海杂波FRFT域的分形特征分析及小目标检测方法

行鸿彦; 张强; 徐伟

doi:10.7498/aps.64.110502

摘要

针对海杂波背景下海情对小目标检测的严重影响, 本文研究了实测海杂波在分数阶Fourier变换(FRFT)域的分形特征, 分别提出了单、高尺度下的分形检测方法. 由数学定义推得, FRFT 在不同阶数和尺度情况下, 不具有一致的自相似特性, 采用多重分形趋势波动分析法确定分形参数H(q), 分析了海杂波在不同海情、距离和极化条件下的分形特征. 在单尺度基础上结合FRFT的变阶优势, 提出了阶数自适应的小目标检测方法; 高尺度条件下, 比较了不同因素对海杂波FRFT域多重分形参数的影响. 结果表明:海杂波FRFT域可用变换阶数的方法检测到湮没在复杂海情中的小信号, 检测门限多数提高200%以上, 比采用时域信号提高26.3%. H(q) 在负高尺度上具有明显的多重分形特征差异, H(q)-q曲线满足反正切分布, 纯海杂波与含目标数据的拟合幅值比分别大于1.8(HH)和1.4(VV), 为海杂波背景小目标检测提供了判定依据.

关键词:

Abstract

Because the detection of small target in the background of sea clutter is strongly influenced by the sea condition, this paper studies the fractal property of sea clutter in fractional Fourier transform (FRFT) domain and proposes the fractal detection method in single and high dimensions. The FRFT deduced from mathematical definition is not consistent with the self-similar properties in orders and scales. Multifractal detrended fluctuation analysis (MF-DFA) method is used to determine the fractal parameter H(q) and analyze the fractal property of the sea clutter in different situations, distances, and polarizations. In single dimension, the small target detection method is proposed based on an adaptive order. By comparing different factors of the multifractal parameters, the results show that the transform order method in sea clutter FRFT domain can detect small signals under complicated sea conditions. The detection threshold mostly increases above 200%, which is 26.3% higher than the method of time domain signal. H(q) has an obvious multifractal difference on high negative scale, the H(q)-q curve satisfies the arctangent distribution. The fitting amplitude ratios of pure sea clutter and target data are greater than 1.8 (HH) and 1.4 (VV), which provide the basis for the small target detection in sea clutter background.

Keywords:

作者及机构信息

1.
南京信息工程大学, 气象灾害预报预警与评估协同创新中心, 南京 210044;

2.
南京信息工程大学, 江苏省气象探测与信息处理重点实验室, 南京 210044

基金项目: 国家自然科学基金(批准号:61072133)、江苏普通高校研究生实践创新计划项目(批准号:SJZZ_0112)、江苏省产学研联合创新资金计划(批准号:BY2013007-02,BY2011112)、江苏省高校科研成果产业化推进项目(批准号:JHB2011-15)、江苏省“信息与通信工程”优势学科和江苏省“六大人才高峰”计划资助的课题.

Authors and contacts

1.
Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology, Nanjing 210044, China;

2.
Key Laboratory for Aerosol-Cloud-Precipitation, China Meteorological Administration, Nanjing University of Information Science & Technology, Nanjing 210044, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61072133), the Practice Innovation Program of Colleges and Universities Postgraduates of Jiangsu Province, China (Grant No. SJZZ_0112), the Production, Learning and Research Joint Innovation Program of Jiangsu Province, China (Grant Nos. BY2013007-02, SBY201120033), the Industrialization of Research Findings Promotion Program of Institution of Higher Education of Jiangsu Province, China (Grant No. JHB2011-15), the Advantage Discipline Platform “Information and Communication Engineering” of Jiangsu Province, China, and the “Summit of the Six Top Talents” Program of Jiangsu Province, China.

参考文献

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[3]	Ritchie M A, Woodbridge K, Stove A G 2010 IEEE Gros. Remo. Sens. 48 497
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[8]	Mandelbrot B B 1982 The Fractal Geometry on Nature (New York:Freeman)
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[10]	Savaidis S, Jaggard D L, Hizanidis K, Frangos P 1995 Optics letters 20 2358
[11]	Hu J, Gao J, Posner F L, Zheng Y, Tung W 2006 Fractals 14 189
[12]	Gao J B, Hu J, Tung W W, Cao Y H 2006 Physical Review E 74 066204
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[17]	Guan-Lei X, Xiao-Tong W, Xiao-Gang X 2010 Chin. Phys. B 19 014203
[18]	Wen B Y, Wang S. 2006 J. H. U. S. T (N. S. E) 34 70 (in Chinese) [文必洋, 王颂 2006 华中科技大学学报(自然科学版) 34 70]
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[20]	Xing H Y, Gong P, Xu W 2012 Acta Phys. Sin. 61 160504 (in Chinese) [行鸿彦, 龚平, 徐伟 2012 61 160504]
[21]	Xing H Y, Cheng Y Y, Xu W, Gong P 2013 IET International Conference on Information and Communications Technologies Beijing, China, April 27-29, 2013 p333
[22]	Xing H Y, Gong P, Xu W 2013 J. Syst. Simu. 25 1223 (in Chinese) [行鸿彦, 龚平, 徐伟 2013系统仿真学报 25 1223]
[23]	Mandelbrot B B, Van Ness J W 1968 SIAM Rev. 10 425
[24]	Lu X, Li H 1999 Chemical Engineer Journal 75 117
[25]	Chen X L, Liu N B, Song J, Guan J, He Y 2011 J. E. I. T. 33 827 (in Chinese) [陈小龙, 刘宁波, 宋杰, 关键, 何友 2011 电子与信息学报 33 827]
[26]	Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Physical Review E 49 1685
[27]	Kantelhardt J W, Zschiegner S A, Koscielny B E 2002 Physica A 316 87
[28]	Chen X L, Guan J, Liu N B, He Y 2010 J. N. A. A. U. 25 614 (in Chinese) [陈小龙, 关键, 刘宁波, 何友 2010 海军航空工程学院学报 25 614]

施引文献

[1]	Trunk G V, George S F 1970 IEEE Tran. Aero. Elec. Sys. 6 620
[2]	Sayama S, Sekine M 2000 IEICE Tran. Comm. 83 1979
[3]	Ritchie M A, Woodbridge K, Stove A G 2010 IEEE Gros. Remo. Sens. 48 497
[4]	Haykin S, Heung H 1990 Appl. Phys. Lett. 56 593
[5]	Birx D L, Pipenberg S J 1992 IEEE International Joint Confence on Networks Baltimore, MD, Jun 7-11, 1992 p886
[6]	Haykin S, Li X B 1995 Proc. IEEE 83 195
[7]	Cui W Z, Zhu C C, Bao W X, Liu J H 2004 Acta Phys. Sin. 53 3303 (in Chinese) [崔万照, 朱长纯, 保文星, 刘君华 2004 53 3303]
[8]	Mandelbrot B B 1982 The Fractal Geometry on Nature (New York:Freeman)
[9]	Lo T, Leung H 1993 IEE Proc. F 140 243
[10]	Savaidis S, Jaggard D L, Hizanidis K, Frangos P 1995 Optics letters 20 2358
[11]	Hu J, Gao J, Posner F L, Zheng Y, Tung W 2006 Fractals 14 189
[12]	Gao J B, Hu J, Tung W W, Cao Y H 2006 Physical Review E 74 066204
[13]	Guan J, Liu N B, Huang Y, He Y 2012 IET Radar, Sonar & Navigation 6 300
[14]	Shi Z G, Zhou J X, Fu Q 2006 J. Sys. Simu. 18 2289 (in Chinese) [石志广, 周剑雄, 付强 2006 系统仿真学报 18 2289]
[15]	Jiang B, Wang H Q, Li X, Guo G R 2006 Acta Phys. Sin. 55 3985 (in Chinese) [姜斌, 王宏强, 黎湘, 郭桂荣 2006 55 3985]
[16]	Guan J, Liu N B, Zhang J, Song J 2010 J. E. I. T. 32 57 (in Chinese) [关键, 刘宁波, 张建, 宋杰 2010电子与信息学报 32 57]
[17]	Guan-Lei X, Xiao-Tong W, Xiao-Gang X 2010 Chin. Phys. B 19 014203
[18]	Wen B Y, Wang S. 2006 J. H. U. S. T (N. S. E) 34 70 (in Chinese) [文必洋, 王颂 2006 华中科技大学学报(自然科学版) 34 70]
[19]	Jiang B, Wang H Q, Li X, Guo G R 2007 J. Elec. Info. Tech. 29 1811 (in Chinese) [姜斌, 王宏强, 黎湘, 郭桂荣 2007电子与信息学报 29 1811]
[20]	Xing H Y, Gong P, Xu W 2012 Acta Phys. Sin. 61 160504 (in Chinese) [行鸿彦, 龚平, 徐伟 2012 61 160504]
[21]	Xing H Y, Cheng Y Y, Xu W, Gong P 2013 IET International Conference on Information and Communications Technologies Beijing, China, April 27-29, 2013 p333
[22]	Xing H Y, Gong P, Xu W 2013 J. Syst. Simu. 25 1223 (in Chinese) [行鸿彦, 龚平, 徐伟 2013系统仿真学报 25 1223]
[23]	Mandelbrot B B, Van Ness J W 1968 SIAM Rev. 10 425
[24]	Lu X, Li H 1999 Chemical Engineer Journal 75 117
[25]	Chen X L, Liu N B, Song J, Guan J, He Y 2011 J. E. I. T. 33 827 (in Chinese) [陈小龙, 刘宁波, 宋杰, 关键, 何友 2011 电子与信息学报 33 827]
[26]	Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Physical Review E 49 1685
[27]	Kantelhardt J W, Zschiegner S A, Koscielny B E 2002 Physica A 316 87
[28]	Chen X L, Guan J, Liu N B, He Y 2010 J. N. A. A. U. 25 614 (in Chinese) [陈小龙, 关键, 刘宁波, 何友 2010 海军航空工程学院学报 25 614]

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