Fractal property of sea clutter FRFT spectrum for small target detection

Xing Hong-Yan; Zhang Qiang; Xu Wei

doi:10.7498/aps.64.110502

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:

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.

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[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
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[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
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[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 物理学报 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
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[27]	Kantelhardt J W, Zschiegner S A, Koscielny B E 2002 Physica A 316 87
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Cited By

[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 物理学报 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 物理学报 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 物理学报 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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Vol. 64, Issue 11 - 2015-06-05

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