFRFT
    Pd(%)(SCR=–5 dB)39.2657.2635.6855.2449.2171.35
    Pd(%)(SCR=0 dB)52.8476.8462.2772.5863.2885.69
    下载: 导出CSV

    表  8  不同模型目标检测结果(%)[43]

    Table  8.   The detection results of different models(%)[43]

    模型ModelLeNetAlexNetGoogLeNet
    虚警概率False alarm ratio1.240.040.24
    检测概率Detection probability92.2884.4490.94
    下载: 导出CSV

    表  9  基于SVM的检测器与其余检测器的性能对比[77]

    Table  9.   Detection performance comparisons of SVM-based detector and the other detectors[77]

    检测器Detectors检测结果(HH极化,虚警概率为0.001) Detection results (HH polarization, PF = 0.001)
    SCR=–2 dBSCR=17 dB
    基于SVM的检测器SVM-based detector7699
    基于3特征的检测器Tri-feature-based detector5799
    基于分形的检测器Fractal-based detector1879
    下载: 导出CSV

    表  10  基于决策树的检测结果和其余检测器的性能对比[78]

    Table  10.   Detection performance comparisons of the decision tree-based detector and the other detectors[78]

    检测器Detector检测结果Detection
    0 dB5 dB10 dB15 dB
    基于决策树的检测器Decision tree-based detector0.760.840.980.99
    基于3特征的检测器Tri-feature-based detector0.580.650.820.95
    基于分形的检测器Fractal-based detector0.210.320.480.68
    下载: 导出CSV

    表  1  Description of IPIX radar data collected in 1993[28,50]

    Data name Wave heights
    (m)
    Wind speed
    (km/h)
    Primary Secondary
    #17 2.2 9 9 8, 10, 11
    #26 1.1 9 7 6, 8
    #30 0.9 19 7 6, 8
    #31 0.9 19 7 6, 8, 9
    #40 1.0 9 7 5, 6, 8
    #54 0.7 20 8 7, 9, 10
    #280 1.6 10 8 7, 10
    #310 0.9 33 7 6, 8, 9
    #311 0.9 33 7 6, 8, 9
    #320 0.9 28 7 6, 8, 9
    下载: 导出CSV

    表  2  Description of IPIX radar data collected in 1998[28,50]

    Data name Range(m) Primary Secondary Radar direction
    #202225 3201~4011 24 23, 25
    #202525 3201~4011 7 6, 8
    下载: 导出CSV

    表  3  Main characteristics of OTB MS3[11]

    Parameter Value
    Latitude 34°36'55.32"S
    Longitude 20°17'20.11"E
    Ground height 53 m
    Antenna height 56 m
    Distance to sea 1.2 km
    Azimuth coverage 208°~80° N (SSW-ENE)
    Range (CNR > 15 dB) 1.25~4.50 km
    Grazing angle (<15 km) 3.00°~0.16°
    Grazing angle (CNR > 15 dB) 3.0°~0.7°
    下载: 导出CSV

    表  4  Fynmeet system and performance specifications[11]

    System composition System parameters Parameter values
    Transmitter Frequency range 6.5~17.5 GHz
    Peak power 2 kW
    PRF range 0~30 kHz
    Waveforms Fixed frequency waveform, step frequency waveform, frequency agility waveform
    Agile bandwidth 500 MHz pulse to pulse
    Antenna Type Dual-offset reflector
    Gain ≥30 dB
    Beamwidth ≤2° (3 dB beamwidth)
    Slidelobes ≤–25 dB
    Receiver Dynamic range 60 dB (instantaneous)/120 dB (total)
    Sensitivity 0.1 m2 @ 10 km
    Instrumented range 200 m~15 km
    Range gates 1~64; ΔR = 100 ns, 300 ns or 400 ns
    Sampler type Intermediate frequency sampler
    Encoding type Quadrature
    Image rejection ≤–41 dBc
    下载: 导出CSV

    表  5  X-band radar parameters[51]

    Radar parameters Parameters setting
    Working band X
    Frequency range 9.3~9.5 GHz
    Measuring range 0.0625~96 nm
    Scanning bandwidth 25 MHz
    Range resolution 6 m
    Pulse repetition frequency 1.6 K, 3 K, 5 K和10 K
    Transmit peak power 50 W
    Rotating speed of antenna 2 rpm, 12 rpm, 24 rpm, 48 rpm
    Length of antenna 1.8 m
    Antenna operation mode Gaze, circular scanning
    Antenna polarization HH
    Antenna horizontal beam width 1.2°
    Antenna vertical beam width 22°
    Information about the dataset and links to its download are available on the website of the Journal of Radar.
    下载: 导出CSV

    表  6  Features introduction of feature-based detection method

    Existing features
    Fractal features Single fractal features[29,31,67], multifractal features[30,68], fractal features in FRFT[69-73]
    Chaotic characteristics of sea clutter Correlation dimension, Lyapunov exponent, and Kolmogorov entropy[33]
    Features in the time domain Relative average amplitude[28], temporal information entropy[77], temporal Hurst exponent[77], the speckle consistency factor[74]
    Features in the frequency domain Relative Doppler peak height[28], relative vector-entropy[28], frequency peak-to-average ratio[77], Hurst exponent in frequency domain[78]
    Features in the time and frequency domains Micro-Doppler features[41,42], the ridge integration of NTFD[75], the number of connected regions and the maximum size of connected regions in a binary image[75]
    Polarization features Relative surface scattering power[76], relative dihedral scattering power[76], and the relative volume scattering power[76]
    下载: 导出CSV

    表  7  Detection performances of different methods for the detection of micro-motion maritime targets[42]

    Parameter MTD FRFT WVD SPWVD ST-SFT ST-SFRFT
    Pd(%) (SCR = –5 dB) 39.26 57.26 35.68 55.24 49.21 71.35
    Pd(%) (SCR = 0 dB) 52.84 76.84 62.27 72.58 63.28 85.69
    下载: 导出CSV

    表  8  Detection results of different models(%)[43]

    Model LeNet AlexNet GoogLeNet
    False alarm ratio 1.24 0.04 0.24
    Detection probability 92.28 84.44 90.94
    下载: 导出CSV

    表  9  Detection performance comparison between SVM-based detector and other detectors[77]

    Detectors Detection results
    (HH polarization, PF = 0.001)
    SCR = –2 dB SCR=17 dB
    SVM-based detector 76 99
    Tri-feature-based detector 57 99
    Fractal-based detector 18 79
    下载: 导出CSV

    表  10  Detection performance comparisons between the decision tree-based detector and the other detectors[78]

    Detector Detection results
    0 dB 5 dB 10 dB 15 dB
    Decision tree-based detector 0.76 0.84 0.98 0.99
    Tri-feature-based detector 0.58 0.65 0.82 0.95
    Fractal-based detector 0.21 0.32 0.48 0.68
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-06-25
  • 修回日期:  2020-08-14
  • 网络出版日期:  2020-08-28
  • 刊出日期:  2020-09-01

海杂波背景下雷达目标特征检测方法的现状与展望

(中文/English)

doi: 10.12000/JR20084
    基金项目:  国家自然科学基金(61871303),电波环境特性及模化技术重点实验室基金(6142403180204),111引智计划(B18039)
    作者简介:

    许述文(1985–),男,安徽黄山人,博士,副教授,博士生导师,加拿大 Mcmaster 大学访问学者,入选陕西省青年人才托举计划。2011 年在西安电子科技大学获得博士学位,现就职于西安电子科技大学电子工程学院雷达信号处理国家重点实验室。主要研究方向为雷达目标检测、机器学习、时频分析和 SAR 图像处理。E-mail: swxu@mail.xidian.edu.cn

    白晓惠(1998–),女,陕西宝鸡人,西安电子科技大学博士生。主要研究方向为雷达目标检测、机器学习和海杂波信号处理。E-mail: xhbai@stu.xidian.edu.cn

    郭子薰(1994–),女,陕西西安人,西安电子科技大学博士生。主要研究方向为雷达目标检测、机器学习和海杂波信号处理。E-mail: zxguo_724@stu.xidian.edu.cn

    水鹏朗(1967–),男,陕西西安人,博士,教授。1999年在西安电子科技大学获得博士学位,现担任西安电子科技大学电子工程学院雷达信号处理国家重点实验室教授、硕导、博导。主要研究方向为海杂波建模、雷达目标检测和图像处理。E-mail: plshui@xidian.edu.cn

    通讯作者: 许述文 swxu@mail.xidian.edu.cn
  • 责任主编:关键 Corresponding Editor: GUAN Jian
  • 中图分类号: TN95

摘要: 海杂波背景下的雷达目标检测对民用和军事都有着重要的意义。随着海面目标的小型化和隐身化,海面慢速、漂浮小目标已经成为了雷达警戒的重点对象。关于此类小目标的检测一直以来都是海杂波背景下目标检测中的难题。通常,漂浮小目标的雷达散射横截面积(RCS)微弱,并且运动速度慢,常常在时域和频域均存在“超杂波检测”的困难。传统目标检测方法对漂浮小目标的检测存在明显的性能瓶颈。对于海面漂浮小目标的检测,采用高多普勒和高距离分辨体制(“双高”体制)是从雷达体制上解决这个问题的有效途径。在双高体制下,雷达接收的目标回波提供了更多的可用信息。然而,如何将这些更加精细化的信息转化为探测性能的提升,一直以来都是雷达届关注的难点,相关科研成果也一直在不断地推陈出新。近些年,在双高雷达体制下,学者们提出了多种基于特征的目标检测方法,作为对海智能检测的人工特征工程阶段,这些方法缓解了仅依靠能量信息较难检测小目标的困难局面,极大程度地改善了对漂浮小目标的检测性能。为了更好地让相关雷达从业者了解该领域这些年的发展和未来的趋势,该文首先总结了对海检测的难点和常用的目标检测方法,然后分析了特征检测的原理和通用框架以及国内外几种典型的基于特征的检测方法,最后对特征检测方法发展趋势进行了展望。

注释:
1)  责任主编:关键 Corresponding Editor: GUAN Jian

English Abstract

许述文, 白晓惠, 郭子薰, 等. 海杂波背景下雷达目标特征检测方法的现状与展望[J]. 雷达学报, 2020, 9(4): 684–714. doi:  10.12000/JR20084
引用本文: 许述文, 白晓惠, 郭子薰, 等. 海杂波背景下雷达目标特征检测方法的现状与展望[J]. 雷达学报, 2020, 9(4): 684–714. doi:  10.12000/JR20084
XU Shuwen, BAI Xiaohui, GUO Zixun, et al. Status and prospects of feature-based detection methods for floating targets on the sea surface[J]. Journal of Radars, 2020, 9(4): 684–714. doi:  10.12000/JR20084
Citation: XU Shuwen, BAI Xiaohui, GUO Zixun, et al. Status and prospects of feature-based detection methods for floating targets on the sea surface [J]. Journal of Radars, 2020, 9(4): 684–714. doi:  10.12000/JR20084
    • 我国拥有长达1.8×104 km的海岸线和3×106 km2的蓝色国土,岛礁星罗棋布,领海、专属经济区、大陆架的无缝监控和管理成了建设海洋强国的首要任务之一。随着我国建设海洋大国基本国策的确立,海面监视对于海洋国土保护起到越来越重要的作用。各种类型的雷达系统构成了实施海环境全天候、全天时监控的主要装备。利用雷达技术对海面进行观测是实现海面动态监测以及海面目标预警监视的一个重要手段。随着雷达对海观测在军事科技领域的广泛应用和在民事领域的迅速发展,针对海面电磁散射回波的研究也受到人们越来越多的重视。研究复杂海面回波信号的主要目的通常有两种:一是从海面的回波信号中提取反映海洋动态特性的信息(例如浪高、浪向、风速等);二是从复杂海面回波信号中探测出目标(例如船只、浮冰、飞机等),此时海面回波信号便是一种干扰因素,通常被称为海杂波。

      海杂波定义为雷达电磁波照射到海表面时接收到的海表面后向散射回波[1-4]。海杂波产生的物理机理复杂,依赖于很多因素,其中包括了复杂海面本身的状况以及雷达的工作状态。由于受到环境因素和雷达设备参数的影响,海杂波的特性也不断改变;相较于地面杂波,海杂波的空时变化要更为复杂。目前,海面微弱目标检测面临的主要困难来自于4个方面:

      (1) 慢速小目标回波微弱。小型船只、冰山、蛙人、碎片、潜艇潜望镜、隐身目标等海面小型目标有很小的雷达散射截面积(如图1所示)。由于回波较弱,这些目标在常规雷达中具有非常低的信杂比(Signal Clutter Ratio, SCR)。虽然海上反入侵雷达设计成高的空间和多普勒分辨率,以便将SCR提升到临界值使得感兴趣的目标可检测,但即便如此,在低SCR情况下传统检测方法依然很难进行检测。同时,由于目标运动速度较慢,且海杂波具有较宽的多普勒带宽,目标和海杂波在多普勒上很难区分,因此这类检测通常被称为“超杂波检测”。传统的自适应类检测方法在这种情况下很难奏效。

      图  1  常见的海面小目标

      Figure 1.  Some common small targets on the sea

      (2) 空时变海杂波异常复杂,海杂波特性认知难度大。雷达系统的距离方位以及多普勒的高分辨率观测使得海杂波已然不满足于传统的大尺度下的统计特性,具有更加复杂的特征。受海洋气象、地理环境等诸多因素的影响,海面非线性随机变化,机理非常复杂。同时,海浪随风速的增加而增高,在重力作用下,当海浪失去平衡状态时产生破碎波,而在海浪彻底破碎之前的“劈结构”使得其出现类镜面反射,从而出现较强的回波,即为海尖峰[3-8]。而与目标特性极其相似的海尖峰分量的出现,使得杂波的建模变得异常复杂[9,10]。同时,随着我们的关注点从近岸转向远海,对海雷达必须对一定范围的陌生海洋环境进行监控和侦查。海杂波的“三非”特性,也就是非均匀、非平稳和非高斯特性更加明显。如图2(a)所示,海杂波的功率图呈现出很强的非均匀和非平稳特性。如图2(b)中所示,杂波的经验概率密度函数严重偏离了瑞利幅度分布,呈现出明显的非高斯特性。强烈的非均匀和非平稳特性意味着海杂波的特性仅在临近的距离-方位分辨单元可以认为是保持不变的,而随着空间距离的增加,海杂波的同分布程度大为下降。虽然海杂波在慢时间维的特性变化比较缓慢(与气象条件和海况变化的时间尺度同阶),但大场景扫描观测雷达缺乏长时间驻留观测的时间资源,从而很难在慢时间维上获取大量独立同分布样本。也就是说,雷达对海探测虽然可以得到整个场景下大量的海杂波数据样本,但估计一个雷达分辨单元的海杂波特性时,完全独立同分布的样本只有局部的、短时间区间内的小数目样本。因此,海杂波特性感知本质上是一个“小样本”问题,我们称之为“本性小样本”问题。同时,由于大场景海杂波的特性是空变和时变的,因此必须实时在线感知大场景中随着空间和时间变化的海杂波特性,才能实现真正意义上的恒虚警检测。

      图  2  实测数据功率图及幅度拟合结果

      Figure 2.  Power map of measured data and amplitude fitting results

      (3) 目标模型难以建立。大型船舶的运动和姿态几乎不受海浪的影响,而海面小目标的运动和姿态会受到海风和海浪的严重干扰。由于海面小目标的复杂运动模式(包括横滚、俯仰、偏航等),目标甚至会在某段时间里,部分或全部被海浪遮挡,因此小目标回波具有严重的RCS起伏及复杂的振幅和多普勒调制现象。海面目标的种类多种多样,通常可以分为以下3类:第1类是海面上空低空掠行的目标,这类目标运动速度快,机动性强,能够被雷达有效地检测;第2类是海面上的大型目标,如大型舰船、游轮等,这类目标的实际物理尺寸较大,RCS较大,也能够被雷达有效地检测;而第3类就是海面上的漂浮小目标,如飞机残骸、蛙人、潜望镜等,这类目标的RCS小,并且雷达回波常常会被淹没在海杂波中,不容易被检测,属于海面低可观测目标,如何有效地对海杂波背景下的海面低可观测目标进行检测是研究人员一直在探索的问题[12,13]。因此,在所有情况下建立类似于自适应检测类方法中目标的简单参数模型来描述感兴趣目标的回波是困难的,必须发展新的特征检测方法。

      (4) 目标、海杂波类别非平衡。在对海观测中,海场景较大,而在海面上游弋的微弱小目标相对海面回波却数量有限。因此,获取的大量数据中,绝大部分的数据均为海杂波回波数据,而目标回波数据的数据量远小于海杂波,这在机器学习和模式识别中,称为“类别非平衡问题”,这个现象造成的原因在于目标相对于海杂波的稀疏性。传统的模式识别和机器学习中的方法对于处理类别非平衡问题,会出现分类性能下降的情况。因此,传统机器学习方法在海杂波背景下微弱小目标检测上也同样面临着挑战。

      由于目标类型的不断出现和雷达体制的不断变化,对海微弱小目标雷达探测是一个长期的话题,经久不衰。随着雷达体制的变革和新的信号处理技术手段的出现,对海目标雷达探测领域涌现出了许多新问题和针对这些问题的新方法。本文首先总结一下目前常用的对海目标雷达检测的方法。然后,作为对海目标智能检测算法评估的一个重要组成部分,本文介绍了目前常用的用于设计和测试特征检测方法性能的数据集,并逐一介绍了目前涌现出的一系列特征检测类的方法,最后对海杂波背景下基于特征的目标检测技术进行展望。

    • 随着建设海洋强国战略的确立,对海雷达装备快速发展,后发优势使我国完成了硬件上的“追赶超越”,形成了对海雷达“硬超越,软滞后”的局面。对海雷达面临共性问题:“临界信杂比下的目标检测问题”。低分辨警戒、预警雷达对于传统大型舰船的检测难度不大,通常采用非相干或者相干的检测方法。其中,非相干类检测方法主要是利用雷达回波的幅度和功率进行检测,主要方法有单元平均恒虚警率(Cell-Average Constant False Alarm Rate, CA-CFAR)检测器,最大选择(Greatest Of, GO)或最小选择(Smallest Of, SO) CFAR检测器等,常用于早期非相干雷达脉冲体制的检测中[14-16]。在相干雷达脉冲体制下,自适应类检测算法是将海杂波建立于某种特定的统计模型下,从而发展出一系列对应于该模型的最优或近最优检测器,检测方法流程图如图3所示。

      图  3  自适应检测方法流程图

      Figure 3.  The flowchart of the adaptive detection methods

      在小擦地角情况下,随着雷达分辨率的提高,海杂波可以被建模为复高斯分布模型,基于该背景,Kelly[17]和Robey[18]分别提出了广义似然比检测器(Generalized Likelihood Ratio Test, GLRT)和自适应匹配滤波(Adaptive Matched Filter, AMF)检测器,它们均具有良好的检测效果。然而在高分辨雷达和低掠射角情况下,海杂波具有强的非高斯性,复高斯分布模型不再适用,此时可以将海杂波建模为复合高斯模型(Compound Gaussian Model, CGM)[19],即一个慢变的纹理分量和一个快变的散斑分量的乘积

      $${{c}}\left( n \right) = \sqrt {{{\tau}} \left( n \right)} {{u}}\left( n \right)$$ (1)

      Conte[20]和Richmond等人[21]基于复合高斯模型提出了归一化匹配滤波检测器(Normalized Matched Filter, NMF)和自适应归一化匹配滤波检测器(Adaptive Normalized Matched Filter, ANMF)。在一个雷达相干处理时间内(Coherent Processing Interval, CPI),复合高斯模型可以退化为球不变随机向量模型(Spherically Invariant Random Vector, SIRV),此时的纹理分量为正的随机常数,散斑分量服从复高斯分布

      $${{c}} = \sqrt {{\tau}} {{u}}$$ (2)

      根据纹理分量分别服从Gamma分布、逆Gamma分布和逆高斯分布的随机变量,发展了K分布下的最优检测器(Optimum K-distributed Detector, OKD)[22,23],广义Pareto功率分布下的最优广义似然比线性门限检测器(Generalized Likelihood Ratio Test-Linear Threshold Detector, GLRT-LTD)[24,25]和IG-CG分布下最优逆高斯纹理的广义似然比检测器(Generalized Likelihood Ratio Test with Inverse Gaussian texture, GLRT-IG)[26]等。此外,由于K分布下最优检测器工程上的不可实现性,匹配于形状参数的α-AMF检测器[27]被提出,其结构更简单并且检测性能与OKD近似且工程上可实现。自适应类的检测方法适用于短时相干累积,常用于海面上大型目标、运动目标的检测。这类检测器主要用于广域的警戒雷达和监视雷达,由于要兼顾扫描效率,所以通常在一个波位驻留时间内,可积累的脉冲数有限。但是,海杂波具有较宽的多普勒带宽,当海面目标速度较低或较小时,目标回波往往会淹没在强的海杂波中,因此对于海面微弱目标,自适应检测算法性能存在较大程度的下滑。因此,这类方法很难用于检测海面的微弱目标。目标回波数据的信杂比可以利用目标所在距离单元数据的功率进行估计,首先从纯杂波单元估算海杂波的平均功率${\bar p_c}$,如果假设雷达回波与海杂波是相互独立的,那么平均信杂比可以用如式(3)进行估计

      $$ {\rm{ASCR = 10\lg}}\left( {\frac{{1/N\displaystyle\sum\limits_{n = 1}^N {{{\left| {{{x}}(n)} \right|}^2}} - {{\bar p}_c}}}{{{{\bar p}_c}}}} \right) $$ (3)

      其中,${{x}}(n)$表示目标所在单元回波序列,N为序列长度。实际信杂比在平均信杂比附近有一定起伏。

      对于要发现隐身舰船这类小RCS目标,传统检测方法处于临界信杂比状态,需通过“认知海杂波抑制”突破困局。比如,濒海战斗舰的RCS约为100 m2,美国朱姆沃尔特级驱逐舰DDG1000的RCS仅为60 m2,而隐身快艇的RCS也仅为30 m2。这些隐身设计舰船的出现同样也使得低分辨警戒雷达和预警雷达的目标检测难度有所增加。我们通过TSC模型,仿真了VV逆风情况下,海况4级的时候针对各种不同的舰船的信杂比。从图4可以看出,利用传统方法,对于10脉冲最小可检测的SCR,在50~300 km的范围里,RCS为30 m2和60 m2的舰艇,均很难进行检测。因此需要改变雷达工作体制和发展新型的目标检测算法。

      图  4  VV极化、逆风情况下,海况4级时各种不同舰船的信杂比

      Figure 4.  In the case of headwind situation, SCR for various ships at sea state 4 (VV polarization)

    • 海面目标除了大型舰船目标还包括近距离慢速小目标,由于“空间分辨率性能瓶颈”限制,如前文所述,低分辨雷达难以发现。传统基于MTI和MTD以及自适应检测类的目标检测是基于精确的杂波和目标回波统计模型的,因此各种最优和近最优的检验统计量扮演了检测的“主角”。随着观测手段的精细化,背景杂波和目标回波变得极其复杂以致难以进行精确的统计建模。在这种情况下,空间高分辨、多普勒高分辨的“双高”体制是主要的技术途径。目前实现双高的雷达体制主要有如图5所示3种情况,分别是宽发窄收模式,泛探雷达体制以及快速普查加疑似点驻留的模式。

      图  5  可实现“双高”体制的雷达工作模式

      Figure 5.  Radar working modes that realize the "double high" system

      高分辨小目标探测雷达需要面对极其复杂的高分辨海杂波特性和小目标回波特性,那么突破临界信杂比检测性能的关键在于:海杂波特性的深度认知(deep cognition)、精细感知(elaborate perception)和充分利用(full utilization)。这种情况下通常采用杂波和目标回波的一个或多个差异性特征实现联合检测,这类方法被称为基于特征的检测技术,简称为特征检测技术。特征检测技术在图像处理、模式识别等领域里已经广泛普及并产生了良好的效果,特征检测技术可以认为是智能检测的初步版本,是进入智能检测时代的必经之路。海杂波背景下基于多特征的检测方法是通过对雷达和目标回波提取具有差异性的特征,将杂波与目标高重叠的观测空间降维到低重叠的特征空间,在特征空间中对目标进行检测。传统的雷达目标检测算法都是基于某个特定的检验统计量,对海杂波背景下的微弱目标检测性能有限。因此,本课题组将多特征联合技术应用到了小目标检测中来,提出了联合3特征的检测方法[28],改善了传统方法的性能损失问题。特征是用以描述杂波与目标之间差异性的指标,检测中不必局限于特定的特征,而是根据实际环境和雷达的设备信息,从雷达回波的幅度、多普勒谱、时频图、极化信息等不同方面进行提取,由此提出基于不同特征的检测方法。同时,随着特征的增多,能够更全面地反映目标和杂波的差异性,利用机器学习算法对高维特征空间进行目标检测的方法也相继被提出,极大程度地提高了检测性能。作为海杂波中特征检测问题的尝试,国内外学者很早就开始了相关的研究,并获得了大量的研究成果,提出了许多特征检测类方法,如基于海面分形和混沌特征、时频分析方法、人工智能类方法等,图6为特征检测方法的流程图。下面来简要概述一下这几种方法,在后续的第4节有更详细的介绍。

      图  6  特征检测流程图

      Figure 6.  The flowchart of the feature-based detection methods

      (1) 基于海面分形和混沌特征的检测方法:分形理论是20世纪70年代由Mandelbrot提出的一种理论,用于表征复杂图形和复杂过程,是非线性科学研究中一个十分活跃的分支。1993年Mcmaster大学的T. Lo等人[29]通过对实测海杂波数据的研究,根据海杂波与目标呈现出不同的分形特性,提出了一种新的基于分形理论的目标检测方法。2006年Hu Jing等人[30]引入了基于多重分形理论的海杂波目标检测算法,通过分析实测海杂波数据,提出海杂波数据在0.01 s到几秒范围内存在多重分形特征,并通过计算海杂波的Hurst指数来检测目标,并具有良好的检测性能。海军航空大学的何友院士、关键教授、刘宁波、陈小龙等人[31,32]也在这方面做了大量的工作。基于分形的方法具有计算简单、效率高等特点,但由于海杂波时间序列只有在一定的时间尺度的无标度区内具有分形特征,该区间随雷达参数、海况、极化的改变而不同,且对无标度区估计出现偏差也会影响检测器的性能。当观测时间较长时,该类方法可以获得对海面漂浮小目标较好的检测性能,然而如果观测时间较短时,检测器的性能下滑严重。1995年以来,Mcmaster大学Simon Haykin教授等人[33,34]提出海杂波具有混沌特性且海杂波是短期可以预测的。根据海杂波的短期可预测性,通过对海杂波回波序列构建一个非线性预测模型,利用预测误差进行统计假设检验,以达到目标检测的目的。后来Haykin对他之前提出的海杂波混沌模型提出了质疑,且当信杂比持续降低时,检测结果不理想,很难实现对慢速微弱小目标的检测。

      (2) 基于时频分析的检测方法:近些年,国内外学者提出了许多基于时频分析的方法用来检测海面目标[35-40]。这些方法通过时频分析工具如短时傅里叶变换(Short-Time Fourier Transform, STFT)、Wigner-Ville分布(Wigner-Ville Distribution, WVD)、平滑伪Wigner-Ville分布(Smoothed Pesudo-Wigner-Ville Distribution, SPWVD)、分数阶傅里叶变换(FRactional Fourier Transform, FRFT)等,通过参数或非参数化方法在二维平面上提取与目标对应的特征来完成海杂波背景下目标的检测。在基于时频分析的方法中,通过进行适当的时频变换,可以得到更多从时域中无法得到的细节与信息,克服了傅里叶分析时域和频域完全分离的缺点,可以兼顾时域和频域。然而根据海森堡的测不准原理,STFT中时间窗函数的长度越长,频率分辨率就越高,而时间分辨率则会越差。采用双线性形式的Wigner-Ville变换可以提高时域和频域的分辨率,但由于非线性变换,当出现多个信号成分时会出现严重的交叉项,交叉项的出现会降低检测器对微弱目标的检测性能。而SPWVD虽然可以很好地抑制交叉项,但是牺牲了算法的运算效率,并且联合时频分辨率也同时下降。采用FRFT的时频分析方法虽然不存在交叉项,对大型舰船目标具有较好的检测性能,但是对于复杂海面上慢速微弱小目标依然检测性能不佳。海面微弱小目标由于受到海浪的影响,运动复杂,目标信号通常表现为弱的非线性调频信号,这使得这类检测方法在实际应用中面临诸多挑战。近年来,学者们对微多普勒理论的研究逐渐增多。微多普勒是由目标的微动所引起的多普勒频移,反映了多普勒特性上的变化,目标的微动状态能够良好地反映目标的精细特征,因此微动目标的回波特征可以与杂波特征进行有效的区分。基于微多普勒特征的检测方法是将微动目标的回波信号建立为合适的模型,采用傅里叶变换、时频分布等方法对微动特征进行分析,从而提升海面微弱目标的检测能力。现有的基于微多普勒理论的海面目标检测方法有:基于高斯短时分数阶Fourier变换的海面微动目标检测方法[41]、基于短时稀疏时频分布的雷达目标微动特征提取及检测方法[42]、基于卷积神经网络的海上微动目标检测与分类方法[43]等。

      (3) 基于人工智能的海面目标检测方法:基于人工智能方法的海面目标检测开始于Haykin等人[33]提出的神经网络类的方法,取得了一定的进展。随着人工智能和机器学习技术的发展,一些学者们把人工智能的新技术引入到了海杂波的目标检测中[44-48]。近年,Nerea del-Rey-Maestre和David Mata-Moya等人[49]将人工智能用于海杂波目标检测并进行了实测数据的验证。在他们的复合假设检验问题中,神经网络检测器可被近似成奈曼-皮尔逊准则(Neyman-Pearson, NP)检测器。他们分析了基于约束广义似然比(Constrained Generalized Likelihood Ratio, CGLR)的次优方法,并与基于多普勒滤波的常规方法进行了比较。其中,基于2阶的神经网络的人工智能解决方案提供了最好的结果,同时可以实时并以极低的计算成本来近似CGLR。

    • 检测器的性能优劣需要用实测数据进行验证。由加拿大McMaster大学Haykin教授[50]带领的团队分别在1993年和1998年利用IPIX(Intelligent PIxel processing X-band)雷达采集了大量高分辨海杂波数据并公开在他们的网站上。IPIX雷达可以发射水平极化(H-polarization)和垂直极化(V-polarization)电磁波,并可以利用两个线性接收器完成水平接收和垂直接收,因此雷达进行数据采集时通常可以得到HH, VV, HV和VH 4种极化的雷达回波数据。

      这里主要介绍10组在1993年采集的数据和2组1998年采集的数据。两次采集数据时雷达工作地点、数据采集参数和合作目标有一定区别。采集1993年数据时雷达架设在加拿大东海岸,新斯科舍省达特茅斯(Dartmouth, Nova Scotia)附近30 m高的悬崖上,雷达朝大西洋海面照射,待检测目标是被铝丝包裹直径1 m的漂浮圆球。雷达工作频率为9.3 GHz,波束宽度为0.9°,距离分辨率为30 m。雷达工作在驻留模式,脉冲重复频率(Pulse Recurrence Frequency, PRF)为1000 Hz,驻留时间约为131 s,每组数据包含14个距离单元。由于雷达以低掠射角照射目标,目标起伏和摆动导致目标能量扩散,并且在进行数据采集时采取了距离过采样,因此目标所在单元周围的临近单元会受到目标能量的影响,记为受影响单元。1993年数据的风速和浪高可以从网上数据采集时的环境记录中获得,数据详情如表1所示。

      表 1  1993年IPIX雷达数据说明[28,50]

      Table 1.  The description of IPIX radar data collected in 1993[28,50]

      数据名称Data name浪高(m) Wave heights (m)风速(km/h) Wind speed (km/h)目标所在单元Primary受影响单元Secondary
      #172.2998, 10, 11
      #261.1976, 8
      #300.91976, 8
      #310.91976, 8, 9
      #401.0975, 6, 8
      #540.72087, 9, 10
      #2801.61087, 10
      #3100.93376, 8, 9
      #3110.93376, 8, 9
      #3200.92876, 8, 9

      根据Douglas海况标准,后9组数据为2~3海况,有少量破碎波和白帽现象的存在。由于海浪较低,目标绝大部分时间均可以被雷达波照射到;第1组数据为3~4海况,破碎波和白帽现象出现频率增加,测试目标有时会被海浪遮住无法被雷达波直接照射。同时可以看出浪高与风速没有直接联系,这是由于浪高与多种因素有关,大的涌浪通常可以从浪高较高的完全发展海域传播很远,短时间较大的局部风通常不会对浪高造成太多的影响,但会一定程度增加破碎浪的出现频率。

      1998年IPIX雷达被安置在安大略湖(Lake Ontario)的格里姆斯比(Grimsby, Ontario)采集了一组新的数据,雷达架设高度为20 m,待测目标为漂浮的小船。距离分辨率为30 m,距离上临界采样,脉冲重复频率为1000 Hz,驻留时间为60 s,包含28个距离单元。目标采集时的浪高等环境信息没有在网上公布,数据信息如表2所示。

      表 2  1998年IPIX雷达数据说明[28,50]

      Table 2.  The description of IPIX radar data collected in 1998[28,50]

      数据名称Data name距离范围(m) Range(m)目标所在单元Primary受影响单元Secondary雷达照射方向Radar direction
      #2022253201~40112423, 25
      #2025253201~401176, 8
    • CSIR雷达部署在奥弗山测试范围(Overberg Test Range, OTB)的3号测量站(MS3)上,位置分别为南纬34°36'56.52",东经20°17'17.46"。部署现场的平面图如图7所示,试验架设位置如图8所示。

      图  7  部署现场平面图[11]

      Figure 7.  A plan overview of the deployment site[11]

      图  8  2006年试验架设位置(OTB)[11]

      Figure 8.  Location of the deployment site in 2006 (OTB)[11]

      表3显示了部署站点雷达的主要特性。

      表 3  OTB MS3的主要特性[11]

      Table 3.  Main characteristics of OTB MS3[11]

      参数Parameter数值Value
      纬度Latitude34°36'55.32"S
      经度Longitude20°17'20.11"E
      地面高度Ground height53 m
      天线高度Antenna height56 m
      离海距离Distance to sea1.2 km
      方位角范围Azimuth coverage208°~80° N (SSW-ENE)
      距离Range(CNR > 15 dB) 1.25~4.50 km
      擦地角Grazing angle(< 15 km) 3.00°~0.16°
      擦地角Grazing angle(CNR > 15 dB) 3.0°~0.7°

      Fynmeet动态雷达横截面积(RCS)测量设备由CSIR开发,并由CSIR,南非军备公司(ARMSCOR)和南非空军(SAAF)共同拥有。从本质上讲,它是经过校准的相干RCS测量设备,其工作频率为6.5~17.5 GHz,该系统相关系统参数如表4中所示。

      表 4  Fynmeet系统和性能参数[11]

      Table 4.  Fynmeet system and performance specifications[11]

      系统组成System composition系统参数System parameters参数设置Parameter values
      发射机Transmitter频率范围Frequency range6.5~17.5 GHz
      峰值功率Peak power2 kW
      PRF范围PRF range0~30 kHz
      波形Waveforms固定频率波形,步进频率波形,频率捷变波形Fixed frequency waveform, step frequency waveform, frequency agility waveform
      捷变带宽Agile bandwidth脉冲间500 MHz 500 MHz pulse to pulse
      天线Antenna类型Type双偏移反射器Dual-offset reflector
      增益Gain≥ 30 dB
      波束宽度Beamwidth≤ 2° (3 dB波束宽度) ≤2° (3 dB beamwidth)
      旁瓣Slidelobes≤ –25 dB
      接收机Receiver动态范围Dynamic range60 dB (瞬时) / 120 dB (总计) 60 dB (instantaneous)/120 dB (total)
      灵敏度Sensitivity0.1 m2 @ 10 km
      仪表范围Instrumented range200 m~15 km
      距离门Range gates1~64; ΔR = 100 ns, 300 ns or 400 ns
      采样器类型Sampler type中频采样器(IFS) Intermediate frequency sampler
      编码类型Encoding type正交编码Quadrature
      镜像抑制Image rejection≤ –41 dBc

      在试验期间布置了以下外围记录设备:两个气象站分别以15 min和1 h的间隔记录环境状况,定向记录波浪浮标以30 min为间隔记录重要的波浪高度,最大波浪高度,波浪方向和波浪周期。

      试验期间4天采用了3艘合作船只,分别为WaveRider刚性充气船(RIB),Machann快艇和Timothy渔船,如图9所示,用来记录回波数据等测量结果。测量试验定义了一系列海杂波和回波数据测量,包括在不同发射频率下针对不同波形,方位角和范围的测量。此测量试验采用的原理是,只要环境条件发生显著变化,就会重复进行这组测量。实际上,这组测量每天重复一次。在计划阶段,整个测量过程大约需要6.5~7.0 h,即一整天。因此试验定义了测量的子集(例如,仅在单个频率,单个方位角的情况下),仅需要较少的时间来完成。最小的测量子集需要2 h完成。

      图  9  试验合作船只[11]

      Figure 9.  Experimental cooperative boats[11]

      试验对海杂波成功记录并预处理了156个测量数据集,总计超过160 min。此外,记录了113个目标回波测量数据集(127 min),使试验过程中记录的数据集总数达到269个,总记录时间为289 min。大多数数据集都记录了固定频率的波形。在子集中,大多数数据集在9 GHz和6.9 GHz的发送(Tx)频率下以15 m分辨率记录。由于试验期间经历的平均风速较高,因此大多数数据集都是以165°N的天线方位角记录的。只要有可能,就在不同的方位角(通常以15°的间隔)进行测量。定期记录了其他频率(8 GHz和10.3 GHz)以及其他波形的测量结果,从而可以研究不同波形和Tx频率的海浪杂波和船回波特性之间的相关性。

    • 从海杂波特性和海上目标探测技术研究需求出发,借鉴加拿大McMaster大学的IPIX雷达数据集和南非CSIR的Fynmeet雷达数据集在数据采集和记录方面的成功经验,海军航空大学海上目标探测课题组推出一项“雷达对海探测数据共享计划”,旨在利用X波段固态全相参雷达分阶段分批次开展对海探测试验,获取多种条件下雷达实测数据和试验辅助数据,构建形成可以用于支持海杂波特性认知、海杂波抑制、海上目标检测跟踪与分类识别技术研究的数据集,分批次公开共享。

      试验中所使用的雷达为X波段固态功放监视/导航雷达,主要用于船舶导航和海岸监视等场景,能清晰分辨多种量程下的各种目标,具有高距离分辨率、高可靠性、距离探测盲区小等特点,如图10所示。雷达采用固态功放组合脉冲发射体制(见图11),以提高距离分辨率,减小距离盲区,降低雷达辐射功率,发射时间为40 ns~100 μs,利用接收信号和发射信号的时差计算目标距离,水平面内360°全方位扫描。雷达技术参数如表5所示。

      表 5  X波段试验雷达参数[51]

      Table 5.  X-band radar parameters[51]

      雷达参数Radar parameters参数设置Parameters setting
      工作频段Working bandX
      工作频率范围Frequency range9.3~9.5 GHz
      量程Measuring range0.0625~96 nm
      扫描带宽Scanning bandwidth25 MHz
      距离分辨率Range resolution6 m
      脉冲重复频率Pulse repetition frequency1.6 K, 3 K, 5 K和10 K
      发射峰值功率Transmit peak power50 W
      天线转速Rotating speed of antenna2 rpm, 12 rpm, 24 rpm, 48 rpm
      天线长度Length of antenna1.8 m
      天线工作模式Antenna operation mode凝视、圆周扫描Gaze, circular scanning
      天线极化方式Antenna polarizationHH
      天线水平波束宽度Antenna horizontal beam width1.2°
      天线垂直波束宽度Antenna vertical beam width22°

      图  10  X波段固态功放监视/导航雷达[51]

      Figure 10.  X-band solid-state power amplifier surveillance/navigation radar[51]

      图  11  组合脉冲发射的3种模式[51]

      Figure 11.  Three modes of combined pulse transmission[51]

      该数据集相关的资料和数据下载链接可以在《雷达学报》网站上进行获取。

    • 从公开文献来看,国外较为典型的岸基雷达海杂波测量试验还有澳大利亚国防科技署(Defence Science and Technology Organization, DSTO)的多波段(L, S和X波段)雷达海杂波测量试验[52-54]、美国海军研究实验室(Naval Research Laboratory, NRL)的X波段雷达海杂波测量试验[55]、西班牙南海岸Ka波段高分辨率雷达海杂波测量试验[56]等。除此之外,还包括美国海军空战中心的多波段(UHF, L, S, C, X和Ku波段)雷达小擦地角海杂波测量试验[57,58]、英格兰南海岸多波段(S, X和Ku波段)雷达海杂波测量试验[59]、日本的X波段雷达海杂波测量试验[60]、德国和法国联合开展的MARLENE(Mediterranean RFC and Sea Clutter Environmental Experiment)多波段(C, X, Ku, Ka和W波段)雷达海杂波测量试验[61]、伦敦大学(University College London, UCL)的S波段NetRAD单/双基地雷达海杂波测量试验[62-66]等。

    • 如前文所述,随着观测手段的精细化,背景杂波和目标回波变得极其复杂以致难以进行精确的统计建模。在这种情况下,空间高分辨、多普勒高分辨的“双高”体制是主要的技术途径。而高分辨小目标探测雷达需要面对极其复杂的高分辨海杂波特性和小目标回波特性,那么突破临界信杂比检测性能的关键在于:海杂波特性的深度认知、精细感知和充分利用。本节将着重介绍基于高距离分辨和长时间观测雷达体制下的基于特征的检测器的发展历程和动态。需要说明的是,本文中主要涉及信号层面的特征,没有涉及航迹和数据层面的特征,因此对数据级层面的特征将不进行介绍。

      基于特征的检测方法现有的特征列表如表6。分形特征是早期特征检测采用的单一特征,在长时观测下对海面漂浮小目标有良好的检测效果[29,31,67],随后,大量学者研究了多重分形特征[30,68]、不同变换域上的分形特征[69-73]并取得良好的检测结果;海杂波的混沌特征认为海杂波时间序列可以利用某种非线性动态模型来描述其演化规律并进行预测[33],利用预测误差来进行判断。基于海杂波的复合高斯模型,为了消除长时观测下复合高斯模型中纹理分量非平稳性的影响,提出了散斑一致性因子特征[74],它也属于时域特征的一种。单一特征检测均利用所计算的特征值与给定虚警概率下的门限进行比较,从而判断目标的有无。随着特征检测方法的发展,大量不同层面的特征被提出,基于时域能量和频谱差异的特征[28],基于时频分析的适用于微动目标的微多普勒特征[41,42]和基于海杂波归一化时频分布差异的特征[75],以及极化特征[76]表6给出了常用的几种特征。随着特征数目的增多,单一特征检测会造成一定的性能损失,联合多特征进行检测是大势所趋。然而,联合多特征检测中如何确定检测器门限成为了多特征检测的难题。本课题组在文献[28]提出了凸包学习算法,将检测问题视为单分类问题,检测门限的确定转化为检测判决区域的选取,然而其具有一定的局限性,仅适合三维特征空间的检测,随着维数的增加,凸包学习算法的复杂度提高,难以进行检测。随后,基于机器学习的算法被提出,文献[77,78]分别利用支撑向量机和决策树算法选取判决区域,突破了维数的限制,可有效利用多维特征进行检测,并可以取得良好的检测结果。下面对几种特征及检测方法进行详细的介绍。

      表 6  现有特征检测方法的特征

      Table 6.  Features introduction of feature-based detection method

      现有特征Existing features
      分形特征Fractal features单分形特征[29,31,67]、多重分形特征[30,68]、分数阶傅里叶变换域的分形特征[69-73] Single fractal features[29,31,67], multifractal features[30,68], fractal features in FRFT[69-73]
      海杂波混沌特征Chaotic characteristics of sea clutter关联维、Lyapunov指数以及Kolmogorov熵 Correlation dimension, Lyapunov exponent, and Kolmogorov entropy[33][33]
      时域特征Features in the time domain相对平均幅度[28]、时域的信息熵[77]、时域的Hurst指数[77]、散斑一致性因子特征[74] Relative average amplitude[28], temporal information entropy[77], temporal Hurst exponent[77], the speckle consistency factor[74]
      频域特征Features in the frequency domain相对多普勒峰高[28]、相对多普勒谱熵[28]、频谱峰值与均值之比[77]、频域Hurst指数[78] Relative Doppler peak height[28], relative vector-entropy[28], frequency peak-to-average ratio[77], Hurst exponent in frequency domain[78]
      时频域特征Features in the time and frequency domains微多普勒特征[41,42]、归一化时频分布的时频累积[75]、由归一化时频分布亮像素构成二值图像中的连通区域数目和最大连通区域的尺寸[75] Micro-Doppler features[41,42], the ridge integration of NTFD[75], the number of connected regions and the maximum size of connected regions in a binary image[75]
      极化特征Polarization features相对体散射机制对应能量[76]、相对二面角散射机制对应能量[76]和相对面散射机制对应能量[76] Relative surface scattering power[76], relative dihedral scattering power[76], and the relative volume scattering power[76]
    • 受检测器设计的维度限制,早期的海面小目标检测方法以单特征检测为主,单特征检测器由于检测器设计简单和检测器门限易于确定,所以一直以来受到学者们的关注。国内外学者基于不同的方法,在不同的表示域,提出了很多有效的特征检测方法。

      分形(fractal)理论是20世纪70年代由Mandelbrot提出的一种理论,它用来描述传统欧几里德几何学无法分析的不规则自然特征,大到山川、闪电、海岸线、宇宙星系,小到雪花、冰晶、树叶等大自然形成的图形和复杂过程,是非线性科学研究中一个十分活跃的分支[79,80]。分形可以描述大自然中从宏观到微观不同尺度具有一定自相似性的现象或物质。海面本身波浪起伏,大尺度的涌浪携带着不同波长海浪同样具有一定的分形特性。D. L. Jaggard等人[81,82]经过对具有分形特性的粗糙表面的光和电磁波反射回波的分析发现,回波同样具有一定的分形特性。G. Franceschetti等人[83]进一步将从自然粗糙表面反射的电磁回波描述为二维分形布朗运动。F. Berizzi等人[84]经过对海面以及海杂波的分析,进一步提出海杂波在一定程度上满足分形特性,并具有与海面近似相同的分形维数。在此基础上,F. Berizzi等人[85]利用分形的方法生成海杂波,该方法可以描述杂波与海态、雷达等的关系,克服了传统利用统计模型的方法生成海杂波与操作条件和环境无关的缺点,同时将海杂波的分形特性保留在生成的杂波中。

      1993年T. Lo等人[29]对实测海杂波数据研究发现,海杂波的分形维数大约是1.75,而当海杂波中存在目标信号时,海面原本的分形程度降低了,由此在分形理论的基础上提出了一种新的目标检测方法。分形布朗运动(Fractional Brownian Motion, FBM)是最简单的单分形模型。因为分形布朗运动经过傅里叶变换后依然具有分形特征,有学者在将海杂波幅度回波序列建模为分形布朗运动的基础上,对实测海杂波频谱的分形特性进行了研究,并对检测海面目标进行了尝试[31,67]。2002年Gao等人[68]分析了海杂波的幅度分布、时空相关等特性,并从理论上证明了实测海杂波数据是多重分形的。2006年Hu Jing等人[30]引入了基于多重分形理论的海杂波目标检测算法,通过分析实测海杂波数据,提出海杂波数据在0.01 s到几秒范围内存在多重分形特征,通过计算海杂波的Hurst指数,提出的目标检测算法具有良好的检测性能。检测方法如下:

      (1) 接收到的海杂波时间序列为${{x}} = \left\{ \left. {{{x}}\left( i \right)} \right|i = 1, 2,···, N \right\}$,将其看作是一个随机游走模型。

      (2) 检验是否满足关系式(4)

      $${F^{\left( q \right)}}\left( m \right) = {\left\langle {\left| {{{x}}\left( {n{\rm{ + }}m} \right) - {{x}}{{\left( n \right)}^q}} \right|} \right\rangle ^{1/q}}\sim {m^{H\left( q \right)}}$$ (4)

      H(q)是实值q的函数,如果满足关系式,即说明海杂波序列是分形过程。

      (3) 将${F^{\left( q \right)}}\left( m \right)$${m^{H\left( q \right)}}$在双对数坐标下画出,在近似线性区域通过直线拟合,求出其斜率即为H(q)。

      (4) 当H(q)不随q的变化而变化时,序列即为单分形,否则认为是多分形序列。当q=2时,通常称为Hurst指数,通过比较Hurst指数的大小,基于Hurst指数构建基于分形的检测器。

      (5) 设定门限,如果序列Hurst指数大于门限时,即可判断有目标存在。

      可以通过实测海杂波数据验证该检测器的检测性能。当q=2时,如图12所示。实心线代表纯海杂波距离单元回波数据,空心线为目标单元及目标单元周围的影响距离单元回波数据。从图12(a)中可以看出从24~212区间也就是0.08~4.00 s近似为线性,可以认为在该区间内海杂波数据具有分形结构,被称为无标度区。用最小二乘法对无标度区曲线进行拟合,求得直线的斜率H(2),即Hurst指数,所得结果如图12(b)所示,可以看出目标单元及其周围影响单元的Hurst指数明显高于纯杂波单元。因此利用Hurst指数可以完成对海面目标的检测。

      图  12  14个距离单元分形特性分析[30]

      Figure 12.  Analysis of fractal characteristics in 14 range cells[30]

      下面检验该实测海杂波数据是否为多分形结构,H(q)与q的关系图如图13所示,同样,实心线代表纯杂波单元,空心线代表目标单元及影响单元。可以看到H(q)是q的函数,由此可得海杂波数据具有多分形特征,特别是回波中含有目标时,H(q)随$q$的变换更剧烈。

      图  13  14个距离单元H(q)趋势图[30]

      Figure 13.  The trends of H(q) in 14 range cells[30]

      利用Hurst指数构建的目标检测器,在对IPIX雷达93年10组HH极化下海杂波数据的检测结果如图14

      图  14  HH极化下纯杂波单元与含目标单元Hurst频率分布图[30]

      Figure 14.  Hurst frequency distribution of clutter cells and target cells under HH polarization[30]

      实心代表目标单元,空心代表纯杂波单元,可以看到检测结果非常理想。实验数据HH极化下纯杂波单元与目标单元Hurst指数可以完全分开。该种方法在其他极化下的检测效果也较为理想。但由于93年数据每个距离单元观测时间较长约为131 s,该种方法随着观测时间的缩短,检测性能下降很快。

      学者们也将时域的非线性分形特征检测器推广到其他的变换域。分数阶傅里叶变换域(FRFT)的分形特性也是学者们研究的热点。文献[69,70]对海杂波FRFT谱的多重分形特性进行了研究,并在实测数据上进行了验证。文献[71]提出了一种基于FRFT域空间分形特征差异的海面弱目标检测方法,提高了海杂波背景下弱目标的检测性能。文献[72]基于海杂波FRFT谱计算了多尺度Hurst指数,相较于传统多尺度Hurst指数,有效提升了目标检测性能。近些年,南京邮电大学团队提出了一种FRFT域分形特征检测器[73],主要基于FRFT域的分形特征进行分析海杂波与漂浮小目标的差异性特征,通过去趋势波动分析法,得到目标与海杂波的分形曲线,选取适合的尺度不变区间提取分形维和分形维方差,通过凸包判决完成两特征的联合检测分析,并与单特征检测和均值类CFAR检测器性能对比,验证所提算法的有效性。

      图15为FRFT域分形特征检测器的原理框图。通过对海杂波与目标在FRFT域的分形维和分形维方差进行了研究,图16为去趋势波动分析法确定的分形曲线,通过尺度不变区间的选取得到分形维和分形维方差两组特征,图17为虚警为10–3和10–2时训练样本和待分类样本的平面示意图。图18为FRFT域两特征联合检测器与均值类CFAR检测器的性能对比图。

      图  15  分形特征检测器的原理框图[73]

      Figure 15.  The flowchart of fractal-based detector[73]

      图  16  分形曲线[73]

      Figure 16.  Fractal curves[73]

      图  17  训练样本和待分类样本在二维特征平面的显示图[73]

      Figure 17.  The distribution of training samples and test samples on the two-dimensional feature plane[73]

      图  18  经典CFAR算法检测曲线[73]

      Figure 18.  Classic CFAR algorithm detection curves[73]

      基于海杂波的分形特性,近些年衍生出了一系列基于分形理论的检测算法,包括单分形特征、多重分形特征[86,87]、多重分形关联谱[88]、高阶分形特征、扩展自相似特性、模糊分形理论等。随着分形理论的发展,越来越多的检测方法不断出现,成为目标检测方向的研究热门。

    • 海面是一个非常复杂的动力学系统,由此得到的海面雷达回波受到风向、浪高、浪向、洋流等因素的影响,海杂波回波序列具有明显的非线性特性。1995年,Haykin教授等人[33]运用了关联维、Lyapunov指数以及Kolmogorov熵3个指标,并指出,海杂波具有有限相关维数;其最大Lyapunov指数为正;海杂波是短期可以预测的。其中,相关维数和最大Lyapunov指数对于构成时间序列的雷达信号分量都是必不可少的,并且不会随海况或地理位置发生显著变化。这些结果表明,可能存在导致海杂波产生的普遍混沌结构,从而确定了海杂波时间序列具有明显的混沌特性。根据海杂波的短期可预测性,通过对海杂波回波序列构建一个非线性预测模型,利用预测误差进行统计假设检验,以达到目标检测目的[89-93]。基于混沌理论模型认为海杂波时间序列可以利用某种非线性动态模型来描述其演化规律并进行预测,因此利用神经网络学习方法可以对海杂波序列完成非线性拟合,通过预测误差完成目标检测。混沌系统对噪声异常敏感,具有明显的“蝴蝶效应”,然而实际系统中不可避免地受到各种噪声的影响[94],进而引起系统的异常和不稳定。海杂波混沌模型在学术界一度引起了争议,后来Haykin对之前提出的海杂波混沌模型提出了修正,认为海杂波本质上可能由随机混沌或多个确定性混沌或两者混合产生,而越来越多的学者指出海杂波不具有混沌特性[95-97]。但是这种基于神经网络以及支撑矢量机(Support Vector Machine, SVM)等预测器提供的异常检测思想成为了特征检测研究的一条思路。基于海杂波混沌模型建立起的检测算法的主体思想如图19所示。

      图  19  基于神经网络预测的检测器框图[33]

      Figure 19.  The flowchart of detector based on neural network prediction[33]

      ${{{x}}_{\rm{A}}}\left( n \right)$是实际接收到的信号,${{\overset{-} {{x}}} _{\rm{A}}}\left( n \right)$是基于神经网络算法所得到的预测信号。当${{{x}}_{\rm{A}}}\left( n \right)$只包含海面回波,输出预测误差$e\left( n \right)$较小;但当${{{x}}_{\rm{A}}}\left( n \right)$中包含目标回波时,输出$e\left( n \right)$会有一个较大的值。基于此可以得到基于混沌模型的目标检测算法如下:

      (1) 对于一个回波信号${{{x}}_{\rm{A}}}\left( n \right)$,其中$n = 1,2,···,{N_{\rm{T}}}$,通过神经网络模型得到预测值${{\overset{-} {{x}}} _{\rm{A}}}\left( n \right)$,计算预测误差$e\left( n \right) = {{{x}}_{\rm{A}}}\left( n \right) - {{\overset{-} {{x}}} _{\rm{A}}}\left( n \right)$

      (2) 在观测时间内计算累计预测均方误差得到

      $$ {E_e} = \frac{1}{{{N_{\rm{T}}}}}\sum\limits_0^{{N_{\rm{T}}}} {{e^2}\left( n \right)} $$ (5)

      其中${N_{\rm{T}}}$为观测时间内信号长度。

      (3) 将${E_e}$与给定虚警概率的门限进行比较,如果超过门限,认为存在目标H1假设成立;否则认为没有目标H0假设成立。

      图20为检测结果ROC曲线,实线为传统多普勒恒虚警检测算法,虚线为基于神经网络的恒虚警检测算法,可以看出基于神经网络算法的检测性能优于传统多普勒算法。

      图  20  基于神经网络检测器和传统多普勒CFAR检测器的ROC曲线[33]

      Figure 20.  ROC curves of the detector based on neural network and traditional Doppler CFAR detector[33]

      基于神经网络的检测方法通过对海杂波时间序列的学习,能够对海杂波序列进行良好的拟合,从而通过预测海杂波时间序列,利用预测误差对目标进行检测。其检测框图如图21所示。神经网络对海杂波时间序列的学习规则,可以理解为用神经网络建立了复杂的非线性映射,海杂波的所有特征都是神经网络的学习对象,因此基于该网络预测误差的检测方法是基于海杂波全特征的检测方法。然而基于全特征的检测方法具有较多的缺点,由于海杂波与目标的共性特征比差异性特征多且贡献少,挤占了大量神经网络的资源,增加了网络的学习规模并降低了学习效率,其规模过大的网络使得学习过程训练过多的精细特征,产生“过拟合”现象,网络的泛化能力较差。因此,基于神经网络的学习在很长一段时间受到研究人员的冷落。

      图  21  基于预测的检测方法流程图

      Figure 21.  The flowchart of detection methods based on prediction

      然而,随着深度学习和人工智能的发展,基于神经网络的学习方法在雷达目标检测中产生了良好的应用[98]。典型的深度学习网络有卷积神经网络(Convolutional Neural Network, CNN)、稀疏自编码器(Sparse AutoEncoder, SAE)、深度置信网络(Deep Belief Network, DBN)等等,它们均在合成孔径雷达(Synthetic Aperture Radar, SAR)图像中展开了广泛的应用并且产生了良好的结果,其中,CNN的应用最为广泛。CNN主要包含卷积层、池化层和全连接层,卷积层提取输入图像低级到复杂的特征,池化层对于该图像进行下采样处理,从而减少特征,一定程度上控制过拟合,全连接层将上一层所得到的特征进行排列,对其进行神经网络的连接。SAE方法能够在无监督情况下提取特征,因此成为人们研究的重点。将CNN与SAE结合起来可以得到卷积自编码器(Convolutional Automatic Encoder, CAE),在实际应用中也可以产生良好的效果。深度学习网络的出现为海面目标检测引领了新的方向,基于海面目标的微动特征,有学者提出了利用CNN对海面目标的微多普勒谱图进行分析和处理,相较于传统方法产生了良好的结果[43],越来越多的学者也在尝试利用深度学习网络对海面目标进行检测和分类,神经网络在海面目标检测中的应用还在不断发展和扩大。

    • 现代雷达为了提高距离高分辨率和探测距离,通常发射信号选用大时宽带宽积信号,线性调频信号(Linear Frequency Modulation, LFM)模拟和数字产生均比较方便,形式简单,因此对其的研究也较为深入。时频分析方法能提供较好的时域和频域联合分布信息,在信号处理领域得到了广泛应用,成为了分析时变非平稳信号的有力工具。当目标相对于雷达进行匀加速或匀减速运动时,由于多普勒效应,目标回波为线性调频信号,国内外学者利用时频分析工具如短时傅里叶变化、分数阶傅里叶变换(FRFT), Wigner-Hough变换,伪维格纳-威利分布(Pesudo-Wigner-Ville Distribution, PWVD), Radon-Wigner变换[99,100], Radon-ambiguity变换[101], Chirplet transform[102]等,通过参数与非参数方法完成对非平稳背景下线性调频信号的检测[103]

      根据SAR图像中舰船尾迹的特性,Radon变换和Hough变换被应用于对海面舰船的检测[104,105],这类方法需要完成对观测区域的成像,检测性能的好坏与成像品质关系密切。针对海杂波的非均匀非平稳特性,国内外学者提出了许多基于时频分布的检测方法用来检测目标[106-111]。海杂波和目标在时频聚集性和持续时间上具有一定差异,基于此,有学者通过对时频迭代分解算法进行目标检测[112,113]。分数阶傅里叶变化可以看作对时频平面的旋转操作,且没有交叉项困扰,十分适合处理线性调频信号,国内有学者将分数阶傅里叶变化应用在海面匀加速目标检测中[114-116]。然而海面目标通常会受到海浪的影响,目标信号表现为非线性调频信号,这使得此类检测方法在实际应用中检测性能存在一定的下滑。为了提高对海面目标的检测性能,近年来,中外学者通过时频分析提出了新的检测方法[35-40]。Haykin在文献[35]中通过将海面背景下目标检测问题转换为模式识别中的双分类问题,利用主成分分析法(Principal Component Analysis, PCA)从时频平面中提取时频特征,通过神经网络算法完成杂波与目标的分类。然而实际中雷达需要对未知目标进行探测,因此目标的特征是无法确切获得的,限制了该方法在实际当中的应用,但这种将目标检测问题转化为双分类问题的思想给海面漂浮小目标的检测提供了一个新的思路。小波变换以其优秀的时频局部特性,可以观测到雷达回波中不同的细节信息,因此也有学者尝试用小波变换检测海面中的目标[117]。近些年,很多学者基于微多普勒理论以及基于雷达回波时频图的深度神经网络目标检测方法,也属于时频分析类方法的范畴。

      微多普勒理论是近年来目标探测领域的热点,通过对微动目标的回波进行分析和建模,提取目标的微动特征并利用不同的检测方法对其进行检测。将微多普勒理论引入海面微弱目标检测中,产生了良好的检测结果。海军航空大学团队基于微多普勒理论提出了基于高斯短时分数阶Fourier变换的海面微动目标检测方法[41]、基于短时稀疏时频分布的雷达目标微动特征提取及检测方法[42]、基于卷积神经网络的海上微动目标检测与分类方法[43]等。

      (1) 基于高斯短时分数阶Fourier变换的海面微动目标检测方法[41]。文献[118]介绍了海面刚体目标微动特征的建模,并分别对短时观测条件下和长时观测条件下的微动目标模型进行了研究。海面目标的运动是在三维空间中的复合运动,其微动特征可以表现为目标平动中的非匀速运动以及3轴转动,文献[41]应用了短时观测的条件下海面微动目标的模型,将其建模为幅度起伏的调频信号,同一距离单元内海面微动目标回波可以建模为

      $$ \begin{split} {{x}}\left( t \right) =\,& {{s}}\left( t \right) + {{c}}\left( t \right) = \sum\limits_i {{{A}}_i}\left( t \right)\exp\left( {{\rm{j}}2\pi {f_i}t + {\rm{j}}\pi {k_i}{t^2}} \right) \\ & + {{c}}\left( t \right), \quad \quad \quad \left| t \right| \le {T} \\[-10pt] \end{split} $$ (6)

      其中,${{{A}}_i}\left( t \right)$表示第i个微动信号的幅度,${f_i}$为中心频率,${k_i}$为调频率。在高海情状态下,海尖峰呈现微多普勒特性,雷达常会将海尖峰误判为目标信号,因此,研究微动目标之前采用Fred Posner等人[119]提出的基于3特征参数的海尖峰识别方法对海尖峰进行抑制。对提取出海尖峰的海杂波时间序列采用基于高斯窗函数的STFR-FT(Gaussian STFRFT, GSTFRFT)方法进行运算,通过将变换后的幅值作为检验统计量并与给定虚警概率下的检测门限进行比较,判断有无目标。图22为海杂波抑制后的微动信号变换域特征,图23为海杂波抑制后基于STFT和GSTFRFT的微动信号检测结果比较。在GSTFRFT域中,微动信号的能量得到积累,峰值较为尖锐且旁瓣较低,由于对海尖峰的抑制,对SCR进行了改善,从而提升了检测概率,相较于经典MTD算法,GSTFRFT检测方法可以提升30%以上的检测性能。

      图  22  海杂波抑制后的微动信号变换域特征(N=256)[41]

      Figure 22.  Micro-motion signal features after sea clutter suppression (N=256)[41]

      图  23  海杂波抑制后基于STFT和GSTFRFT的微动信号检测结果比较(N=512)[41]

      Figure 23.  Comparison of micro-motion target detection results based on STFT and GSTFRFT after sea clutter suppression (N=512)[41]

      (2) 基于短时稀疏时频分布的雷达目标微动特征提取及检测方法[42]。文献[42]采用式(6)表示的微动信号,选取了几种常用的时频分布对海面微动信号进行分析,即短时傅里叶变换(STFT)、Wigner-Vill分布(WVD)、平滑的伪Wigner-Vill分布(Smoothed Pseudo WVD, SPWVD)及分数阶傅里叶变换(FRFT),其中,STFT技术的时频分辨力较差,WVD具有严重的交叉项,SPWVD难以突出微动信号的高分辨瞬时调频特性,而FRFT作为参数搜索类方法,参数的估计精度会受到时频分辨力等因素的限制。针对微动信号与海杂波稀疏性的不同,可以利用稀疏分解的思想,将稀疏时频分布(STFD)引入海面目标检测,提出了两种短时稀疏时频分布(ST-SFTD)的微动特征提取和检测方法,分别为短时稀疏傅里叶变换(ST-SFT)和短时稀疏分数阶傅里叶变换(ST-SFRFT)。图24图25分别为基于ST-SFT的海上微动目标检测结果和基于ST-SFRFT的海上微动目标检测结果。表7为不同方法海上微动目标检测性能对比结果。通过比较传统的TFD方法和ST-STFD方法,由于ST-STFD方法在微动信号的最优稀疏域设计检测算法,其检测性能明显提高,然而ST-STFD方法的计算效率仍有待提高。

      表 7  不同方法海上微动目标检测性能对比[42]

      Table 7.  Detection performance of different methods of micro-motion model of maritime targets[42]

      参数ParameterMTDFRFTWVDSPWVDST-SFTST-SFRFT
      Pd(%)(SCR=–5 dB)39.2657.2635.6855.2449.2171.35
      Pd(%)(SCR=0 dB)52.8476.8462.2772.5863.2885.69

      图  24  基于ST-SFT的海上微动目标检测结果(起始时间=20 s)[42]

      Figure 24.  ST-SFT-based micro-motion targets detection results (starting time=20 s)[42]

      图  25  基于ST-SFRFT的海上微动目标检测结果(起始时间=20 s)[42]

      Figure 25.  ST-SFRFT-based micro-motion targets detection results (starting time=20 s)[42]

      (3) 基于CNN的海上微动目标检测与分类方法[43]。随着深度学习的迅速发展,更多的智能化手段应用到了海面目标检测中。基于目标微动特征的时变性,可以利用时频图对微动目标进行有效的分析。文献[43]通过CNN对雷达回波时频图进行了检测和分类,并产生了良好的检测结果。常用的卷积神经网络有LeNet, AlexNet和GoogLeNet, LeNet是最早用于数字识别的卷积神经网络;AlexNet比LeNet层次更深,能够对更复杂的对象进行学习;而GoogLeNet增加了神经网络的深度和宽度,并且保证了计算资源的不变。文献[43]中目标检测的训练集和测试集均分为杂波和目标两类,实测海杂波数据短时傅里叶变换后得到的时频图作为杂波训练集和测试集,通过海面微动目标建模按照一定的信杂比仿真的目标信号作为目标训练集和测试集,首先利用训练集对CNN模型进行训练,之后利用3种CNN模型对测试集进行了检测,3种CNN模型对信号处理效率相当,其中LeNet模型检测概率最高,而AlexNet模型的虚警概率更低。图26为基于CNN的检测方法流程图,其检测结果如表8所示。相较于传统的SVM方法对目标时频图进行分类和检测,基于CNN的检测方法具有更高的检测概率和更低的虚警率,但后者容易受到信杂比的影响。

      表 8  不同模型目标检测结果(%)[43]

      Table 8.  The detection results of different models(%)[43]

      模型ModelLeNetAlexNetGoogLeNet
      虚警概率False alarm ratio1.240.040.24
      检测概率Detection probability92.2884.4490.94

      图  26  基于CNN的检测方法流程图[43]

      Figure 26.  Processing flow diagram of method based on CNN[43]

    • 近些年,基于杂波和目标的特征差异,有学者提出了利用散斑平稳性作为特征差异在海杂波中检测目标[74]。海杂波具有非平稳特性,具体体现在海杂波的纹理是非平稳的,海杂波的散斑在一定时间内是近似平稳的。纹理的非平稳对海面目标检测不利,需要先进行去除,因此该方法首先从非平稳的海杂波中提取出散斑,之后基于散斑的特性来设计检测统计量。由于海面漂浮小目标具有较强的结构性,而散斑的结构特性没有海面漂浮小目标明显,即随着时间的推移,海杂波散斑的一致性要弱于目标的一致性。结合上述两个物理依据,提出了散斑的一致性作为特征对海面漂浮小目标进行检测,其检测流程如图27所示。

      图  27  散斑的平均一致性因子检测器的流程图[74]

      Figure 27.  The flowchart of a feature-based detector using the average consistency factor of speckle[74]

      首先,利用参考样本${{{r}}_{q,k}}$进行归一化样本协方差矩阵(Normalized Samples Covariance Matrix, NSCM)估计,得到NSCM估计值${{{M}}_q}$,其中q为时间间隔,K为参考单元数目,N为积累脉冲个数

      $$ {{{M}}_q} = \frac{N}{K}\sum\limits_{k = 1}^K {\frac{{{{{r}}_{q,k}}{{r}}_{q,k}^{\rm{H}}}}{{{{r}}_{q,k}^{\rm H}{{{r}}_{q,k}}}}}, \;\;\;q = 1,2,···,Q $$ (7)

      式(8)对式(7)结果进行标准化处理,得到${ {\overline {{M}}}_q}$, tr(·)表示求矩阵的迹

      $$ { {\bar{{M}}}_q} = \frac{{N{{{M}}_q}}}{{{\rm{tr}}({{{M}}_q})}},\;\;\;\;\;\;\;q = 1,2,···,Q $$ (8)

      然后,利用归一化值${\bar {{M}}_q}$按照式(9)计算散斑的一致性因子, τ为时间间隔,${{\left\| \cdot \right\|}_{2}}$为矩阵的2-范数

      $$ \begin{split} & \rho (\tau ) = \frac{1}{{Q - \tau }}\sum\limits_{q = 1}^{Q - \tau } {\frac{{{{\left\| {{{\bar {{M}}}_q} - {{\bar {{M}}}_{q + \tau }}} \right\|}_2}}}{{{{\left\| {{{\bar {{M}}}_q}} \right\|}_2} + {{\left\| {{{\bar {{M}}}_{q + \tau }}} \right\|}_2}}}}, \\ & \tau = 1,2,···,Q - 1 \end{split} $$ (9)

      最后对散斑的一致性因子进行均值处理,得到散斑的平均一致性因子

      $$\rho = \frac{1}{{{\tau _2} - {\tau _1}}}\sum\limits_{\tau = {\tau _1}}^{{\tau _2}} {\rho (\tau )} $$ (10)

      其中$[{\tau _1},{\tau _2}]$为平均时间间隔。散斑的一致性体现了散斑的协方差矩阵在时间上的相似程度,进一步可以反映为散斑的结构平稳性。平均一致性因子越小,说明散斑在时间上的平稳性越强。漂浮小目标结构性强于海杂波的结构性,所以含有漂浮小目标的数据其散斑的平均一致性因子会小于纯海杂波的散斑的一致性因子。

      图28为4种极化下散斑一致性因子的分布图,图29为利用散斑一致性因子特征检测器在实测数据中的性能对比。

      图  28  4种极化下纯杂波和目标杂波的平均一致性因子[74]

      Figure 28.  The average consistency factors of pure clutter and clutter with target under 4 polarization channels[74]

      图  29  L=1024, 4种极化下4种检测器的检测概率[74]

      Figure 29.  L = 1024, the detection probabilities of the four detectors under 4 polarization channels[74]

    • 随着雷达分辨率的进一步提高和驻留时间的增长,很多新的信号处理方法得以应用,这样就产生了多种可以有效检测目标的特征,而多个特征之间对于不同类型的目标会产生互补作用,能极大地提升检测器的鲁棒性。随着新的多特征检测器的成功设计和信号处理硬件水平的逐步提升,目前基于特征工程的多特征检测方法以及基于人工智能自主选择多特征的检测方法越来越成熟,成为了海面目标特征检测的一个重要的研究方向。

    • 在特征检测中,特征的提取至关重要。特征区分目标和杂波的能力很大程度上决定了检测器的性能。特征的提取可以从提取目标和杂波具有差异性的数字特征,借鉴传统雷达目标检测中使用的传统检验统计量,通过对目标回波特性的全面认知,按照认知结论帮助选择差异性特征。假设雷达在一个波位发射长度为N的相干脉冲串,通过I/Q通道接收,可以得到每个距离单元的复回波数据。那么雷达目标检测问题可以表述成如式(11)二元假设问题

      $$\left. \begin{aligned} & { {H_0}:\left\{ {\begin{array}{*{20}{l}} {{{x}}\left( n \right) = {{c}}\left( n \right), \;\;\;\;\;\; n = 1,2, ··· ,N } \\ {{{{x}}_p}\left( n \right) = {{{c}}_p}\left( n \right), \;\;\;\;\;\; p = 1,2, ··· ,P} , \end{array} } \right.} \\ & {{H_1}:\left\{ {\begin{array}{*{20}{l}} {{{x}}\left( n \right) = {{s}}\left( n \right) + {{c}}\left( n \right), \;\;\;\;\;\; n = 1,2, ··· ,N } \\ {{{{x}}_p}\left( n \right) = {{{c}}_p}\left( n \right), \;\;\;\;\;\; p = 1,2, ··· ,P } \end{array}} \right.} \end{aligned}\right\}\!\!\! $$ (11)

      其中,x(n)表示待检测单元CUT的接收时间序列,s(n)表示来自目标的时间序列,c(n)表示接收的海杂波时间序列,N是脉冲累积数目,P是CUT周围的参考单元的数目。H0假设表示雷达回波仅包含海杂波和噪声,H1假设表示雷达回波中包含目标。从接收的雷达回波中可以得到大量的纯杂波数据,从而能够提取到纯杂波的特征向量${{{\xi}} _i}$,这些特征向量可以构成纯杂波模式的训练样本${{{L}}_{{H_0}}} = \{ {{{\xi}} _i} \in {R^3}: i = 1, 2, ··· ,I\}$。当接收到的雷达回波中包含目标时,由于海面目标的复杂性和多样性,难以获取各类目标的回波以及特征向量,无法获得足够的训练样本。因此,可以利用纯杂波模式下的训练样本训练得到判决区域,通过判断待检测单元回波的特征向量是否落入判决区域来判断目标是否存在,若落入判决区域,则目标存在;若没有落入判决区域,则目标不存在。

      (1) 基于原始3特征的检测方法[28]。尽管分形特征在长时间观测的情况下具有良好的检测性能,然而在实际海面目标检测中,观测条件无法达到理想的长时观测,无法在实际应用中达到理想的效果。为了改善基于分形特征检测器的问题,漂浮小目标的联合3特征检测方法[28]被提出,其主要思想是利用区分目标和杂波具有互补特性的3类特征对海面漂浮小目标进行检测,将检测问题转化为特征空间中的单分类问题,随后利用快速凸包学习算法确定判决区域,从而进行目标检测。

      在雷达回波中,分别从时域和频域提取具有可分性的3种特征,时域的能量信息可以作为区分目标和杂波的标志,利用频谱的差异性也可以对目标和杂波进行区分,由此可以提取出相对平均幅度(Relative Average Amplitude, RAA)、相对多普勒峰高(Relative doppler Peak Height, RPH)和相对多普勒谱熵(Relative Vector-Entropy, RVE)。图30为一组雷达数据的三维特征空间分布情况,观测时间分别为0.512 s, 1.024 s, 2.048 s和4.096 s。随着观测时间的增加,目标与杂波的分离性越好,检测性能越好。

      图  30  纯杂波与目标在特征空间中的分布情况

      Figure 30.  Distributions of features of clutter-only vectors and vectors with target in 3D feature space

      快速凸包学习算法将给定虚警率下最优检测判决区域简化为如式(12)的凸包区域

      $$ \begin{split} & \mathop {\rm{{min}}}\limits_\varOmega \left\{ {{\rm{Volume}}\left( \varOmega \right)} \right\} ,\\ \\ &\; {\rm{s.t.}}\frac{{\# \{ i:{{{\xi}} _i} \in \varOmega \} }}{I} = 1 - {P_{\rm F}} \end{split} $$ (12)

      其中,$\# {\rm A}$代表集合A的元素个数,${P_{\rm F}}$为虚警概率,I为纯杂波特征向量总数。图31示意了原始的纯杂波数据生成的凸包和给定虚警概率下缩小的凸包。

      图  31  原始数据生成的凸包和给定虚警率的凸包

      Figure 31.  Convex hull with the original training data and convex hull with given false alarm rate

      基于3特征的检测器检测步骤分为训练和检测两部分。在训练部分,需要采集杂波样本,提取纯杂波特征,然后利用快速凸包学习算法训练出满足虚警条件的检测判决区域,如图31;在检测部分,需要对待检测样本进行采集,提取该样本特征,通过判断样本特征是否落在判决区域内判断待检测单元是否存在目标。

      (2) 基于SVM的特征检测方法[77]。随着特征检测的发展,越来越多有效特征被用于区分海杂波和目标回波。通过有效特征的提取,可以将在海杂波中的目标检测问题转化为特征空间的一种特殊二分类问题。众所周知,机器学习算法中有很多优异的算法可以很好地实现二分类问题,比如支撑矢量机(Support Vector Machine, SVM)、神经网络(Neural Network, NN)等等。但是,由于传统机器学习算法的核心在于搜索一个可以使得两类错误率均衡且最小的分类面,但是在雷达目标检测中对虚警概率的要求远远高于漏检概率(通常,漏检概率可达十分之几,但是虚警概率一般低于10–3)。所以,结合机器学习算法和目标检测问题的核心在于,如何准确的控制虚警概率。2019年,Li等人通过将SVM和雷达目标检测问题结合起来,构建了一种基于SVM的特征检测方法,其不仅实现了可控虚警,更与其余检测器相比具有更优秀的检测性能。

      首先从接收海杂波序列中提取了3类特征,即时域的信息熵(Temporal Information Entropy, TIE),时域的Hurst指数(Temporal Hurst Exponent, THE)和频谱峰值与均值之比(Frequency Peak to Average Ratio, FPAR),并通过它们建立了一个三维的特征向量${{{F}}_i}$,用${y_i}$={+1, –1}分别标记目标(+1)和海杂波(–1),那么M个训练样本标记后可以表示成$\left\{ {\left( {{{{F}}_i},{y_i}} \right),i = 1,2, ··· ,M} \right\}$。在此特征空间中,目标和杂波的特征向量是线性不可分的。为了解决该问题,可以利用非线性核函数将三维特征向量${{{F}}_i}$映射到高维的特征空间,可将线性不可分的数据转换成线性可分的数据,在此,可以将径向基函数作为核函数构建SVM检测器

      $$k\left( {{{{F}}_1},{{{F}}_2}} \right) = \exp\left( { - \frac{{\left\| {{{{F}}_1} - \left. {{{{F}}_2}} \right\|} \right.}}{{2{\delta ^2}}}} \right)$$ (13)

      映射到高维空间后,下一步是寻找一个可以分离映射在高维特征空间中线性可分的目标与杂波的超平面:${{{w}}^{\rm{T}}}{{F}} - b = 0$,通过求解以下优化问题可以确定$w$$b$

      $$ \begin{split} & \mathop {\rm{{min}}}\limits_{w,b,\xi } \frac{1}{2}{\left\| {{w}} \right\|^2} + \sum\limits_{i = 1}^M {\left( {\frac{{1 - {y_i}}}{2}{b_0} + \frac{{1 + {y_i}}}{2}{b_1}} \right){\xi _i}}, \\ & \quad {\rm{s.t.}} \;{\rm{C}}1:{y_i}[k({{w}},{{{F}}_i}) - b] \ge 1 - {\xi _i},i = 1,2, ··· ,M \\ & \qquad\ \ {\rm{C}}2:{\xi _i} \ge 0,i = 1,2, ··· ,M \\[-10pt] \end{split} $$ (14)

      其中,${{{\xi}} _i}$为松弛变量,通过控制β0β1的变化可以用来控制虚警概率。根据SVM的理论基础,上式可以通过序列最小优化算法来解决。得到超平面${{{w}}^{\rm{T}}}{{F}} - b = 0$后,当${{{w}}^{\rm{T}}}{{F}} - b > 0$时,${y_j} = {\rm{ + }}1$即可判定为目标;当${{{w}}^{\rm{T}}}{{F}} - b \le 0$时,${y_j} = - 1$即可判定为杂波。表9为其检测结果。

      表 9  基于SVM的检测器与其余检测器的性能对比[77]

      Table 9.  Detection performance comparisons of SVM-based detector and the other detectors[77]

      检测器Detectors检测结果(HH极化,虚警概率为0.001) Detection results (HH polarization, PF = 0.001)
      SCR=–2 dBSCR=17 dB
      基于SVM的检测器SVM-based detector7699
      基于3特征的检测器Tri-feature-based detector5799
      基于分形的检测器Fractal-based detector1879

      基于SVM算法的特征检测方法相较于3特征和分形检测方法大幅度提升了检测性能,并且能够突破凸包学习算法的局限性,对三维以上的高维特征空间进行检测。

      (3) 基于决策树的特征检测方法[78]。除了上文提到的基于SVM的检测器,Zhou等人将决策树算法和雷达目标检测问题相结合,提出了一种基于决策树的检测器,并且实现了虚警的有效控制。决策树是一种常用的分类算法,它是根据数据的属性或特征而建立的树状模型。常用的决策树算法包括ID3,分类回归树(Classification And Regression Tree, CART), C4.5,随机森林(random forest)等。决策树只有一个根节点,多个内部节点和多个叶子节点。首先,所有的训练样本都被分配给内部节点,其分配规则为通过选择合适的特征和合适的阈值尽可能使得内部节点的纯度最大。整个过程由上而下,递归进行。

      文献提取了海杂波数据中的时域Hurst指数、频域Hurst指数以及频谱峰值与均值比3类特征,并将其构造为三维的特征向量。对每一个特征向量,分别将目标向量贴标签为1,杂波向量贴标签为0,利用著名的分类回归树(CART)算法构造决策树。首先,所有的特征向量处于一个根结点,通过选择基尼指数最小(基尼指数越小,纯度越大)的特征和阈值来进行分类,产生子结点。重复此类操作,直到产生的子结点不可再分,即为叶子结点。最后生成的叶子节点可以将特征空间分为两部分。分类正确的目标样本和所有目标样本之比即为检测概率。图32为整个算法的流程图。表10为其检测结果。

      表 10  基于决策树的检测结果和其余检测器的性能对比[78]

      Table 10.  Detection performance comparisons of the decision tree-based detector and the other detectors[78]

      检测器Detector检测结果Detection
      0 dB5 dB10 dB15 dB
      基于决策树的检测器Decision tree-based detector0.760.840.980.99
      基于3特征的检测器Tri-feature-based detector0.580.650.820.95
      基于分形的检测器Fractal-based detector0.210.320.480.68

      图  32  基于决策树的检测器流程图[78]

      Figure 32.  The flowchart of the decision-tree-based detector[78]

      基于决策树的特征检测方法将检测与分类相结合,提升了检测性能,同基于SVM的检测方法一样可以在高维的特征空间中进行检测。

      基于机器学习算法的特征检测方法能够对检测性能进行大幅度的改善,由于凸包学习算法仅能利用在三维及以下的特征空间中,而机器学习算法它们均能够突破高维特征空间的限制,意味着可以将更多的特征利用到基于特征的检测中来,从而进一步改善检测性能。

    • 在检测海杂波背景下的漂浮小目标时,为了使目标回波获得足够的积累增益,提升检测性能,通常需要观测时间达到秒级,而在长时观测的情况下,海杂波时间非平稳且纹理随着时间变化,所以海杂波时间序列建模为时变纹理的复合高斯模型。同时,漂浮小目标回波在秒级时间尺度上呈现幅度起伏和多普勒调制,因而目标回波建模为具有幅度起伏的未知非线性调频信号[120-122]。因此,在长的累积时间内,海杂波背景下漂浮小目标的检测问题可以等价于在时变纹理的复合高斯杂波中寻找未知的非线性调频信号的问题。

      由于时频分布(Time-Frequency Distribution, TFD)实现了未知调频信号的短时相干累积,在白噪声背景下检测未知调频信号时常采用TFD[120-125]。而在设计合适的TFD时,非线性调频信号的能量可以完全集中在其瞬时频率曲线上(Instantaneous Frequency Curve, IFC)。由于接收回波序列的归一化时频分布(Normalized Time-Frequency Distribution, NTFD)可以增强杂波回波的时频特性,并且目标回波可以用分段线性调频信号近似,可以采用平滑的伪魏格纳-威利分布(Smoothed Pseudo Wigner-Ville Distributions, SPWVD)[125,126]计算NTFD。海杂波和含目标的回波在NTFD上表现出了不同的特性。通过这些不同的特性可以提取3个时频特征:NTFD的时频累积、由NTFD亮像素构成二值图像中的连通区域数目和最大连通区域的尺寸[75]

      同3特征检测器的检测步骤类似,时频3特征检测器同样分为训练部分和检测部分。训练部分通过接收大量的纯杂波数据提取特征向量,利用快速凸包学习算法来训练单分类器,并且为检测部分提供均值向量和标准差向量进行归一化处理。检测部分通过计算待检测单元和参考单元的接收时间序列的特征向量,利用训练部分得到的均值向量和标准差向量进行归一化等操作。通过对待检测单元特征向量的计算,判断其是否落入判决区域,从而得到判决结果。基于时频3特征的检测器,相较于基于原始3特征的检测器有了一定的性能提高,然而在个别数据上检测概率略有下降。这说明了特征提取对于联合多特征检测器的性能至关重要。

    • 基于时域、频域特征和基于时频域特征的检测方法对数据的处理往往只是分别使用了4个极化通道HH, HV, VH, VV,然而随着全极化雷达的普及和雷达设备的更新换代,全极化方法在图像处理领域越来越成熟,雷达数据全极化处理成为可能。文献[76]尝试使用全极化的方法处理海面漂浮小目标的检测问题。

      全极化雷达接收到的每组数据集都包含HH, HV, VH和VV 4种数据,通常使用极化散射矩阵来表征接收到的回波数据。根据散射矩阵可以提取极化相干矩阵或极化协方差矩阵。一般通过分解散射矩阵、相干矩阵或协方差矩阵来提取极化特征。对于海面漂浮小目标检测而言,当雷达波束照射在平静海面、海浪或是目标物体时,可能发生面散射、二面角散射和体散射。当波束照射在平静海面或是在垂直浪面以及在目标表面镜面反射时,会发生面散射;当波束照射在海浪形成的二面角或是目标与海面所形成的二面夹角时,可能会发生二面角散射;而当波束照射在破碎的浪花(白冠)或是目标复杂结构内时,将会发生体散射。雷达波束照射区域内有无目标会影响照射区域的散射类型和散射能量的大小,由此可以利用该差异性提取相关极化特征进行漂浮小目标检测。

      基于极化目标分解理论基础,文献[76]根据海面漂浮小目标检测场景,选取Freeman-Durden三分量分解方法[127]分别对3种散射机制进行建模,确定3种散射机制下的能量大小,选取待检测单元和参考单元能量的相对比值从而提取到3个极化特征,分别为相对体散射机制对应能量、相对二面角散射机制对应能量和相对面散射机制对应能量。利用这3类特征通过凸包学习算法对海面漂浮小目标进行特征检测。图33为极化3特征与原始3特征的检测性能对比图。

      图  33  极化3特征检测方法与原始3特征检测方法检测概率柱状图[76]

      Figure 33.  Detection probabilities of polarization features-based detector and tri-detector at HH, VV, HV, and VH polarizations for ten data sets[76]

      基于极化3特征的检测方法与原始单极化工作方式下的基于原始3特征的检测方法相比,检测器性能有了一定的提升且检测器具有鲁棒性。由于基于极化3特征的检测方法利用了4个极化通道的雷达数据从而提取到具有可分性的杂波和目标特征,所以检测效果比基于单极化工作方式的检测器效果更优。利用全极化信息进行检测可以充分利用雷达所接收到的信息,有效提升检测性能,可以在此对特征提取进行进一步的研究。

    • 海杂波背景下漂浮小目标的检测是一类国内外公认的难题,随着海面目标隐身化与小型化,提高对漂浮小目标的检测能力对于海面目标检测具有重要意义。基于特征类的漂浮小目标检测方法经历了多个发展阶段,从提取单一特征进行检测到联合3特征的检测方法再到基于机器学习算法的高维特征空间检测;而提取特征的范围也从时域、频域的一维变换为时频域的二维,且不拘泥于单极化的工作模式,转而向全极化工作模式下的特征发展,本文介绍了现有的几种基于特征的漂浮小目标检测方法,简单分析了它们的检测原理,其检测性能各有优劣。现有的检测器仍有充足的发展空间。为了进一步提升检测概率,改善检测器性能,未来基于特征的检测器的发展方向可以从以下几个方面来进行研究:

      (1) 提取更多能够有效区分杂波和目标的特征。接收的雷达信号中包含大量的杂波和目标各个方面的信息,利用时域、频域及时频域等不同变化域和不同层面的杂波与目标的各类信息,提取新的适用于特征检测的特征。杂波与目标在特征空间中的可分性越强,说明该特征更适用于特征检测,所得到的检测器拥有更强的检测性能。

      (2) 利用新兴学科改进检测算法。异常检测下对单分类器的设计常采用的凸包类学习算法具有一定的局限性,即无法对高维特征向量进行处理。随着人工智能的发展,越来越多的学习算法能够利用到特征检测中来,二者之间的学科融合已经成为发展趋势,它们可以突破高维特征空间的限制,能够将更多的特征利用到特征检测中,从而使检测性能进一步改善。

      (3) 发展新体制雷达。基于特征的检测方法在检测过程中需要较长的观测时间,而在实际应用中的雷达往往达不到所需长时间观测的要求。传统雷达一个波位上的长驻留时间和扫描效率之间的冲突是难以调和的,这也是无法长时观测的原因。2003年,MIT的林肯实验室提出了使用MIMO数字阵的泛探雷达的概念[128],实现了在所有方向下的全时间观测。这类新体制雷达的发展,更有利于对杂波和目标特征的提取,在特征空间的可分性越强,所设计的检测器更能达到良好的性能。

    • (1) 由于军事应用的特殊性,人工智能在军事领域应用的广度和深度远远不及互联网商业领域。而这种差异与军事人工智能系统可用的数据有很大关系。以海面目标检测为例,对于非合作目标很难收集到足够的数据来训练相应的人工智能算法。人工智能算法(尤其是深度学习)通常需要大量数据,这些数据必须经过精确标记,并与每个特定问题域相关。在有关军事局势的信息被损坏或者得到的数据集不完备,我们做出的决策可能远非最佳。因此,小样本或者残缺样本下的基于人工智能的海面目标检测需要进一步研究。

      (2) 随着机器学习模型复杂度的日益增加,对于目前常用的机器学习方法,我们已经无法从直观上去理解机器如何做出决策。如果仅仅将机器学习模型用来推荐一部电影或者推荐一家餐厅,我们可能并不需要模型对结果做出解释,但是在雷达对海目标检测领域,我们不仅希望知道模型结果,还需要了解这些决策是如何做出来的。当前模型的可解释性技术,主要是对输入的各个特征进行定量评价,找到对结果影响最大的特征。或者进行进一步的分析,考察特征的相关性。对于列表型数据,每一列即为一个特征;而对于图像、文本或其他非列表型数据,我们还需要先对其进行预处理,构建易于理解的特征。可解释性是机器学习的一个重要的研究方向,也同样是对海目标检测领域迈不过去的一道坎。因此,如何设计可解释的人工智能方法是需要研究的重要课题。

      (3) 基于人工智能的方法,学习是其中的重中之重。人的学习学的不是知识,而是获取数据、信息、知识经验的方法;而机器的学习学的是数据、信息和知识,还不会活学活用。对于雷达探测来说,准确的检测器设计必须建立在大量不同情况下的海量数据之上,而这种学习的过程必然耗费大量的时间,对于瞬息万变的战场环境,特别是海面环境的高动态变化,基于人工智能方法的检测器的检测准则确定的速度严重依赖于算法特别是硬件平台的计算能力,因此,将人工智能推向实用的有一个重要的难点是算法设计的高效性以及硬件平台计算能力的不断提升。

    • 本文首先分析了目前对海探测面临的热点和难点问题,并介绍了目前常用于进行特征检测算法验证的数据集,随后具体说明了基于特征的检测方法的原理,同时介绍了几种海杂波背景下基于特征的海面慢速、漂浮小目标检测方法,并对它们的检测性能进行了分析。海面慢速、漂浮小目标的检测对于海洋军事的发展具有重大的意义,如何提高海面弱小目标智能检测的性能,是当前研究的重点。随着新兴学科的发展,雷达目标检测与各类新兴学科的融合已经成为了发展趋势。将新兴学科的智能化与基于特征的检测方法结合,能够更有效地对目标进行检测,改善海杂波背景下慢速、漂浮小目标的检测性能。

    • Various types of radar systems constitute the main equipment for the all-time monitoring of sea environments. Sea surface observation by radar technology is an important means to realize the dynamic monitoring of the sea surface, and the early warning and surveillance of sea-surface targets. With the wide application and rapid development of the radar observation of the sea in the field of military science and technology and civil affairs, increasing attention has been paid to the research on electromagnetic scattering echoes from the sea surface. There are two main purposes to study the complex sea surface echoes: one is to extract the information on the ocean dynamic characteristics (such as wave height, wave direction, and wind speed) from the sea surface echo signals; the other is to detect the target (such as boats, ice floes, and aircraft) from the complex sea surface echoes, whereby the sea surface echo is a kind of interference factor, usually called sea clutter.

      Sea clutter is defined as the received backscattered echo of the sea surface when the radar electromagnetic wave illuminates the sea surface[1-4]. The physical mechanism of sea clutter is complex and depends on many factors, which include the condition of the complex sea surface and the working state of radar. Due to the influence of environmental factors and radar equipment parameters, the characteristics of sea clutter are constantly varying, and the space-time variation of sea clutter is more complicated than that of ground clutter. At present, the main difficulties in the detection of slow small targets on sea surface come from the following four aspects:

      (1) The weakness of slow small-target echo: Small sea surface-targets such as small boats, icebergs, frogmen, debris, submarine periscope, and stealthy targets, as shown in Fig. 1, have weak Radar Cross Section (RCS). Because of weak returns, these targets have a very low Signal Clutter Ratio (SCR). Although the maritime anti-intrusion radar is designed with high spatial and Doppler resolution to raise the SCR to a critical value to enable target detection, detection using the traditional detection methods is still difficult under low SCR. Meanwhile, the target moves slowly and the sea clutter has wide Doppler bandwidth, making it difficult to distinguish the target from the sea clutter in the Doppler domain; this kind of detection is usually called “over-clutter detection”. Traditional adaptive detection methods are difficult to work in this case of slowly moving targets.

      Figure 1.  Some common small targets on sea

      (2) The high complexity of space-time-varying sea clutter and the difficulty of recognizing sea clutter characteristics: The range and azimuth of the radar system and high-resolution observations make the sea clutter more complex, and it becomes difficult to satisfy the traditional large-scale statistical characteristics. Influenced by numerous factors such as marine meteorology and the geographical environment, the sea surface changes nonlinearly and randomly, and the change mechanism is very complex. Moreover, the wave height increases with wind speed. When the wave is out of balance under gravity, a breaking wave is produced, and the “split structure” before the wave is completely broken makes mirror-like reflection, then a strong echo appears, which is called the sea spike[3-8]. However, the appearance of the sea spike component, which is similar to the target, complicates the clutter modeling[9,10]. Meanwhile, as our focus shifts from the nearshore region to the open sea, the maritime radar must monitor and detect a range of unfamiliar marine environments. The three “non” characteristics of sea clutter, which are non-uniform, non-stationary, and non-Gaussian characteristics, are more obvious. As shown in Fig. 2(a), the power map of sea clutter exhibits strong non-homogeneous and non-stationarity. As shown in Fig. 2(b), the empirical probability density function of the clutter substantially deviates from the Rayleigh amplitude distribution and exhibits a significant non-Gaussian property. The strong non-homogeneous and non-stationarity mean that the sea clutter characteristics can be considered invariable only in near-range azimuth resolution cells, and the probability of the same distribution of sea clutter decreases greatly with the increase in space range. Although the sea clutter characteristics slowly change in the slow time dimension (the same order as the time scale of the change of weather conditions and sea conditions), the large scene-scanning observation radar lacks the time resources for long-term observation, and it is difficult to obtain a large number of independent and identically distributed samples in the slow time dimension. That is, although a large number of sea clutter samples can be obtained from maritime radar, during the estimation of the sea clutter characteristics of a radar resolution cell, only a small number of local samples within a short time interval are completely independent and identically distributed. Therefore, sea clutter characteristic perception is essentially a “small sample” problem, which is called “nature small sample” problem. Meanwhile, since the sea clutter characteristics in large scenes are space-varying and time-varying, it is necessary to perceive the sea clutter characteristics online varying with space and time in large scenes in order to achieve constant false alarm detection.

      Figure 2.  Power map of measured data and amplitude fitting results

      (3) The difficulty of obtaining the target model: The motion and attitude of large ships are hardly affected by sea waves, while those of small targets on the sea surface are severely disturbed by wind and waves. Due to the complex motion patterns (including roll, pitch, yaw) of small targets on the sea surface, the targets may be partially or even completely blocked by waves for a period; thus, small-target returns have severe RCS fluctuations, complex amplitude and Doppler modulation phenomena. There are many kinds of targets on the sea surface, which can be divided into the following three types: (i) flying targets over the sea surface, which can be easily detected by radar because of their high speed and strong maneuverability; (ii) large targets on the sea surface, such as large ships and cruise ships, which have larger RCS and can be effectively detected; (iii) SFTs on the sea surface, such as aircraft wreckage, frogman, and periscope. The RCS of the SFTs is small, and returns are often submerged in the sea clutter, which is not easy to be detected. How to effectively detect this kind of low-observable targets in the sea clutter background is a problem that researchers have been exploring[12,13]. Therefore, it is difficult to construct a simple parametric model of target similar to the adaptive detection method to describe the returns of the target of interest, and it is necessary to develop new feature-based detection methods.

      (4) The class imbalance of target and sea clutter: The observation scene is large, but the amount of small and weak targets on the sea surface is limited. Therefore, most of the received data are sea clutter, and the amount of the target returns is much less than sea clutter data; this problem is called “imbalance problem” in machine learning and pattern recognition and is caused by the sparsity of the target relative to the sea clutter. The traditional methods in pattern recognition and machine learning may degrade the classification performance when dealing with class-imbalance problems. Therefore, the traditional machine learning method also faces challenges in the detection of SFTs in the sea clutter background.

      Because of the variety of target types and the change of radar systems, the detection of SFTs on the sea surface has been long discussed. With the revolution of radar systems and the emergence of new signal-processing techniques, many new problems and new methods have emerged in the field of the radar detection of sea targets. This paper first summarizes the common methods of radar target detection in the sea clutter background. Then, as an important part of the evaluation of the algorithm for the intelligent detection of targets on the sea surface, this paper introduces the datasets that are commonly used to verify the performance of the feature-based detection methods, and a series of feature-based detection methods are introduced in sequence. Finally, the prospect of feature-based target detection in the sea clutter background is discussed.

    • A common problem for sea radars is target detection under critical SCR. The detection of low-resolution radar for traditional large ships is not difficult, and non-coherent or coherent detection methods are generally adopted. The non-coherent detection methods are mainly based on the amplitude and power of radar echoes. The main methods are the cell-average Constant False Alarm Rate (CFAR) detector and the greatest-of or the smallest-of CFAR detectors, which are often applied in the detection of early incoherent radar pulse systems[14-16]. In coherent radar system, the adaptive detection method is based on a certain statistical model of sea clutter, and then a series of optimal or near-optimal detectors corresponding to the model are developed. The flowchart of the detection method is displayed in Fig. 3.

      Figure 3.  Flowchart of adaptive detection methods

      Sea clutter can be modeled as a complex Gaussian distribution model in the low resolution case. Kelly[17] and Robey[18] proposed the generalized likelihood ratio test and Adaptive Matched Filter (AMF) detectors, respectively, which achieved good detection performance. However, in the case of high-resolution radar and low grazing angle, sea clutter has strong non-Gaussian property, which makes the complex Gaussian distribution model no longer suitable. Then, sea clutter can be modeled as a Compound Gaussian Model (CGM)[19], which is the product of a slowly varying texture component and a rapidly varying speckle component:

      $$ {{c}}\left( n \right) = \sqrt {{{\tau}} \left( n \right)} {{u}}\left( n \right) $$ (1)

      Conte[20] and Richmond[21] proposed the normalized matched filter and adaptive normalized matched filter detectors based on the CGM. In a coherent processing interval, the CGM can be reduced to a spherically invariant random vector, in which the texture component is a positive random constant, and the speckle component obeys the complex Gaussian distribution:

      $$ {{c}} = \sqrt {{\tau}} {{u}} $$ (2)

      Texture components obey the Gamma distribution, the inverse Gamma distribution, and the inverse Gaussian distribution. Based on this, the Optimum K-distributed Detector (OKD)[22,23], the Generalized Likelihood Ratio Test-Linear Threshold Detector (GLRT-LTD)[24,25], and the Generalized Likelihood Ratio Test with Inverse Gaussian texture (GLRT-IG)[26] have been developed. In addition, because of the engineering unrealizability of the OKD, a shape parameter-dependent adaptive detector called α-AMF[27] has been proposed, which has a simpler structure than the OKD, has a detection performance similar to that of the OKD, and is engineering realizable. The adaptive detection method is suitable for short-time coherent accumulation and is often used to detect large targets and moving targets on the sea surface. This kind of detector is mainly used in wide-area surveillance radar systems. Because of the scanning efficiency, the number of accumulated pulses is limited in the dwell time of a beam position. However, sea clutter has a wide Doppler bandwidth. When the velocity of the target is low or the RCS is small, the target return may be submerged in the strong sea clutter, and the performance of the adaptive detection method largely degrades. Therefore, it is difficult for this method to detect SFTs on the sea surface. The SCR of the target returns can be estimated by the power in target range cells. First, the average power ${\bar p_c}$ of the sea clutter is estimated from the pure clutter cells. If the target returns and sea clutter are assumed to be independent, then the average SCR can be estimated by Eq. (3):

      $$ {\rm{ASCR = 10lg}}\left( {\frac{{{1/N}\displaystyle\sum\limits_{n = 1}^N {{{\left| {{{x}}(n)} \right|}^2}} - {{\bar p}_c}}}{{{{\bar p}_c}}}} \right) $$ (3)

      where ${{x}}(n)$ is the echo sequence of the target range cell, and N is the sequence length. The actual SCR fluctuates around the average SCR.

      For the detection of small RCS targets such as stealth vessels, the traditional detection method features a critical SCR and thus requires “cognitive sea clutter suppression”. For example, the littoral combat ship has an RCS of about 100 m2, the stealth large ship has an RCS of only 60 m2, and the stealth boat has an RCS of only 30 m2. The appearance of these stealth ships also makes the target detection more difficult for low-resolution-surveillance early warning radars. The Technology Service Corporation (TSC) model is used to simulate the SCR of different ships in the case of VV polarization and headwind situation at sea level 4. As shown in Fig. 4, it is difficult to detect ships with 30 m2 and 60 m2 RCS in the range of 50~300 km through the traditional method. Therefore, it is necessary to change the radar working system and develop new target detection methods.

      Figure 4.  SCRs for various ships at sea state 4 (VV polarization), in the case of headwind

    • In addition to large ship targets, sea-surface targets also include small slow targets. Due to the “spatial resolution performance bottleneck”, as mentioned above, it is difficult to detect these targets using low-resolution radar. Traditional target detection methods such as moving target indication, Moving Target Detection (MTD), and adaptive detection methods are based on accurate statistical models for clutter and target; therefore, all kinds of optimal and near-optimal test statistics play a key role in detection. With the refinement of observation means, background clutter and target returns become complex, and it is difficult to build an accurate statistical model. In this case, the “double-high” system with high spatial resolution and high Doppler resolution is the main technical approach. At present, there are three radar working modes to realize the “double-high” system. They are the wide transmitting beam and narrow receiving beam model, ubiquitous radar system, and quick scanning plus beam park model for suspected targets (Fig. 5).

      Figure 5.  Radar working modes that realize the “double-high” system

      High-resolution small-target detection radar faces the problems of extremely complex high-resolution sea clutter characteristics and small-target characteristics, and the key to breaking through the critical SCR and detection is deep cognition, elaborate perception, and the full utilization of sea clutter. In this case, one or more different features of clutter and target returns are usually extracted to realize the combination detection, and this technique is called feature-based detection. The feature-based detection method has been widely used in image processing, pattern recognition, and other fields and has produced good results. This method can be considered as a preliminary version of intelligent detection and is a necessary technique in the era of intelligent detection. The detection method based on multiple features in sea clutter background is to reduce the observation space with high overlap to the feature space with low overlap by extracting different features between clutter and target returns, and detect targets in the feature space. The traditional radar target detection algorithm is based on a specific test statistic, and its performance is limited in SFT detection in the sea clutter background. Therefore, the multi-feature combination method is applied to small-target detection, and the tri-feature-based detector[28] has been proposed, which improves the performance loss of the traditional method. A feature is an index used to describe the difference between clutter and target. Feature-based detection is not limited to specific features but is based on the actual environment and radar equipment information, and the detection method can be based on different features extracted from the amplitude, Doppler spectrum, Time-Frequency (TF) image, and polarization information of radar returns. Moreover, with the increase in the number of features, the difference between target and clutter can be reflected more completely. The method based on machine learning algorithms to detect targets in high-dimensional feature space has been proposed, which greatly improves the detection performance. To solve the problem of feature-based detection in sea clutter background, scholars have started relevant research and have obtained a large number of results and proposed many kinds of feature-based detection methods, for example, detectors based on the fractal and chaotic features of the sea clutter, TF analysis, and artificial intelligence. Fig. 6 displays the flowchart of the feature-based detection methods. These methods are briefly summarized below and are described in more detail in Section 4.

      Figure 6.  Flowchart of the feature-based detection methods

      (1) Sea-surface target detection methods based on fractal and chaotic features: The fractal theory proposed by Mandelbrot in 1970s, an active branch of nonlinear science, is used to represent complex graphs and complex processes. According to the different fractal characteristics between the sea clutter and the target, a new target detection method based on the fractal theory was proposed by Lo T[29] from McMaster University in 1993. In 2006, Hu Jing[30] introduced a sea-surface target detection algorithm based on the multifractal theory. By analysis of the measured sea clutter data, it has been found that the sea clutter has multifractal characteristics in the time scale range of 0.01 s to several seconds, and the Hurst index of sea clutter is calculated to detect the target, which has good detection performance. He You, Guan Jian, Liu Ningbo, Chen Xiaolong[31,32] from Naval Aeronautical University have also performed much work in this field. The target detection methods based on the fractal theory are simple and efficient, but because the fractal characteristics of sea clutter time series exist only in the range of a certain time scale, which varies with the change of radar parameters, sea state, and polarization, the detector performance is affected by estimation errors in the scaling range. When the observation time is long, this kind of method can exhibit good detection performance, but if the observation time decreases, the detector performance will remarkably decline. In 1995, Simon Haykin[33,34] from McMaster University proposed that sea clutter is chaotic and predictable in the short term. According to the short-term predictability of sea clutter, a nonlinear prediction model is constructed for sea clutter time sequence, and the prediction error is used to test statistical hypotheses. Haykin later questioned the sea clutter chaotic model, and when the SCR is continuously reduced, the detection performance is not ideal, and the detection of slow small targets becomes difficult.

      (2) Sea-surface target detection methods based on TF analysis: In recent years, many methods based on TF analysis have been proposed to detect sea-surface targets[35-40]. Through TF analysis tools such as Short-Time Fourier Transform (STFT), Wigner-Ville Distribution (WVD), Smoothed Pseudo-Wigner-Ville Distribution (SPWVD), and FRactional Fourier Transform (FRFT), the feature corresponding to the target is extracted by parametric or non-parametric methods in a 2D plane to detect the target in the sea clutter background. More details and information can be obtained by TF analysis, which overcomes the shortcoming of the complete separation between the time domain and the frequency domain by Fourier analysis and balances both the time domain and frequency domain. However, according to the Heisenberg uncertainty principle, the longer the time window function in the STFT, the higher the frequency resolution and the worse the time resolution. The resolution in the time and frequency domains can be improved by using the bilinear Wigner-Ville transform, but due to the nonlinear transformation, cross-terms will appear when multiple signal components are present, which will reduce the detector performance for slow small targets. Although the SPWVD can suppress the cross-terms, the algorithm efficiency is sacrificed, and the joint TF resolution is also reduced. Although the TF analysis method based on FRFT has good detection performance for large ship targets without the occurrence of cross-terms, it is still not good for slow small targets on the sea surface. Due to the complex motion of the slow small targets in the sea, the target signal usually appears as a weak nonlinear Frequency Modulation (FM) signal, and consequently, the detection method faces many challenges in practical applications. In recent years, the micro-Doppler theory has been studied. Micro-Doppler is caused by the Doppler shift of the target, which reflects the change of characteristics in the Doppler domain. The micro-states of the target can well reflect the refined characteristics of the target, so the characteristics of the micro-moving target can be effectively distinguished from the sea clutter. The detection method based on micro-Doppler features is to establish the target echo signal as an appropriate model and to analyze the micro-moving features by Fourier transform or TF analysis to enhance the detection performance of slow small targets on the sea surface. The existing methods of sea-surface target detection based on the micro-Doppler theory include sea-surface micro-motion target detection method based on Gaussian Short-Time FRactional Fourier Transform (GSTFRFT)[41], micro-Doppler features extraction and detection via Short-Time sparse TF Distribution (ST-STFD)[42], and detection and classification of maritime micro-motion targets based on Convolutional Neural Network (CNN)[43].

      (3) Sea-surface target detection methods based on artificial intelligence: Sea-surface target detection based on artificial intelligence methods originated from the neural network method proposed by Haykin[33] and has made some progress. With the development of artificial intelligence and machine learning, some scholars have proposed new detection methods of sea-surface targets[44-48]. In recent years, Nerea del-Rey-Maestre and David Mata-Moya[49] applied artificial intelligence to sea-surface target detection and verified the detection method by the measured data. In their compound hypothesis testing problem, the neural network detector could be approximated to a Neyman-Pearson criterion detector. They analyzed the suboptimal method based on Constrained Generalized Likelihood Ratio (CGLR) and compared it with the conventional method based on Doppler filtering. Artificial intelligence solutions based on second-order neural networks provide the best performance and approximate CGLR in real time and at very low computational cost.

    • The detector performance needs to be verified by the measured data. In 1993 and 1998, a group led by Professor Haykin[50] of McMaster University in Canada collected large amounts of high-resolution sea clutter data by the intelligent pixel (IPIX) processing band X-band radar and shared them on its website. The IPIX radar can transmit horizontal polarization (H-polarization) and vertical polarization (V-polarization) electromagnetic waves and can receive both horizontally and vertically by two linear receivers; therefore, the measured data under four polarization channels HH, HV, VH, and VV can be obtained.

      In this paper, 10 sets of data collected in 1993 and 2 sets of data collected in 1998 are presented. There are some differences in radar location, parameters, and cooperative targets between the data of the two experiments. The radar for the 1993 data collection was deployed on a 30-meter-high cliff on the east coast of Canada, at the Dartmouth, Nova Scotia, and the investigation was directed toward the Atlantic Ocean. The test target was an anchored spherical block of Styrofoam wrapped with wire mesh of 1 m diameter. The carrier frequency of the IPIX radar was 9.3 GHz, the beam width was 0.9°, and the range resolution was 30 m. The radar worked in the dwell mode, with a Pulse Repetition Frequency (PRF) of 1000 Hz and a dwell time of about 131 s. Each set of data contained 14 range cells. As the radar illuminated the target at a low grazing angle, the undulation and oscillation of the target caused the energy diffusion, and the range oversampling was adopted in the data acquisition; therefore, the adjacent range cells around the target range cell will be affected by the energy of the target and are regarded as secondary cells. The wind speed and wave height for the 1993 measured data could be obtained from environmental records at the time of online data collection, and the details are presented in Tab. 1.

      Table 1.  Description of IPIX radar data collected in 1993[28,50]

      Data name Wave heights
      (m)
      Wind speed
      (km/h)
      Primary Secondary
      #17 2.2 9 9 8, 10, 11
      #26 1.1 9 7 6, 8
      #30 0.9 19 7 6, 8
      #31 0.9 19 7 6, 8, 9
      #40 1.0 9 7 5, 6, 8
      #54 0.7 20 8 7, 9, 10
      #280 1.6 10 8 7, 10
      #310 0.9 33 7 6, 8, 9
      #311 0.9 33 7 6, 8, 9
      #320 0.9 28 7 6, 8, 9

      In terms of the Douglas sea state, the last nine sets of data are at sea state 2~3, with a small number of breaking waves and whitecap. Due to the low wave, the target can be illuminated by radar most of the time. The first set of data is at sea state 3~4, and the frequency of breaking waves and whitecap increases, while test targets are sometimes blocked by waves and cannot be directly illuminated by radar. Meanwhile, there is no direct connection between wave height and wind speed. This is because wave height is related to many factors. Large swells can usually spread far from the fully developed sea area where wave height is higher, and short-time strong local wind usually does not influence the wave height, but it can increase the frequency of breaking waves to some extent.

      In 1998, the IPIX radar was located at Grimsby, on Lake Ontario, to collect a new set of data. The radar was set at an altitude of 20 m, and the test target was a floating boat. The range resolution was 30 m, the PRF was 1000 Hz, the dwell time is 60 s, and the number of range cells was 28. The environmental information of the dataset is not published on the websites, and the data information is presented in Tab. 2.

      Table 2.  Description of IPIX radar data collected in 1998[28,50]

      Data name Range(m) Primary Secondary Radar direction
      #202225 3201~4011 24 23, 25
      #202525 3201~4011 7 6, 8
    • The Council for Scientific and Industrial Research (CSIR) radar was deployed at measurement station 3 at the Overberg Test Range (OTB), with location 34°36'56.52" S, 20°17'17.46" E. The plan of the deployment site is shown in Fig. 7, and the location of the deployment site is depicted in Fig. 8. The main characteristics of the deployment site are presented in Tab. 3.

      Table 3.  Main characteristics of OTB MS3[11]

      Parameter Value
      Latitude 34°36'55.32"S
      Longitude 20°17'20.11"E
      Ground height 53 m
      Antenna height 56 m
      Distance to sea 1.2 km
      Azimuth coverage 208°~80° N (SSW-ENE)
      Range (CNR > 15 dB) 1.25~4.50 km
      Grazing angle (<15 km) 3.00°~0.16°
      Grazing angle (CNR > 15 dB) 3.0°~0.7°

      Figure 7.  A plan overview of the deployment site[11]

      Figure 8.  Location of the deployment site in 2006 (OTB)[11]

      The RCS measuring equipment was developed by CSIR and owned by CSIR, the Armaments Corporation of South Africa, and the South African Air Force. It is a calibrated coherent RCS measuring equipment with an operating frequency from 6.5 GHz to 17.5 GHz. The system parameters are presented in Tab. 4.

      Table 4.  Fynmeet system and performance specifications[11]

      System composition System parameters Parameter values
      Transmitter Frequency range 6.5~17.5 GHz
      Peak power 2 kW
      PRF range 0~30 kHz
      Waveforms Fixed frequency waveform, step frequency waveform, frequency agility waveform
      Agile bandwidth 500 MHz pulse to pulse
      Antenna Type Dual-offset reflector
      Gain ≥30 dB
      Beamwidth ≤2° (3 dB beamwidth)
      Slidelobes ≤–25 dB
      Receiver Dynamic range 60 dB (instantaneous)/120 dB (total)
      Sensitivity 0.1 m2 @ 10 km
      Instrumented range 200 m~15 km
      Range gates 1~64; ΔR = 100 ns, 300 ns or 400 ns
      Sampler type Intermediate frequency sampler
      Encoding type Quadrature
      Image rejection ≤–41 dBc

      During the experiment, peripheral recording equipment was deployed as follows: Two weather stations recorded environmental conditions at intervals of 15 min and 1 h, and directional wave-recording buoys recorded important wave heights and maximum wave heights, wave direction, and wave period at intervals of 30 min.

      Three cooperative boats, a WaveRider rigid inflatable boat, a Machann speedboat, and a Timothy fishing vessel (Fig. 9), were deployed on four days during the trial for the recording of boat reflectivity measurements. A series of sea clutter and boat reflectivity measurements was defined, including measurements at different transmit frequencies for different waveforms, azimuth angles, and ranges. This set of measurements was repeated whenever there was a significant change in environmental conditions. In fact, the measurements were repeated once a day. During the planning phase, the entire measurement process took about 6.5 to 7.0 hours, or a full day. Therefore, subsets of the measurements that would take less time to complete were defined (for example, only at a single frequency, at a single azimuth angle). The minimum measurement subset took 2 h to complete.

      Figure 9.  Experimental cooperative boats[11]

      A total of 156 measurement datasets were successfully recorded and preprocessed for sea clutter, totaling more than 160 min. In addition, 113 datasets of boat reflectivity measurements (127 min) were recorded, bringing the total number of datasets recorded during the experiment to 269, and the total recording time was 289 min. Most datasets were recorded with a fixed-frequency waveform. In the subset, most datasets were recorded at 15 m resolution at 9 GHz and 6.9 GHz transmit (Tx) frequencies. Because of the higher average wind speed during the experiment, most datasets were recorded at 165°N antenna azimuth. Whenever possible, measurements were taken at different azimuth angles (usually at 15° intervals). Measurements at other frequencies (8 GHz and 10.3 GHz) and other waveforms were regularly recorded so that the correlation between the sea clutter and boat reflectivity characteristics at different waveforms and the Tx frequency can be investigated.

    • Based on the requirements of sea clutter characteristics and sea-surface target detection technology, the IPIX radar datasets of McMaster University, Canada, and Fynmeet radar datasets of CSIR in South Africa in data acquisition and recording were used for reference. The maritime target detection group of Naval Aeronautical University has launched a “radar-to-sea measured data-sharing program”, which aims to use X-band solid-state fully coherent radar to perform the test in stages and in batches to obtain the measured data and the test auxiliary data under various conditions. The datasets can be constructed to support the cognition of sea clutter characteristics; sea clutter suppression; and the research of sea-surface target detection, tracking, classification, and recognition, which are publicly shared in batches.

      The X-band solid-state power amplifier surveillance/navigation radar, which is mainly used in ship navigation and coast surveillance, was used in the experiment, and it could clearly distinguish various targets in various ranges. The radar has the characteristics of high range resolution, high reliability, and small blind area of detection range (Fig. 10). The solid-state power amplifier combined pulse-transmitting system (see Fig. 11) was adopted to improve the range resolution, reduce the range blind area, and reduce the radar radiation power. The transmitting time was from 40 ns to 100 μs. The distance of the target was calculated by the time difference between the received signal and the transmitted signal. The radar scans 360 degrees in the horizontal plane, and parameters are presented in Tab. 5.

      Table 5.  X-band radar parameters[51]

      Radar parameters Parameters setting
      Working band X
      Frequency range 9.3~9.5 GHz
      Measuring range 0.0625~96 nm
      Scanning bandwidth 25 MHz
      Range resolution 6 m
      Pulse repetition frequency 1.6 K, 3 K, 5 K和10 K
      Transmit peak power 50 W
      Rotating speed of antenna 2 rpm, 12 rpm, 24 rpm, 48 rpm
      Length of antenna 1.8 m
      Antenna operation mode Gaze, circular scanning
      Antenna polarization HH
      Antenna horizontal beam width 1.2°
      Antenna vertical beam width 22°
      Information about the dataset and links to its download are available on the website of the Journal of Radar.

      Figure 10.  X-band solid-state power amplifier surveillance/navigation radar[51]

      Figure 11.  Three modes of combined pulse transmission[51]

    • From the published literature, the typical sea clutter measurements of shore-based radar in foreign countries include the multi-bands (L, S, and X band) sea clutter measurements of the Australian Defense Science and Technology Organization[52-54], the X-band sea clutter measurements of the Naval Research Laboratory[55], and the Ka-band high-resolution sea clutter measurements of the south coast of Spain[56]. Others are the multi-band sea clutter measurements (L, S, C, X, and Ku bands) of the Naval Air Warfare Center[57,58], the multi-band sea clutter measurements (S, X, and Ku bands) of the south coast of England[59], the X-band sea clutter measurements of Japan[60], the Mediterranean RFC (refractivity from clutter) and sea clutter environmental experiment (C, X, Ku, Ka, and W bands) of Germany and France[61], and the S-band NetRAD sea clutter measurements of the University College London[62-66].

    • As earlier mentioned, with the refinement of radar observation, background clutter and target returns have become so complex that it is difficult to construct an accurate statistical model. In this case, the “double-high” system with high spatial resolution and high Doppler resolution is the main technical approach. However, the high-resolution radar faces the problem of extremely complex high-resolution sea clutter characteristic and the small-target return characteristic; moreover, the key to the performance of sea clutter detection lies in the deep cognition, elaborate perception, and full utilization of sea clutter characteristics. This section focuses on the development and dynamics of feature-based detectors for high range resolution and long-time-observation radars. This paper mainly deals with signal-level features, not track-level and data-level features, so data-level features will not be introduced.

      Existing features of feature-based detection methods are listed in Tab. 6. A fractal feature is a single feature used in early feature-based detection, and it has a good detection performance for SFTs on sea surface under long-term observation[29,31,67]. Moreover, numerous scholars have studied multifractal features[30,68], fractal features in different transform domains[69-73], and obtained good detection results. The chaotic characteristics of sea clutter suggest that the time series of sea clutter can be described and predicted by nonlinear dynamic models[33], and the prediction error is used to make a judgment. To eliminate the influence of texture component non-stationarity in the compound Gaussian model under long-term observation, the speckle consistency factor feature[74], which belongs to the time domain, is proposed based on the compound Gaussian model. The single-feature-based detection compares the computed feature values with the detection threshold under the given false alarm probability to judge the presence or absence of the target. With the development of feature-based detection methods, numerous features in different domains have been proposed, for example, features based on energy differences in the time domain and spectrum differences in the frequency domain[28], micro-Doppler features suitable for micro-motion targets based on TF analysis[41,42], features based on the difference between normalized TF distributions of sea clutter[75], and polarization features[76]. Tab. 6 presents some common features. With the increase in the number of features, single-feature-based detection will cause a certain performance loss, while multi-feature-based detection is the general trend. However, how to determine the detector threshold in multi-feature-based detection becomes a difficult problem. In Ref. [28], our group proposes a convex hull learning algorithm that treats the detection problem as a single classification problem and transforms the determination of the detection threshold into the selection of the detection decision region, and it is only suitable for the 3D feature space. With the increase in feature dimension, the complexity of the convex hull learning algorithm is increased, and it is difficult to realize detection. Also, machine learning-based algorithms have been proposed. In Refs. [77,78], Support Vector Machine (SVM) and decision tree algorithms were used to determine the decision region, and good detection performance was obtained. The following is a detailed description of several features and detection methods.

      Table 6.  Features introduction of feature-based detection method

      Existing features
      Fractal features Single fractal features[29,31,67], multifractal features[30,68], fractal features in FRFT[69-73]
      Chaotic characteristics of sea clutter Correlation dimension, Lyapunov exponent, and Kolmogorov entropy[33]
      Features in the time domain Relative average amplitude[28], temporal information entropy[77], temporal Hurst exponent[77], the speckle consistency factor[74]
      Features in the frequency domain Relative Doppler peak height[28], relative vector-entropy[28], frequency peak-to-average ratio[77], Hurst exponent in frequency domain[78]
      Features in the time and frequency domains Micro-Doppler features[41,42], the ridge integration of NTFD[75], the number of connected regions and the maximum size of connected regions in a binary image[75]
      Polarization features Relative surface scattering power[76], relative dihedral scattering power[76], and the relative volume scattering power[76]
    • Limited by the dimension of detector design, the early detection methods of small targets on sea surface are mainly based on single feature, and as a result, it is easy to design the detector and determine the detector threshold. Therefore, single-feature-based detection has been the focus of scholars. Scholars at home and abroad have proposed many effective feature-based detection methods in different domains.

      The fractal theory was developed by Mandelbrot in the 1970s to describe irregular natural features that could not be analyzed by the traditional Euclidean geometry, including mountains, rivers, lightning, coastlines, galaxies to snowflakes, ice crystals, leaves, and the patterns and complex processes of natural formation; The fractal theory constitutes an active branch of nonlinear science[79,80]. Fractals can be used to describe natural phenomena or substances with certain self-similarity at different scales, from macroscopic to microcosmic. The sea surface is undulating, and the large-scale swell with different wavelengths also has some fractal characteristics. D. L. Jaggard[81,82] found that the reflection of light and electromagnetic waves from rough surfaces with fractal characteristics is also fractal. G. Franceschetti[83] further described electromagnetic echoes from naturally rough surfaces as two-dimensional fractal Brownian motion. According to the analysis of the sea surface and sea clutter, F. Berizzi[84] further pointed out that sea clutter satisfies fractal characteristics to a certain extent and has the same fractal dimension as sea surface. On this basis, F. Berizzi[85] utilized the fractal method to generate sea clutter; this method can describe the relationship between sea clutter and sea state or radar and overcomes the shortcoming that the traditional method of generating sea clutter is independent of operating conditions and environment; at the same time, the fractal characteristics of sea clutter are retained in the generated clutter.

      In 1993, T. Lo[29] found that the fractal dimension of sea clutter is about 1.75, and when there is a target signal in sea clutter, the fractal degree of the sea surface is reduced; therefore, based on the fractal theory, a new target detection method has been proposed. Fractal Brownian motion is the simplest single fractal model. Because the fractal Brownian motion still has the fractal characteristic after the Fourier transform, based on the result that the sea clutter amplitude echo sequence is modeled as the fractal Brownian motion, the fractal characteristic of the measured sea clutter in the frequency domain has been studied, and an attempt has been made to detect sea-surface targets[31,67]. In 2002, the characteristics of amplitude distribution and space-time correlation of sea clutter were analyzed by Gao[68], and it was theoretically proved that the measured sea clutter was multifractal. In 2006, Hu Jing[30] introduced a sea-surface target detection algorithm based on the multifractal theory. According to the analysis of the measured sea clutter data, it was found that the sea clutter data have multifractal characteristics in the range of 0.01 s to several seconds. By calculating the Hurst exponent of sea clutter, the proposed target detection algorithm was found to have good detection performance. The detection method is as follows:

      (1) The received sea clutter time series is ${{x}} = \left\{ {\left. {{{x}}\left( i \right)} \right|i = 1,2, ··· ,N} \right\}$ , which is regarded as a random walk model.

      (2) If the following relation is satisfied, the sea clutter sequence is a fractal process.

      $${F^{\left( q \right)}}\left( m \right) = {\left\langle {\left| {{{x}}\left( {n{\rm{ + }}m} \right) - {{x}}{{\left( n \right)}^q}} \right|} \right\rangle ^{1/q}}\sim {m^{H\left( q \right)}}$$ (4)

      where H(q) is a function of real-valued q.

      (3) ${F^{\left( q \right)}}\left( m \right)$ and ${m^{H\left( q \right)}}$ are drawn in double logarithmic coordinates. In the approximate linear region, the slope H(q) is found through line fitting.

      (4) When H(q) does not change with q, the sequence is a single fractal; otherwise, it is considered as a multifractal sequence. When q = 2, it is usually called Hurst exponent. By comparing the values of the Hurst exponent, a fractal-based detector is constructed based on the Hurst exponent.

      (5) If the Hurst exponent of the sequence is larger than the set threshold, the target can be detected.

      The detection performance of the detector can be verified by the measured sea clutter data. In Fig. 12, the solid line represents the echo of the pure sea clutter range cells when q = 2, and the hollow line is the radar return of the target cell and the secondary cells around the target cell when q = 2. From Fig. 12 (a), in the 24~212 interval, i.e., 0.08~4.00 s, the F(2) trend is approximately linear. It can be considered that the sea clutter data in this interval has a fractal structure, and this interval is called the scale-free region. The slope H(2) of the straight line, i.e., the Hurst exponent, is obtained by fitting the curve in the scale-free region using the least square method. As shown in Fig. 12(b), the Hurst exponent of the radar returns in the target range and secondary ranges is significantly higher than that of the pure sea clutter. Therefore, the Hurst exponent can be used for the detection of sea-surface targets.

      Figure 12.  Analysis of fractal characteristics in 14 range cells[30]

      The relationship between H(q) and q is demonstrated in Fig. 13. Similar to Fig. 12, the solid line represents the pure clutter range cells, and the hollow line represents the target cell and the secondary cells. It can be seen that H(q) is a function of q, from which it can be concluded that the sea clutter has multifractal characteristics; especially, when the radar returns contain targets, H(q) changes more dramatically with q.

      Figure 13.  Trends of H(q) in 14 range cells[30]

      The target detector is constructed by the Hurst exponent, and the Hurst frequency distribution of 10 sets of sea clutter data of the IPIX radar in the HH polarization channel in 1993 is illustrated in Fig. 14.

      Figure 14.  Hurst frequency distribution of clutter cells and target cells under HH polarization[30]

      In Fig. 14, the solid bars represent the target cells, and the hollow bars represent the pure clutter cells. It can be seen that the Hurst exponent of the pure clutter and the target returns can be completely separated under the measured data in HH polarization. This method is also ideal for other polarization channels. However, the observation time of each range cell is about 131 s in the datasets, and the detection performance of this method decreases rapidly with the shortening of the observation time.

      The nonlinear fractal-based detector in the time domain is also extended to the other transform domain. The fractal properties in the FRFT domain are also a hot topic. The multifractal characteristics of sea clutter FRFT spectrum have been studied in Refs. [69,70] and verified by measured data. In Ref. [71], a method based on the difference of spatial fractal features in the FRFT domain is proposed to detect weak targets on sea surface. The multiscale Hurst exponent is calculated based on the FRFT spectrum of sea clutter in Ref. [72]. Compared with the traditional multiscale Hurst index, the target detection performance is effectively improved. Recently, a team from Nanjing University of Posts and Communications developed a fractal-based detector in the FRFT domain[73], which analyzes the difference between sea clutter and SFTs based on the fractal features in the FRFT domain. The fractal curves of the target and sea clutter were obtained by detrended fluctuation analysis; the fractal dimension and the fractal dimension variance were extracted from the appropriate scale-invariant interval; and the detection analysis of the two features was completed by the convex hull learning algorithm. The effectiveness of the proposed algorithm compared with that of the single-feature-based detector and CFAR detectors was verified.

      Fig. 15 is the flowchart of a fractal-based detector in the FRFT domain. The fractal dimension and fractal dimension variance of sea clutter and target in the FRFT domain were studied, and Fig. 16 is the fractal curve determined by detrended fluctuation analysis. Fractal dimension and fractal dimension variance were obtained by selecting a scale-invariant interval. Fig. 17 is the distribution of training samples and test samples on the two-dimensional feature plane when the false alarm ratio is 10–3 and 10–2. Fig. 18 compares the performances of the two-feature-based detector in the FRFT domain and CFAR detectors.

      Figure 15.  Flowchart of fractal-based detector[73]

      Figure 16.  Fractal curves[73]

      Figure 17.  Distribution of training samples and test samples on the two-dimensional feature plane[73]

      Figure 18.  Classic CFAR algorithm detection curves[73]

      Based on the fractal characteristics of sea clutter, a series of detection algorithms based on fractal theory has been developed in recent years, including single-fractal features, multifractal features[86,87], multifractal correlation spectrum[88], higher-order fractal features, extended self-similarity, and the theory of modulus and fractal. With the development of the fractal theory, more and more detection methods are being developed, and these methods have become an active research direction in target detection.

    • The sea surface is a very complex dynamical system, and the radar echo is influenced by several factors, including the wind direction, wave height, wave direction, and ocean current. In 1995, Haykin[33] applied correlation dimension, Lyapunov index, and Kolmogorov entropy and indicated that sea clutter has finite correlation dimension; its largest Lyapunov exponent is positive, and sea clutter is short-term predictable. The correlation dimension and the largest Lyapunov exponent are both necessary for the time series components and do not change significantly with the sea state or geographical locations. These results indicate that there may be a general chaotic structure that leads to sea clutter generation. In conclusion, the sea clutter time series has significant chaotic characteristics. According to the short-term predictability of sea clutter, a nonlinear prediction model has been constructed for sea clutter, and the prediction error was used to test the statistical hypothesis[89-93]. Based on the chaos theory model, the sea clutter time series can be described and predicted by some nonlinear dynamic models. Therefore, the sea clutter time series can be nonlinearly fitted by the neural network learning method, and target detection is accomplished by prediction error. Chaotic systems are extremely sensitive to noise and feature the “butterfly effect”. However, in actual systems, they are affected by various noises[94], which lead to system anomalies and instability. The sea clutter chaotic model was once controversial in the academic world. Haykin proposed a modification to the previously proposed sea clutter chaotic model. It is believed that the sea clutter may be generated by random chaos, multiple deterministic chaoses, or a mixture of both, and an increasing number of scholars point out that sea clutter does not have chaotic characteristics[95-97]. However, the idea of anomaly detection based on neural network and SVM has become an idea of feature-based detection research. The main idea of the detection algorithm based on the sea clutter chaotic model is illustrated in Fig. 19.

      Figure 19.  Flowchart of detector based on neural network prediction[33]

      Here, ${{{x}}_{\rm{A}}}\left( n \right)$ is the actual received signal, and ${\bar {{x}}_{\rm{A}}}\left( n \right)$ is the prediction signal based on the neural network. When ${{{x}}_{\rm{A}}}\left( n \right)$ only contains the sea clutter, the output prediction error $ e\left( n \right) $ is small, but when the target returns exist in ${{{x}}_{\rm{A}}}\left( n \right)$ , the output $e\left( n \right)$ will be a larger value. Based on this, we can get the target detection algorithm based on the chaos model as follows:

      (1) For a radar echo ${{{x}}_{\rm{A}}}\left( n \right)$ , $n = 1, ··· ,{N_{\rm{T}}}$ , the prediction value ${\bar {{x}}_{\rm{A}}}\left( n \right)$ is obtained by the neural network model; then the prediction error is calculated as $e\left( n \right) = {{{x}}_{\rm{A}}}\left( n \right) - {\bar {{x}}_{\rm{A}}}\left( n \right)$ .

      (2) The cumulative mean square error of the prediction in the observation time is calculated as,

      $$ {E_e} = \frac{1}{{{N_{\rm{T}}}}}\sum\limits_0^{{N_{\rm{T}}}} {{e^2}\left( n \right)} $$ (5)

      where ${N_{\rm{T}}}$ is the signal length in the observation time.

      (3) Comparing $ {E_e} $ with the threshold of the given false alarm probability, if the threshold is exceeded, the target exists and the H1 hypothesis is considered valid; otherwise, the target does not exist and the H0 hypothesis is considered valid.

      Fig. 20 displays the Receiver Operating Characteristic (ROC) curves of the detection results, where the solid line represents the traditional Doppler CFAR detector, and the broken line represents the neural network-based detector. It can be seen that the detection performance based on the neural network algorithm is better than that of the traditional Doppler CFAR detector.

      Figure 20.  ROC curves of neural network-based detector and traditional Doppler CFAR detector[33]

      By learning the sea clutter time series, the neural network-based detection method can fit the sea clutter time series well, so that the sea clutter time series can be predicted and the target can be detected by prediction error. The flowchart is shown in Fig. 21. The learning rules of neural network for sea clutter time series can be understood as the establishment of complex nonlinear mapping by neural networks. All sea clutter features are the learning objects of the neural network; therefore, the detection method based on the prediction error of the network is based on the full features of sea clutter. However, the method based on full features has many disadvantages. The amounts of common features of sea clutter and target are more than different features; thus, this method consumes a large amount of neural network resources, and the learning scale of the network is increased, and the learning efficiency is reduced. The over-large network makes the learning process train many fine features, resulting in the “overfitting” phenomenon, and the network has poor generalization ability. Therefore, neural network-based learning has been neglected by researchers for a long time.

      Figure 21.  Flowchart of detection methods based on prediction

      However, with the development of deep learning and artificial intelligence, the neural network-based learning method has good application in radar target detection[98]. Typical deep learning networks include CNN, Sparse AutoEncoder (SAE), and deep belief network. They are widely used in Synthetic Aperture Radar (SAR) images and produce good results, and CNN is the most widely used. A CNN mainly consists of a convolution layer, pooling layer, and fully connected layer. The convolution layer extracts the low-level to complex features of the input image. In the pooling layer, the image is oversampled to reduce the feature dimension and control the overfitting. The fully connected layer arranges the features obtained from the previous layer and connects them with the neural network. The SAE method can extract features without supervision; thus, it has become the research focus. The convolutional autoencoder can be obtained by combining CNN and SAE, and it has good performance in practical applications. The emergence of deep learning networks leads to a new direction of sea-surface target detection. Based on the micro-motion characteristics of sea-surface targets, some scholars have proposed to analyze and process the micro-Doppler spectrum of sea-surface targets by CNN, which achieves better detection performance than the traditional methods[43]. An increasing number of scholars are trying to utilize deep learning networks to detect and classify sea-surface targets, and the application of neural networks in sea-surface target detection is still developing and expanding.

    • To improve the range resolution and detection range, modern radars usually transmit signals with large time-bandwidth product. Linear Frequency Modulation (LFM) signals can be easily produced through both analog and digital techniques, and their form is simple; therefore, the research on LFM signals is more in-depth. The TF analysis method can provide better joint distribution information in the time domain and the frequency domain; it is widely used in signal processing and has become a powerful tool for the analysis of time-varying non-stationary signals. When the target is moving at a constant acceleration or deceleration relative to the radar, the target echo is an LFM signal due to the Doppler effect. Scholars have used several TF analysis tools such as the STFT, FRFT, Wigner-Hough transform, pseudo-Wigner-Ville distribution, Radon-Wigner transform[99,100], Radon-ambiguity transform[101], and chirplet transform[102]. The detection of LFM signals in non-stationary backgrounds is accomplished by parametric and non-parametric methods[103].

      According to the characteristics of ship wakes in SAR images, Radon transform and Hough transform are applied to detect ships on sea surface[104,105]. In these method, the observed area needs to be imaged, and the detection performance is closely related to the image quality. Given the non-uniformity and non-stationarity of sea clutter, many detection methods based on TF distribution have been proposed for target detection[106-111]. Due to the differences between sea clutter and target in TF clustering and duration, some researchers have used TF iterative decomposition algorithms for target detection[112,113]. The FRFT can be regarded as a rotation operation on the TF plane, and it has no cross term; thus, it is very suitable for processing LFM signals. Some scholars have applied the FRFT to the detection of uniformly accelerated targets on sea surface[114-116]. However, the sea-surface targets are usually affected by the sea waves, and the target signal is a nonlinear FM signal, which makes the detection performance of this kind of detection method in practical applications have a certain decline. To improve the detection performance of sea-surface targets, in recent years, scholars have proposed new detection methods based on TF analysis[35-40]. In Ref. [35], Haykin transformed the problem of target detection in the sea background into the problem of double classification in pattern recognition and used principal component analysis to extract TF features from a TF plane. The clutter and target classification was accomplished by a neural network algorithm. However, in practice, radar needs to detect unknown targets, so the characteristics of targets cannot be obtained exactly, which limits the practical application of this method. Nonetheless, the method in which the target detection problem is transformed into a double classification problem provides a new idea for the detection of SFTs on sea surface. Because of the excellent TF localization characteristics, wavelet transform can be adopted to observe different details in radar echoes; thus, some scholars try to use wavelet transforms to detect sea-surface targets[117]. In recent years, many scholars have proposed target detection methods based on deep neural networks, the micro-Doppler theory, and TF maps; these methods also belong to the category of TF analysis.

      The micro-Doppler theory has been a hot spot in the field of target detection in recent years. Based on the analysis and modeling of the echo of a micro-motion target, the micro-motion features of the target are extracted and detected by different detection methods. The micro-Doppler theory has been introduced into the detection of dim targets on the sea surface, and good detection results have been obtained. Based on the micro-Doppler theory, the Naval Aeronautical University team proposed a sea-surface micro-motion target detection method based on GSTFRFT[41], a radar target micro-motion feature extraction and detection method based on ST-STFD[42], and a sea-surface micro-motion target detection and classification method based on CNN[43].

      (1) Sea-surface micro-motion target detection method based on GSTFRFT[41]: In Ref. [118], the modeling of the micro-motion features of a rigid body target on the sea surface is introduced, and the micro-motion target models under the conditions of short-term observation and long-term observation were studied. The motion of a target on the sea surface is a compound motion in the 3D space, which can be characterized by the non-uniform motion and the three-axis rotation of the target in translational motion. In Ref. [41] the model of the sea-surface micro-motion target was applied under short-time observation; the target could be modeled as an amplitude fluctuation FM signal, and the target returns in the same range cell could be modeled as

      $$ \begin{split} {{x}}\left( t \right) \,& = {{s}}\left( t \right) + {{c}}\left( t \right) \\ & = \sum\limits_i {{{{A}}_i}\left( t \right)\exp\left( {{\rm{j}}2\pi {f_i}t + {\rm{j}}\pi {k_i}{t^2}} \right) + {{c}}\left( t \right),\left| t \right| \le {T}} \end{split} $$ (6)

      where ${{{A}}_i}\left( t \right)$ is the amplitude of the first i micro-motion signal, ${f_i}$ represents the central frequency, and ${k_i}$ is the FM. At the high sea state, the sea spike presents the micro-Doppler characteristic, and the radar will often misjudge the sea spike as the target. Therefore, the method of sea spike identification based on three characteristic parameters proposed by Fred Posner[119] was used to suppress the sea spike before the research of the micro-motion target. The time series of sea clutter extracted from sea spike were calculated by GSTFRFT, and the transformed amplitude was used as the test statistic and compared with the detection threshold under the given false alarm probability, to judge the existence of the target. Fig. 22 displays the features after the sea clutter suppression in the transform domain, and Fig. 23 compares the results of the methods based on STFT and GSTFRFT after sea clutter suppression. In the GSTFRFT domain, the energy of the micro-motion signal is accumulated, and the peak value is sharp and the side lobe is low. Because of the sea spike suppression, the SCR and the detection probability are improved. Compared with the traditional MTD, GSTFRFT can improve the detection performance by more than 30%.

      Figure 22.  Micro-motion signal features after sea clutter suppression (N = 256)[41]

      Figure 23.  Comparison of micro-motion target detection results based on STFT and GSTFRFT after sea clutter suppression (N = 512)[41]

      (2) Radar target micro-motion feature extraction and detection method based on ST-STFD[42]: In Ref. [42], several common TF distributions of the micro-motion signals expressed by Eq. (6) were selected to analyze the signals from the sea surface; the distributions were the STFT distribution, WVD, SPWVD, and FRFT. Among them, the TF resolution of the STFT was poor, and the WVD had a serious cross term. It was difficult for SPWVD to consider the high-resolution instantaneous FM of the micro-motion signal, while for FRFT as a parameter searching method, the accuracy of parameter estimation was limited by the TF resolution. Given the difference between micro-motion signals and sea clutter, using the idea of sparse decomposition, the Sparse TF Distribution (STFD) was introduced to sea-surface target detection, and two micro-motion feature extraction and detection methods based on ST-STFD were proposed, which are ST-SFT and ST-SFRFT. Fig. 24 and Fig. 25 show the detection results of the ST-SFT-based and ST-SFRFT-based detection methods. Tab. 7 compares the performances of different methods for the detection of micro-motion targets. The detection performance of ST-STFD method was significantly better than that of the traditional TFD method, because the ST-STFD method was designed in the optimal sparse domain of the micro-motion signal, but the efficiency of the ST-STFD method still needs to be improved.

      Table 7.  Detection performances of different methods for the detection of micro-motion maritime targets[42]

      Parameter MTD FRFT WVD SPWVD ST-SFT ST-SFRFT
      Pd(%) (SCR = –5 dB) 39.26 57.26 35.68 55.24 49.21 71.35
      Pd(%) (SCR = 0 dB) 52.84 76.84 62.27 72.58 63.28 85.69

      Figure 24.  ST-SFT-based micro-motion target detection results (starting time = 20 s)[42]

      Figure 25.  ST-SFRFT-based micro-motion targets detection results (starting time = 20 s)[42]

      (3) Detection and classification method of sea-surface micro-motion targets based on CNN[43]: With the rapid development of deep learning, more intelligent methods are being applied to sea-surface target detection. Based on the time-varying characteristics of micro-motion targets, the TF image can be used to effectively analyze the targets. In Ref. [43], the TF images of radar echoes were detected and classified by CNN, and good results were obtained. Common CNNs are LeNet, AlexNet, and GoogleLeNet. LeNet was first used for digit recognition; AlexNet is deeper than LeNet and can learn more complex objects; and GoogleLeNet increases the depth and width of neural networks, and it guarantees the invariability of computing resources. The training set and the test set of target detection in Ref. [43] were divided into clutter and target, and the TF image obtained from the measured sea clutter data was used as the training set and the test set. The simulated target signal of a certain SCR based on a sea-surface moving target model was regarded as the target training set and the test set. First, the CNN model was trained by the training set, and then the test set was detected by CNN. The three CNN models had the same signal-processing efficiency, among which the LeNet model had the highest detection probability and the AlexNet model had the lowest false alarm probability. Fig. 26 is the processing flow diagram of the CNN-based method, and the results are presented in Tab. 8. Compared with the traditional SVM method, the CNN-based method had a higher detection probability and lower false alarm rate, but the latter was easily affected by the SCR.

      Table 8.  Detection results of different models(%)[43]

      Model LeNet AlexNet GoogLeNet
      False alarm ratio 1.24 0.04 0.24
      Detection probability 92.28 84.44 90.94

      Figure 26.  Processing flow diagram of CNN-based method[43]

    • In recent years, considering the difference between the features of clutter and target, some scholars have proposed speckle stationarity as a feature to detect targets on sea surface[74]. Sea clutter is non-stationary, which is embodied by the non-stationary texture of sea clutter, and the speckle of sea clutter is approximately stationary within a certain time. The non-stationarity of the texture is disadvantageous to the detection of sea-surface targets, and the texture non-stationarity needs to be first eliminated. Therefore, the speckle is first extracted from the non-stationary sea clutter, and then the test statistic is designed based on the speckle characteristics. Because of the strong structure of the SFT, the speckle structure is not as obvious as that of the SFT; that is, the consistency of the speckle is weaker than that of the target. Therefore, the speckle consistency is proposed as a feature to detect SFTs on sea surface. The flowchart of the detection is displayed in Fig. 27.

      Figure 27.  Flowchart of a feature-based detector using the average speckle consistency factor[74]

      First, using the reference samples ${{{r}}_{q,k}}$ , we estimate the Normalized Samples Variance Matrix (NSCM) and obtain the NSCM estimation ${{{M}}_q}$ , where q is the interval, K is the number of reference cells, and N is the number of cumulative pulses.

      $$ {{{M}}_q} = \frac{N}{K}\sum\limits_{k = 1}^K {\frac{{{{{r}}_{q,k}}{{r}}_{q,k}^H}}{{{{r}}_{q,k}^H{{{r}}_{q,k}}}}}, \quad q = 1,2,··· ,Q $$ (7)

      Eq. (8) standardizes the results of Eq. (7), and ${\bar {{M}}_q}$ is obtained; tr(·) represents the trace of the matrix.

      $$ {\bar {{M}}_q} = \frac{{N{{{M}}_q}}}{{{\rm{tr}}({{{M}}_q})}},\quad q = 1,2, ··· ,Q $$ (8)

      Then, by the normalized value ${\bar {{M}}_q}$ , the speckle consistency factor is calculated according to Eq. (9), where τ is the time interval and $ {\Vert \cdot \Vert }_{2}$ is the 2-norm of the matrix:

      $$ \begin{split} & \rho (\tau ) = \frac{1}{{Q - \tau }}\sum\limits_{q = 1}^{Q - \tau } {\frac{{{{\left\| {{{\bar {{M}}}_q} - {{\bar {{M}}}_{q + \tau }}} \right\|}_2}}}{{{{\left\| {{{\bar {{M}}}_q}} \right\|}_2} + {{\left\| {{{\bar {{M}}}_{q + \tau }}} \right\|}_2}}}} \\ & \qquad \tau = 1,2, ··· ,Q - 1 \end{split} $$ (9)

      Finally, the average consistency factor of the speckle is obtained as

      $$\rho = \frac{1}{{{\tau _2} - {\tau _1}}}\sum\limits_{\tau = {\tau _1}}^{{\tau _2}} {\rho (\tau )} $$ (10)

      where $[{\tau _1},{\tau _2}]$ is the average time interval. The speckle consistency reflects the time similarity of the covariance matrix of the speckle and further reflects the speckle structural stationarity. The smaller the average consistency factor, the stronger the time stationarity of the speckle. The structure of the SFT is stronger than that of the sea clutter; therefore, the average consistency factor of the speckle of the returns with SFTs is smaller than that of the pure sea clutter.

      Fig. 28 shows the distribution of the speckle consistency factor under four polarization channels. Fig. 29 compares the performances of the speckle consistency factor detectors from the measured data.

      Figure 28.  Average consistency factors of pure clutter and clutter with target under four polarization channels[74]

      Figure 29.  The detection probabilities of the four detectors under four polarization channels, L = 1024[74]

    • With the further improvement of radar resolution and the increase in dwell time, many new signal-processing methods have been applied, resulting in a variety of features that can effectively detect targets. Multiple features can complement each other for different types of targets, which can greatly improve the detector robustness. With the successful design of the new multi-feature detector and the gradual improvement of the signal-processing hardware level, multi-feature detection methods based on feature engineering or artificial intelligence self-selection are becoming increasingly mature, and they have become an important research direction of sea-surface target feature-based detection.

    • In feature-based detection, feature extraction is very important. The ability to distinguish target and clutter largely determines the detector performance. The feature can be extracted from the different digital features of the target and clutter. From the traditional test statistics used in the traditional radar target detection and the overall recognition of the target return characteristics, different features are extracted according to cognitive conclusions. If the radar transmits a coherent pulse of length N at a wave position and receives it through the I/Q channel, the complex data of each range cell can be obtained. Then, the problem of radar target detection can be expressed as the binary hypothesis problem of Eq. (11):

      $$\left. \begin{aligned} & { {H_0}:\left\{\!\!\! {\begin{array}{*{20}{l}} {{{x}}\left( n \right) = {{c}}\left( n \right),\quad n = 1,2, ··· ,N } \\ {{{{x}}_p}\left( n \right) = {{{c}}_p}\left( n \right),\quad p = 1,2, ··· ,P} \end{array} } \right.} \\ & {{H_1}:\left\{\!\!\! {\begin{array}{*{20}{l}} {{{x}}\left( n \right) = {{s}}\left( n \right) + {{c}}\left( n \right),\quad n = 1,2, ··· ,N } \\ {{{{x}}_p}\left( n \right) = {{{c}}_p}\left( n \right),\quad p = 1,2, ··· ,P } \end{array}} \right.} \end{aligned}\!\!\!\!\right\} $$ (11)

      where x(n) is the time series received by the cell under test(CUT), s(n) is the time series received from the target returns, c(n) is the time series received from the sea clutter, N is the number of accumulated pulses, and P is the number of reference cells around the CUT. The H0 hypothesis indicates that the radar returns only contain sea clutter and noise, and the H1 hypothesis indicates that the radar returns contain targets. A large number of pure clutter data can be obtained from the received radar returns, so the feature vectors ${{{\xi}} _i}$ of pure clutter can be extracted, which can form training samples of pure clutter ${{{L}}_{{H_0}}} = \{ {{{\xi}} _i} \in {R^3}:i = 1,2, ··· ,I\}$ . Because of the sea targets complexity and diversity, it is difficult to obtain the target returns and the feature vectors of all kinds of targets when the targets are included in the radar returns, and consequently, training samples of targets cannot be formed. Therefore, the decision region can be obtained by the training samples of pure clutter, and the target existence can be judged by judging whether the feature vector of the radar returns of the CUT falls into the decision region. If it does not fall into the decision region, the target does not exist; otherwise, the target exists.

      (1) Detection method based on original tri-features[28]: Although fractal-based detectors have good detection performance in the case of long-time observation, in practical sea-surface target detection, the observation condition cannot reach the ideal long time, and fractal-based detectors cannot obtain the ideal effect in practical applications. To mitigate the problem of fractal-based detection methods, a tri-feature-based detection method for SFTs has been proposed[28]. The main idea of this method is to detect SFTs on the sea surface by using three complementary features (the relative average amplitude, relative Doppler peak height, and relative vector-entropy) to distinguish targets and clutter, and to transform the detection problem into a single classification problem in the feature space; then, a fast convex hull learning algorithm is used to determine the decision region for target detection.

      In radar echoes, three kinds of features with separability are extracted from the time domain and the frequency domain. The energy information in the time domain can be used as a mark to distinguish the target and clutter, and the differences in the frequency spectrum can also be used to distinguish the target and clutter. The relative average amplitude, relative Doppler peak height, and relative vector-entropy can be extracted from these differences. Fig. 30 shows the distributions of features in a 3D feature space, under different observation times: 0.512 s, 1.024 s, 2.048 s, and 4.096 s. With the increase in observation time, the separability of target and clutter and the detection performance improved.

      Figure 30.  Distributions of features of clutter-only vectors and vectors with target in 3D feature space

      The fast convex hull learning algorithm reduces the optimal detection decision region to the convex hull region of Eq. (12) under the given false alarm rate

      $$ \begin{split} & \mathop {\min}\limits_\varOmega \left\{ {{\rm{Volume}}\left( \varOmega \right)} \right\} \\ \\ & {\rm{s.t.}}\frac{{\# \{ i:{{{\xi}} _i} \in \varOmega \} }}{I} = 1 - {P_{\rm{F}}} \end{split} $$ (12)

      where $\# {\rm{A}}$ represents the number of elements of set A, ${P_{\rm{F}}}$ is the false alarm ratio, and I is the total number of pure clutter feature vectors. Fig. 31 illustrates the convex hull generated from the original clutter-only data and the convex hull with a given false alarm probability.

      Figure 31.  Convex hull with the original training data and convex hull with given false alarm rate

      The procedure of the tri-feature-based detector is divided into two parts: training and detection. In the training part, we need to collect the clutter samples and extract the pure clutter features. Then, the fast convex hull learning algorithm is used to train the detection decision region that satisfies the false alarm ratio, such as in Fig. 31. In the detection part, features of test samples in the CUT need to be extracted, and the existence of the target is judged by whether the test sample feature falls in the decision region.

      (2) SVM-based sea-surface small-target detection[77]: With the development of feature-based detection, more and more effective features are being used to distinguish sea clutter from target returns. The problem of sea-surface target detection can be transformed into a special binary classification problem in the feature space by effective feature extraction. There are many excellent machine learning algorithms to solve the binary classification problem, such as SVM and neural networks. However, the core of the traditional machine learning algorithm is to search a classification plane, which can make the error rate of the two classes balanced and minimum. In radar target detection, the requirement of the false alarm rate is much higher than that of the false dismissal probability (usually, the false dismissal probability can be up to a few tenths, but the false alarm is generally less than 10–3). Therefore, the key problem of combining machine learning algorithm with target detection is how to accurately control the false alarm rate. In 2019, Li et al constructed an SVM-based sea-surface small-target detection method by combining SVM with radar target detection; the method not only realized controllable false alarm rate but also had better detection performance than other detectors.

      In this SVM method, first, temporal information entropy, temporal Hurst exponent, and the frequency peak-to-average ratio are extracted from the received sea clutter time series, and they are used to construct a three-dimensional feature vector ${{{F}}_i}$ . The target (+1) and sea clutter (–1) are labeled as ${y_i}$ = {+1, –1}; then, M labeled training samples can be represented as $\left\{ \left( {{{{F}}_i},{y_i}} \right), i = 1, 2, ··· ,M \right\}$ . In this feature space, the feature vectors of the target and the clutter are linearly inseparable. To solve this problem, a nonlinear kernel function can be used to map a three-dimensional feature vector ${{{F}}_i}$ to a higher-dimensional feature space and to convert linearly inseparable data into a separable one, and an SVM-based detector can be constructed using radial basis function as a kernel function.

      $$k\left( {{{{F}}_1},{{{F}}_2}} \right) = \exp\left( { - \frac{{\left\| {{{{F}}_1} - \left. {{{{F}}_2}} \right\|} \right.}}{{2{\delta ^2}}}} \right)$$ (13)

      After the mapping to a high-dimensional space, the next step is to find a linearly separable hyperplane ${w^{\rm{T}}}{{F}} - b = 0$ that can separate the target from the clutter in the high-dimensional feature space. The parameters $w$ and $b$ can be determined by solving the following optimization problem

      $$ \begin{split} & \mathop {\min}\limits_{w,b,{{\xi}} } \frac{1}{2}{\left\| w \right\|^2} + \sum\limits_{i = 1}^M {\left( {\frac{{1 - {y_i}}}{2}{b_0} + \frac{{1 + {y_i}}}{2}{b_1}} \right){{{\xi}} _{{i}}}} \\ & {\rm{s.t.}} \;\;{\rm{C}}1:{y_i}[k(w,{{{F}}_i}) - b] \ge 1 - {{{\xi}} _i},i = 1,2, \cdots ,M \\ & \qquad {\rm{C}}2:{{{\xi}} _i} \ge 0,i = 1,2, ··· ,M\\[-10pt] \end{split} $$ (14)

      where ${{{\xi}} _i}$ is the slack variable. The false alarm ratio can be controlled by controlling the change of β0 and β1. According to the theoretical basis of SVM, Eq. (14) can be solved by sequential minimal optimization. After the hyperplane ${{{w}}^{\rm{T}}}{{F}} - b = 0$ is obtained, when ${{{w}}^{\rm{T}}}{{F}} - b > 0$ , ${y_j} = {\rm{ + }}1$ is identified as the target. When ${{{w}}^{\rm{T}}}{{F}} - b \le 0$ , ${y_j} = - 1$ is identified as the sea clutter. The results are presented in Tab. 9.

      Table 9.  Detection performance comparison between SVM-based detector and other detectors[77]

      Detectors Detection results
      (HH polarization, PF = 0.001)
      SCR = –2 dB SCR=17 dB
      SVM-based detector 76 99
      Tri-feature-based detector 57 99
      Fractal-based detector 18 79

      Compared with the tri-feature-based detector and fractal-based detector, the SVM-based detection method has greatly improved detection performance and can break through the limitation of the convex hull learning algorithm to detect in feature spaces of above three dimensions.

      (3) Decision tree-based sea-surface weak target detection[78]: Zhou et al. proposed a decision tree-based detector by combining the decision tree algorithm with the radar target detection problem and realized the effective control of false alarm rate. A decision tree is a common classification algorithm; the tree model is based on the attributes or characteristics of data. Common decision tree algorithms include ID3, Classification And Regression Tree (CART), C4.5, and random forest. The decision tree has only one root node, multiple internal nodes, and multiple leaf nodes. First, all the training samples are allocated to the internal nodes; as the allocation rule, the appropriate features and thresholds to maximize the purity of the internal nodes are selected. The whole process is recursive from top to bottom.

      In Zhou et al.’s study, the Hurst index in the time domain, the Hurst index in the frequency domain, and the peak-to-average ratio in the frequency domain were extracted from sea clutter. For each feature vector, the target feature vector was labeled “1” and the clutter vector was labeled “0”. A decision tree was constructed by the famous CART algorithm. First, all the feature vectors were at a root node, and the child nodes were generated by selecting the features and thresholds with the smallest Gini index (the smaller the Gini index, the higher the purity). This was repeated until the resulting child node was no longer separable, so that it became the leaf node. Finally, the generated leaf nodes could divide the feature space into two parts. The ratio of the correct target samples to all target samples was the detection probability. Fig. 32 is a flowchart of the algorithm. Tab. 10 compares the detection performances of the decision tree-based detector and the other detectors.

      Table 10.  Detection performance comparisons between the decision tree-based detector and the other detectors[78]

      Detector Detection results
      0 dB 5 dB 10 dB 15 dB
      Decision tree-based detector 0.76 0.84 0.98 0.99
      Tri-feature-based detector 0.58 0.65 0.82 0.95
      Fractal-based detector 0.21 0.32 0.48 0.68

      Figure 32.  Flowchart of the decision tree-based detector[78]

      The decision tree-based detection method combines detection and classification, which improves the detection performance and can realize detection in high-dimensional feature spaces as well as the SVM-based method.

      The feature detection method based on machine learning algorithms can greatly improve the detection performance because the convex hull learning algorithm can only be used in the feature spaces of three dimensions or less. In contrast, machine learning algorithms can break through the limitation of high-dimensional feature space, which means more features can be used in feature-based detection to further improve the detection performance.

    • In the detection of SFTs in the sea clutter background, to obtain enough accumulated gain of target returns and improve the detection performance, the observation time usually needs to reach the second level, and in the case of long-time observation, the time series of sea clutter is non-stationary and the texture changes with time; therefore, the sea clutter time series is modeled as a compound Gaussian model with time-varying texture. Moreover, the return of SFTs shows amplitude fluctuation and Doppler modulation on the second time scale, so the target return is modeled as unknown nonlinear FM signals with amplitude fluctuation[120-122]. Therefore, the detection of sea-surface SFTs is equivalent to the problem of finding unknown nonlinear FM signals in the compound Gaussian clutter with time-varying texture.

      Because Time-Frequency Distribution (TFD) realizes the short-time coherent accumulation of unknown FM signals, it is often used to detect unknown FM signals in white noise[120-125]. When the TFD is properly designed, the energy of the nonlinear FM signal can be completely concentrated on the instantaneous frequency curve. Because the Normalized TF Distribution (NTFD) of received radar time series can enhance the TF characteristics of clutter returns, and the target return can be approximated by piecewise linear FM signals, NTFD can be computed by the SPWVD[125,126]. Sea clutter and target returns show different NTFD characteristics. Three TF features can be extracted from these differences: the ridge integration of NTFD, the number of connected regions, and the maximum size of connected regions in a binary image composed of NTFD bright pixels[75].

      Similar to the detection steps of the tri-feature-based detector, the TF-tri-feature-based detector is also divided into the training part and the detection part. In the training part, the feature vectors are extracted from a large number of pure clutter data. The single classifier is trained by the fast convex hull learning algorithm, and the mean vector and the standard deviation vector are provided for the detection part. In the detection part, the feature vectors of the received time series of the CUT and the reference cells are calculated, and the mean vector and the standard deviation vector obtained from the training part are used for normalization. The calculation of the feature vector of the CUT helps determine whether it falls into the decision region, and the decision result is obtained. The performance of the TF-tri-feature-based detector is better than that of the tri-feature-based detector, but the detection probability on some datasets is slightly decreased. This shows that feature extraction is important for the performance of the joint multi-feature-based detector.

    • The methods based on time-domain, frequency-domain, and TF-domain only use data from one of the four polarization channels: HH, HV, VH, and VV, but with the popularization of the full-polarization radar and the renewal of radar equipment, the method of full polarization is increasingly mature in the field of image processing, so it is possible to process radar data with full polarization. In Ref. [76], researchers attempted to use the full-polarization method to deal with the detection of SFTs on sea surface.

      Each set of data received by a full-polarization radar contains four kinds of data in HH, HV, VH, and VV channels. Usually, the polarimetric scattering matrix is used to characterize the received data. Based on the scattering matrix, we can extract the polarization coherent matrix or the polarization covariance matrix. Polarization features are typically extracted by decomposing the scattering matrix, the coherent matrix, or the covariance matrix. For the detection of SFTs on sea surface, surface scattering, dihedral angle scattering, and volume scattering may occur when the radar beam illuminates the calm sea surface, waves, or objects. Surface scattering occurs when the beam illuminates the calm sea surface or produce a specular reflection on a vertical wave surface or the target. Dihedral scattering may occur when the beam illuminates the dihedral angle of the wave or the angle between the target and the sea surface, and when the beam illuminates the broken wave (white cap) or the complex structure of the target, volume scattering will occur. The presence or absence of targets in the radar beam area will affect the scattering type and the scattering energy; thus, the correlation polarization features can be extracted to detect SFTs.

      Based on the theory of polarimetric target decomposition Ref. [76], according to the detection scene of SFTs on sea surface, the three-component Freeman–Durden decomposition method[127] has been used to model three scattering mechanisms, and the energy of the scattering mechanisms was determined. The relative ratio of the energy between the CUT and the reference cells was selected to extract three polarization features: the relative surface scattering power, relative dihedral scattering power, and relative volume scattering power. Using these three features, a convex hull learning algorithm was used to detect the SFT on the sea surface. Fig. 33 compares the detection performances of the polarization feature-based detector and the original tri-feature-based detector.

      Figure 33.  Detection probabilities of polarization feature-based detector and tri-detector at HH, VV, HV, and VH polarizations for 10 datasets[76]

      The polarization feature-based detector is robust and outperforms the tri-feature-based detector. Because the detector uses radar data in four polarization channels to extract separable clutter and target features, the detection performance is better than that of the detector based on a single polarization mode. When full-polarization information is used to detect targets, the information received by radar can be fully used, and the detection performance is effective; thus, further research should be done on feature extraction in full-polarization radar.

    • The detection of SFTs in the sea clutter background is a difficult problem. With the stealth and miniaturization of sea-surface targets, it is important to improve the detection ability of SFTs. The feature-based detection method of SFTs has gone through many development stages, from single-feature detection to three-features detection method to high-dimensional feature space detection based on machine learning algorithms. The range of feature extraction has also changed from one dimension in the time domain or frequency domain to two dimensions in the TF domain, and the feature has developed from single-polarization mode to full-polarization mode. In this paper, several feature-based detection methods of SFTs are introduced, and their detection principles are analyzed. There is still much space for the development of existing detectors. To improve the detection probability and the performance of detectors, the following aspects should be considered in the future development of feature-based detectors:

      (1) Extracting more features that can effectively distinguish clutter from target: The received radar signal contains a large amount of clutter and target information in various aspects, which can be used in the time domain, frequency domain, TF domain, and various levels to extract new features suitable for feature-based detection. The stronger the separability of clutter and target in the feature space, the more suitable the feature is for feature-based detection, and the detector has better detection performance.

      (2) Improving detection algorithm using new subjects: The convex hull learning algorithm commonly used in the design of single classifiers for anomaly detection cannot deal with high-dimensional features. With the development of artificial intelligence, more and more learning algorithms can be used in feature-based detection. The fusion of subjects has become a trend. The multi-feature fusion algorithms can break through the limitation of high-dimensional feature space, and more features can be used in feature-based detection, which can further improve the detection performance.

      (3) Developing new radar systems: The feature-based detection method requires long observation time in the detection process, but the radar in practical applications often cannot meet the requirement of long observation time. It is difficult to reconcile the conflict between the long dwell time and the scanning efficiency of a conventional radar, which is why long-time observation is impossible. In 2003, the Lincoln Laboratory of MIT proposed the concept of a ubiquitous radar using multi-input/multi-output digital arrays[128], enabling full-time observation in all directions. The development of this kind of new radar system is more advantageous to the extraction of clutter and target features. The more the separability in feature space, the better the performance of the designed detector.

    • (1) Because of the particularity of military application, the application of artificial intelligence in the military field is far less extensive than that in the commercial Internet field. This difference is related to the available data in military artificial intelligence systems. Taking sea-surface target detection as an example, it is difficult to collect enough data to train the corresponding artificial intelligence algorithm for non-cooperative targets. Artificial intelligence algorithms, especially deep learning, typically require large amounts of data that must be accurately labeled and relevant to each particular problem domain. The decisions made may be far from optimal when the information about the military situation is corrupted or the available datasets are incomplete. Therefore, sea-surface target detection based on artificial intelligence with small or incomplete samples needs further research.

      (2) With the increasing complexity of machine learning models, we no longer have an intuitive understanding of how machines make decisions based on the commonly used machine learning methods. When machine learning models are used to recommend a movie or a restaurant, an explanation of the results may not be needed, but in the area of radar target detection, we not only want to know the results but also need to understand how these decisions are made. The interpretability technique of the current models is mainly to quantitatively evaluate each input feature and find the feature that most influences the result, or further analyze and inspect feature correlation. For tabular data, each column is a feature; for images, text, or other non-tabular data, they need to first be preprocessed to build a feature that is easy to understand. Interpretability is an important aspect of machine learning, and it is also an obstacle in the field of sea-surface target detection. Therefore, how to design interpretable artificial intelligence methods is an important subject to be studied.

      (3) In artificial intelligence-based methods, learning is a top priority. Human learning is not only about knowledge but also about the methods of acquiring data and information and the experience of knowledge. Machine learning models learn about data, information, and knowledge, but not methods. For radar detection, an accurate detector design must be based on a large amount of data in a variety of situations, and the learning process is time consuming. In a rapidly changing battlefield environment, especially for the high dynamic change of the sea environment, the speed of the detection criterion of the artificial intelligence–based detector heavily depends on the algorithm computing power, especially the hardware platform. Therefore, one of the most important difficulties in artificial intelligence application is the high efficiency of the algorithm design and the improvement of the hardware platform computing power.

    • This paper analyzes the active and difficult problems of sea-surface target detection, introduces the datasets commonly used to verify the feature-based detection methods, and then explains the principle of the detection method. Moreover, several feature-based detection methods of slow and SFTs on the sea surface are introduced, and their detection performances are analyzed. The detection of slow and SFTs is of great significance to the development of marine military. How to improve the performance of the intelligent detection of small targets is the focus of the current research. With the development of new subjects, the integration of radar target detection and various new subjects has become the development trend. Combining the intelligentization of new subjects with feature-based detection methods can result in more effective target detection and improve the detection performance of slow and SFTs in the sea clutter background.

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