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主要研究了分段分数布朗运动(PFBM)模型在雷达海杂波分形建模中的应用.由于自然界和人造系统中研究对象不具有数学上完美的分形特性, 从而研究对象的分形特性无法在整个尺度区间上成立, 传统上, 海杂波的单一分形模型仅利用无标度区间内海杂波的自相似信息进行参数估计, 并没有考虑海杂波在无标度区间以外的尺度下所包含的信息.分段分数布朗运动从频域角度对海杂波频谱进行分段描述, 对应到时域即从粗略尺度和精细尺度两方面描述海杂波时间序列.结合海杂波产生的物理背景, 该模型可以为海杂波时间序列在粗略尺度和精细尺度下表现出的不同粗糙度提供机理性解释.在此基础上, 还研究了具有不同多普勒频率的运动目标对海杂波的影响, 结果表明运动目标对粗略尺度和精细尺度下海杂波的影响程度是不同的.In this paper we mainly study the application of piecewise fractional Brownian motion (PFBM) to modeling radar sea clutter. Because the research objects in nature and man-made systems are usually not perfectly fractal in mathematics, the fractal properties of these researched objects cannot hold in the whole scale interval. Traditionally, the mono-fractal model of sea clutter only makes use of the self-similarity of sea clutter within the scale-invariant interval for parameter estimation but ignores the information contained in the scales outside the scale-invariant interval. The PFBM describes the sea clutter piecewisely in frequency domain, which corresponds to describing the sea clutter in time domain respectively on the large scale and on the fine scale. Combining the physical background, the PFBM model can explain the mechanism of the different roughnesses of a sea clutter time sequence respectively on the large scale and on the fine scale. Subsequently, in the paper, we study the effects of moving targets with different Doppler frequencies on sea clutter. The results show that moving targets can cause different effects on sea clutter respectively on the large scale and on the fine scale.
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Keywords:
- sea clutter /
- piecewise fractional Brownian motion /
- fractal /
- moving target
[1] Savaidis S, Frangos Y 1995 Opt. Lett. 20 2357
[2] Lo T, Leung H, Haykin S 1993 IEE Proc. F 140 243
[3] Chang Y C, Chang S 2002 IEEE Trans. Signal Proc. 50 554
[4] Salmasi M, Modarres-Hashemi M 2009 Chaos, Solitons & Fractals 40 2133
[5] He T, Zhou Z O 2007 Acta Phys. Sin. 56 693 (in Chinese) [贺涛, 周正欧 2007 物理学报 56 693]
[6] 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, 郭桂蓉 2006 物理学报 55 3985]
[7] Xu X K 2010 IEEE Trans. Antenna Propag. 581425
[8] Guan J, Liu N B, Huang Y 2011 Fractal Theory and Its Application in Radar Target Detection (Beijing: Electronic Industry Press) p117 (in Chinese) [关键, 刘宁波, 黄勇 2011 雷达目标检测的分形理论及应用(北京:电子工业出版社) 第117页].
[9] Perrin E, Harba R, Iribarren I, Jennane R 2005 IEEE Trans. Signal Proc. 53 1211
[10] Falconer K 2007 Fractal Geometry: Mathematical Foundations and Applications (2nd Ed.) (Beijing: Posts & Telecom Press) 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]
[11] Reed I S, Lee P C, Truong T K 1995 IEEE Trans. Inf. Theory 41 1439
[12] Deriche M, Tewfik A H 1993 IEEE Trans. Signal Proc. 41 1239
[13] Kaplan L M, Jay Kuo C C 1994 IEEE Trans. Signal Proc. 42 3526
[14] Kaplan L M, Kuo C C 1995 IEEE Trans. Pattern Anal. Mach. Intell. 17 1043
[15] Drosopoulos A 1994 Defence Research Establishment Ottawa, 1994 Tech. Note No. 94-14
[16] Hu J, Tung W W, Gao J B 2006 IEEE Trans. Antenna Propag. 54 136
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[1] Savaidis S, Frangos Y 1995 Opt. Lett. 20 2357
[2] Lo T, Leung H, Haykin S 1993 IEE Proc. F 140 243
[3] Chang Y C, Chang S 2002 IEEE Trans. Signal Proc. 50 554
[4] Salmasi M, Modarres-Hashemi M 2009 Chaos, Solitons & Fractals 40 2133
[5] He T, Zhou Z O 2007 Acta Phys. Sin. 56 693 (in Chinese) [贺涛, 周正欧 2007 物理学报 56 693]
[6] 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, 郭桂蓉 2006 物理学报 55 3985]
[7] Xu X K 2010 IEEE Trans. Antenna Propag. 581425
[8] Guan J, Liu N B, Huang Y 2011 Fractal Theory and Its Application in Radar Target Detection (Beijing: Electronic Industry Press) p117 (in Chinese) [关键, 刘宁波, 黄勇 2011 雷达目标检测的分形理论及应用(北京:电子工业出版社) 第117页].
[9] Perrin E, Harba R, Iribarren I, Jennane R 2005 IEEE Trans. Signal Proc. 53 1211
[10] Falconer K 2007 Fractal Geometry: Mathematical Foundations and Applications (2nd Ed.) (Beijing: Posts & Telecom Press) 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]
[11] Reed I S, Lee P C, Truong T K 1995 IEEE Trans. Inf. Theory 41 1439
[12] Deriche M, Tewfik A H 1993 IEEE Trans. Signal Proc. 41 1239
[13] Kaplan L M, Jay Kuo C C 1994 IEEE Trans. Signal Proc. 42 3526
[14] Kaplan L M, Kuo C C 1995 IEEE Trans. Pattern Anal. Mach. Intell. 17 1043
[15] Drosopoulos A 1994 Defence Research Establishment Ottawa, 1994 Tech. Note No. 94-14
[16] Hu J, Tung W W, Gao J B 2006 IEEE Trans. Antenna Propag. 54 136
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