基于小波leaders的海杂波时变奇异谱分布分析

熊刚; 张淑宁; 赵慧昌

doi:10.7498/aps.63.150503

摘要

海杂波的奇异谱分析不仅能从理论上揭示海洋表面的动力学机理，同时也是对海探测雷达的关键技术之一. 本文提出基于小波leaders的海杂波时变奇异谱分析方法，将时间信息引入海杂波的奇异谱分析之中，从而实现动态的解析描述海杂波随时间变化的奇异谱特性. 在理论上，通过信号自身加窗，将时间信息引入传统的奇异谱（或称多重分形谱），实现了对海杂波时变奇异谱分布分析；在算法上，充分利用了小波leaders技术对于多种奇异性的提取能力（包括chirp奇异性和cusp奇异性），通过对时变奇异性指数和时变尺度函数的Legendre变换，实现对海杂波时变奇异谱分布的计算；在应用部分，采用经典的多重分形模型随机小波序列（RWC）以及三级海态条件下连续波多普勒体制雷达海杂波进行仿真分析，实验结果表明：1）基于小波leaders的奇异谱分布能跟踪海杂波的时变尺度特性，有效展示其时变奇异性谱分布；2）算法具有较好的负矩特性和统计收敛性. 该方法能为复杂非线性系统及随机多重分形信号分析提供参考.

关键词:

Abstract

Singularity spectrum analysis of sea clutter is the key technology of detecting radar for sea target, which can discover the dynamic mechanism of the sea surface theoretically. In this paper, based on wavelet leaders the time-varying singularity spectrum distribution of sea clutters is proposed, which introduces time information to the traditional singularity spectrum, and displays the time-varying characteristic of singularity spectrum analytically. In theory, by way of self-windowed fractal signal, we introduce the time information to the traditional singularity spectrum, and realize multifractal spectrum distribution of sea clutters. In algorithm, based on the wavelet leaders, we adapt the process of embodying chirp-type and cusp-type singularities, and obtain the time-varying singularity spectrum distribution of sea clutters by the Legendre transform of the time-varying scaling function. In practice, we analyze the classical multifractal modelrandom wavelet series and the real sea clutter data of continuous wave Doppler radar in level III sea state. Experiments indicate that (1) the time-varying singularity spectrum distribution based on wavelet leaders can trace the time-varying scale characteristic and display the time-varying singularity spectrum distribution of sea clutters; (2) the algorithm possesses good statistical convergence, low computational cost, and passive moment property. The time-varying singularity spectrum distribution based on wavelet leaders may serve as a reference sample for nonlinear dynamics and multifractal signal processing.

Keywords:

wavelet leaders /
multifractal formalism /
time-singularity multifractal spectrum distribution /
sea clutter

作者及机构信息

1.
上海理工大学光电信息与计算机工程学院/光电信息研究院, 上海 200093;

2.
南京理工大学电子工程与光电技术学院, 南京 210094

基金项目: 国家自然科学基金（批准号：61171168，61301216，60702016）资助的课题.

Authors and contacts

1.
Institute of Photoelectric Information/School of Optical Electrical and Computer Engineering, University of Shanghai for S&T, Shanghai 200093, China;

2.
School of Electronic and Optical Engineering, Nanjing University of S&T, Nanjing 210094, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61171168, 61301216, 60702016).

参考文献

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施引文献

[1]	Aanstassopoulos V, Lampropolous G A 1995 IRC, Washington, DC, p662
[2]
[3]
[4]	Mandelbrot B B 1986 Nonlinear Dynamics, Nijhof, Dordrecht p279
[5]
[6]	Grassberger P, Procaccia I 1983 Phys. Rev. Lett. 50 346
[7]	Frisch U, Sulem P L 1984 Phys. Fluids 27 1921
[8]
[9]	Halsey T C, Jensen M H, Procaccia K P I 1986 Phys. Rev. A 33 1141
[10]
[11]	Kantelhardt J W, Zschiegner S A, Koscielny-Bunde E, Havlin S, Bunde A, Stanley H E 2002 Physica A 316 87
[12]
[13]
[14]	Gu G F, Zhou W X 2006 Physical Rev. E 74 061104
[15]
[16]	Chhabra A, Jensen R 1989 Phys. Rev. Lett. 62 121327
[17]	Gu G F, Zhou W X 2010 Phys. Rev. E. 82 011136
[18]
[19]
[20]	Zhou W X 2008 Physical Rev. E 77 066211
[21]
[22]	Muzy J F, Bacry E, Arneodo A 1991 Phys. Rev. Lett. 67 3515
[23]
[24]	Bacry E, Arneodo A, Muzy J F 1993 J. Stat. Phys. 70 635
[25]	Muzy J F, Bacry E, Arneodo A 1993 Phys. Rev. E 47 875
[26]
[27]
[28]	Arneodo A, Argoul A, Muzy J F, Bacry E 1995 Fractals 1 629
[29]
[30]	Lashermes B, Jaffard S, Abry P 2005 ICASS, Philadelphia, USA 2005 pp161-164
[31]	Xiong G, Yang X N, Zhao H C 2008 ICIC, Shanghai CCIS 15 pp541-548
[32]
[33]
[34]	Arneodo A, Bacry E, Muzy J F. J 1998 Math. Phys. 39 4142
[35]
[36]	Aubry J M, Jaffard S 2002 Commun. Math. Phys. 227 483
[37]
[38]	Xiong G, Yang X N, Zhao H C 2005 IEEE MAPE, Beijing, 8 pp1236-1239
[39]
[40]	Liu N B, Guan J, Huang Y, Wang G Q, He Y 2012 Acta Phys. Sin. 61 190503 (in Chinese) [刘宁波, 关键, 黄勇, 王国庆, 何友 2012 61 190503]
[41]	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]
[42]
[43]	W He J B, Liu Z, Hu S L 2011 Acta Phys. Sin. 60 110208 (in Chinese) [贺静波, 刘忠, 胡生亮 2011 60 110208]
[44]
[45]	Yang J, Bian B M, Yan Z G, Wang C Y, Li Z H 2011 Acta Phys. Sin. 60 100506 (in Chinese) [杨娟, 卞保民, 闫振纲, 王春勇, 李振华 2011 60 100506]
[46]
[47]	Xiong G, Zhang S N, Liu Q 2012 Physica A 391 4727
[48]
[49]	p231 (in Chinese) [Falconer K 2007分形几何: 数学基础及其应用(第2版) (北京: 人民邮电出版社)第231页]
[50]	Falconer K 2007 Fractal Geometry: Mathematical Foundations and Applications (2nd Ed.) (Beijing: Posts & Telecom Press)

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