基于对数行列式散度与对称对数行列式散度的高频地波雷达目标检测器

叶磊; 王勇; 杨强; 邓维波

doi:10.11999/JEIT181078

基于对数行列式散度与对称对数行列式散度的高频地波雷达目标检测器

doi: 10.11999/JEIT181078

叶磊¹,
王勇^{1, 2},
杨强^{1, 2, ,},
邓维波^{1, 2}

1.
哈尔滨工业大学电子与信息工程学院哈尔滨 150001
2.
对海监测与信息处理工业和信息化部重点实验室哈尔滨 150001

基金项目: 国家自然科学基金(61701140, 61571159, 61171182)，中央高校基本科研业务费专项资金(HIT.MKSTISP.2016 13, HIT.MKSTISP.2016 26)

详细信息

作者简介:
叶磊：男，1989年生，博士，研究方向为雷达目标检测、信息几何理论

王勇：男，1979年生，教授，博士生导师，研究方向为雷达信号处理、ISAR图像处理

杨强：男，1970年生，教授，博士生导师，研究方向为雷达目标检测、新体制信号处理和信息提取

邓维波：男，1961年生，教授，博士生导师，研究方向为阵列信号处理、雷达系统

通讯作者:
杨强　yq@hit.edu.cn

中图分类号: TN958.93
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出版历程
- 收稿日期: 2018-11-23
- 修回日期: 2019-04-23
- 网络出版日期: 2019-04-28
- 刊出日期: 2019-08-01

High Frequency Surface Wave Radar Detector Based on Log-determinant Divergence and Symmetrized Log-determinant Divergence

Lei YE¹,
Yong WANG^{1, 2},
Qiang YANG^{1, 2
, ,},
Weibo DENG^{1, 2}

1.
School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China
2.
Key Laboratory of Marine Environmental Monitoring and Information Processing, Ministry of Industry and Information Technology, Harbin 150001, China

Funds: The National Natural Science Foundation of China (61701140, 61571159, 61171182), The Fundamental Research Funds for the Central Universities (HIT.MKSTISP.2016 13, HIT.MKSTISP.2016 26)

摘要

摘要: 高频地波雷达(HFSWR)利用电磁波绕射原理进行目标探测，具有超视距的特性。然而，探测距离的增加会使得雷达目标回波能量减弱，进而使得雷达探测能力下降。为了改善高频地波雷达的探测性能，该文提出了一种基于信息几何理论的局域联合矩阵恒虚警率(CFAR)检测器，利用信号在角度、多普勒速度和距离的多维信息进行检测；并使用对数行列式散度(LDD)和对称对数行列式散度(SLDD)代替黎曼距离(RD)作为距离度量。最后，实验结果验证了该文提出的检测器能够有效地改善雷达对目标的检测性能。
- 高频地波雷达 /
- 目标检测 /
- 信息几何 /
- 对数行列式散度
Abstract: High Frequency Surface Wave Radar (HFSWR) utilizes electromagnetic wave diffracting along the earth to detect targets over the horizon. However, the increase of target distance decreases the received echo energy, and this degrades the detection capability. A joint domain matrix Constant False Alarm Rate (CFAR) detector is proposed to improve the detection performance. It employs the multi-dimensional information of signal in azimuth, Doppler velocity and range domain to detect target, and Log-Determinant Divergence (LDD) and Symmetrized Log-Determinant Divergence (SLDD) are used to replace the Riemannian Distance (RD) as the measure of distance. Finally, the experiment results show that the detector presented by the paper can improve the detection performance effectively.
- High Frequency Surface Wave Radar (HFSWR) /
- Target detection /
- Information geometry /
- Log-Determinant Divergence (LDD)

HTML全文

图 1 雷达接收阵列

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图 2 局域联合处理区域

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图 3 矩阵恒虚警率检测的几何解释

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图 4 局域联合矩阵恒虚警率检测器结构

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图 5 迭代次数选取

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图 6 归一化检测统计量

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图 7 检测概率随SINR变化曲线

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表 1 不同距离度量方法及其几何均值

度量方法	距离计算	几何均值
RD	${{{D}}_R}^2({{{R}}_1},{{{R}}_2}) = {\rm{tr}}[{\lg ^2}({{{R}}_1}^{ - 1/2}{{{R}}_2}{{{R}}_1}^{ - 1/2})]$	${\bar {{R}}_{t + 1}} = \bar {{R}}_t^{1/2}\exp \left[{\rm{ds}} \cdot \frac{1}{N}\mathop \displaystyle\sum \limits_{i = 1}^N \lg (\bar {{R}}_t^{ - 1/2}{{{R}}_i}\bar {{R}}_t^{ - 1/2})\right]\bar {{R}}_t^{1/2}$
LDD	${{{D}}_{\rm{LD}}}({{{R}}_1},{{{R}}_2}) = {\rm{tr}}({{R}}_2^{ - 1}({{{R}}_1} - {{{R}}_2})) - \ln \det({{R}}_2^{ - 1}{{{R}}_1})$	$\bar {{R}} = {\left( {\frac{1}{N}\mathop \sum \limits_{k = 1}^N {{R}}_k^{ - 1}} \right)^{ - 1}}$
SLDD	$\begin{aligned} {{{D}}_{{\rm{SLD}}}}({{{R}}_1},{{{R}}_2}) =& \frac{1}{2}({\rm{tr}}({{R}}_2^{ - 1}({{{R}}_1} - {{{R}}_2})) - \ln \det({{R}}_2^{ - 1}{{{R}}_1}) \\ & + {\rm{tr}}({{R}}_1^{ - 1}({{{R}}_2} - {{{R}}_1})) - \ln \det({{R}}_1^{ - 1}{{{R}}_2})) \\ \end{aligned}$	$\bar {{R}} = {\left( {\frac{1}{N}\mathop \sum \limits_{k = 1}^N {{R}}_k^{ - 1}} \right)^{ - 1}}$

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表 2 基本矩阵运算的复杂度

矩阵运算	表达式	浮点数计算次数	矩阵运算	表达式	浮点数计算次数
矩阵乘法	${{{R}}_1}{{{R}}_2}$	$8{n^3} - 2{n^2}$	矩阵求逆	${{R}}_1^{ - 1}$	$8{n^3} - 2{n^2}$
矩阵加法	${{{R}}_1}{{ + }}{{{R}}_2}$	$2{n^2}$	矩阵开方	${{R}}_1^{1/2}$	$24{n^3} + 2{n^2} - 8n$
矩阵的迹	${\rm{tr}}({{{R}}_1})$	$8{n^2} - 6n - 2$	矩阵指数	$\exp ({{{R}}_1})$	${n^4}/2 + 24{n^3} + 1.5{n^2} - n$
矩阵行列式	$\det ({{{R}}_1})$	$8{n^2} - 2n - 6$	矩阵对数	$\lg ({{{R}}_1})$	${n^4}/2 + 25{n^3} + {n^2} - 1.5n$

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表 3 不同距离度量方法的复杂度

度量方法	距离计算复杂度	几何均值计算复杂度
RD	${n^4}/2 + 73{n^3} + 5{n^2} - 15.5n - 1$	$(N + 1){n^4}/2 + (41N + 88){n^3} - (N + 6.5){n^2} - (1.5N + 9)n$
LDD	$16{n^3} + 14{n^2} - 8n - 6$	$8(N + 1){n^3} - 2{n^2}$
SLDD	$32{n^3} + 28{n^2} - 15n - 11$	$8(N + 1){n^3} - 2{n^2}$

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