雷达信号检测的分形方法研究
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摘要
分形作为一种描述自然界中不规则几何的数学工具，在短短时间内已成功应用
于诸如图象处理、自然表面建模、时间序列分析等领域。由于在雷达系统的许多环
节中存在具有分形特性的过程和现象，因此，可以通过采用分形理论研究和分析雷
达信号处理系统来获得新思路和新方法。本文从理论与实验两个方面探讨了随机分
形理论在雷达信号检测领域的应用，提出了基于随机分形模型的天然粗糙面杂波建
模仿真和目标检测方法。本文主要研究工作及研究成果包括：
1．从分形基本量、分数积分模型和小波模型等三个方面论述和分析了随机分形
信号，并提出了相应的参数估计方法。实验和理论分析表明这些估计方法都
有效，其中分数积分模型的分数差分估计法速度快适于实时估计，基于小波
模型的最大似然估计法鲁棒性强适于弱信噪比下的参数估计。
2．从实测数据和形成机理两个方面进行研究了天然粗糙面杂波的分形特性。一
方面从多角度进行了实测数据的分形特性分析，得出了天然粗糙面杂波具有
随机分形特征的结论；另一方面通过分析时变分形曲面和实际天然粗糙面的
电磁散射基尔霍夫解讨论了分形特征的存在机理，并进一步提出了天然粗糙
面杂波的随机分形模型。实验分析和理论推导都表明天然粗糙面杂波具有随
机分形特征，这为杂波特性分析提供了新的途径。
3．分析和讨论了天然粗糙面杂波的分形模型参数的统计特性和分形特性，采用
任意λ进制正交小波变换不仅证明了杂波随机分形模型的有效性，而且给出
了模型参数的数学描述。结合杂波仿真的传统思路和方法，提出了基于随机
分形模型的λ进制小波仿真法和随机Weierstrass函数仿真法，从而完成了杂
波统计特性和分形特性的融合统一。
4．根据天然粗糙面杂波具有随机分形特征而目标回波不具有的特点，从多重分
形谱、迭代函数系统和小波白化滤波三个方面出发，结合模型匹配和相关检
测理论，提出了基于分形模型的雷达目标检测的方法。实验结果表明所提出
的方法具有良好的检测性能，为强杂波下目标检测提供了新的理论和方法。
As a mathematic tool for irregular geometry in the natural world, fractal theory has
been founding wide application in such fields as image processing, natural surface
modeling, time series analysis etc. successfully. Since the presence of fractal processes
and phenomenon in radar system, the new idea and method can be obtained by applying
the fractal theory to study and analyze radar signal processing system. The application of
the random fractal theory in the field of radar signal detection both theoretically and
experimentally, and some methods for modeling & simulation and target detection based
on the random fractal model for the clutter from natural rough surface are proposed. The
main research work and result is presented as follow:
1 .The random fractal signal is described and analyzed in the respect of fractal basic
quantities, fractional integral model, and wavelet model, and the corresponding
methods for parameter estimation are proposed. The experimental and theoretical
analysis demonstrates that all the methods are available. The fractional differenced
method based on the fractional integral model runs fast and the Maximum
Likelihood Estimation based on the wavelet model has strong rubbish, where the
former is fit for real-time estimation and the latter for estimation under low signal-
noise-ratio.
2.The fractal property of the clutter from natural rough surface is studied on both the
real-life data and the generation mechanism. On the one hand the analysis on
fractal properties of the real-life clutter data is proceeded, and the conclusion that
the clutter from natural rough surface has random fractal characteristic is obtained.
On the other hand the mechanism of the fractal property is discussed by means of
study on Kirchoff solution to the electromagnetic scattering field from both time-
variant fractal surface and natural rough surface, and the random fractal model for
the clutter from natural rough surface is proposed further. The conclusion that both
experimental analysis and theoretically deduction demonstrate that the clutter from
natural rough surface do have random fractal feature provides a new way to study
the property of the clutter.
3 .The statistic and fractal characteristic of the parameters in the random fractal
model for the clutter from natural rough surface is advanced. By applying the
either radix orthogonal wavelet transform, not only the validity of the random
fractal model for the clutter is proved, but also the mathematic expressions for the
parameters in the model is provided. Combining the traditional idea and method
for clutter simulation, the simulation method based on random fractal model is
proposed by using X radix wavelet and random Weierstrass function respectively,
which is the entia of the statistic property and the fractal property.
4.Combining the theory on model matching and correlation detection, the methods
for radar target detection based on the fractal model are proposed in three aspects
of multi-fractal spectrum, iterated function system and wavelet whitening filter
according to the fact that the clutter from natural rough surface has random fractal
feature. Experiment results demonstrate the detection ability of all proposed
methods is better. All that has been done provide new idea and method for target
detection with strong clutter.
于诸如图象处理、自然表面建模、时间序列分析等领域。由于在雷达系统的许多环
节中存在具有分形特性的过程和现象，因此，可以通过采用分形理论研究和分析雷
达信号处理系统来获得新思路和新方法。本文从理论与实验两个方面探讨了随机分
形理论在雷达信号检测领域的应用，提出了基于随机分形模型的天然粗糙面杂波建
模仿真和目标检测方法。本文主要研究工作及研究成果包括：
1．从分形基本量、分数积分模型和小波模型等三个方面论述和分析了随机分形
信号，并提出了相应的参数估计方法。实验和理论分析表明这些估计方法都
有效，其中分数积分模型的分数差分估计法速度快适于实时估计，基于小波
模型的最大似然估计法鲁棒性强适于弱信噪比下的参数估计。
2．从实测数据和形成机理两个方面进行研究了天然粗糙面杂波的分形特性。一
方面从多角度进行了实测数据的分形特性分析，得出了天然粗糙面杂波具有
随机分形特征的结论；另一方面通过分析时变分形曲面和实际天然粗糙面的
电磁散射基尔霍夫解讨论了分形特征的存在机理，并进一步提出了天然粗糙
面杂波的随机分形模型。实验分析和理论推导都表明天然粗糙面杂波具有随
机分形特征，这为杂波特性分析提供了新的途径。
3．分析和讨论了天然粗糙面杂波的分形模型参数的统计特性和分形特性，采用
任意λ进制正交小波变换不仅证明了杂波随机分形模型的有效性，而且给出
了模型参数的数学描述。结合杂波仿真的传统思路和方法，提出了基于随机
分形模型的λ进制小波仿真法和随机Weierstrass函数仿真法，从而完成了杂
波统计特性和分形特性的融合统一。
4．根据天然粗糙面杂波具有随机分形特征而目标回波不具有的特点，从多重分
形谱、迭代函数系统和小波白化滤波三个方面出发，结合模型匹配和相关检
测理论，提出了基于分形模型的雷达目标检测的方法。实验结果表明所提出
的方法具有良好的检测性能，为强杂波下目标检测提供了新的理论和方法。
As a mathematic tool for irregular geometry in the natural world, fractal theory has
been founding wide application in such fields as image processing, natural surface
modeling, time series analysis etc. successfully. Since the presence of fractal processes
and phenomenon in radar system, the new idea and method can be obtained by applying
the fractal theory to study and analyze radar signal processing system. The application of
the random fractal theory in the field of radar signal detection both theoretically and
experimentally, and some methods for modeling & simulation and target detection based
on the random fractal model for the clutter from natural rough surface are proposed. The
main research work and result is presented as follow:
1 .The random fractal signal is described and analyzed in the respect of fractal basic
quantities, fractional integral model, and wavelet model, and the corresponding
methods for parameter estimation are proposed. The experimental and theoretical
analysis demonstrates that all the methods are available. The fractional differenced
method based on the fractional integral model runs fast and the Maximum
Likelihood Estimation based on the wavelet model has strong rubbish, where the
former is fit for real-time estimation and the latter for estimation under low signal-
noise-ratio.
2.The fractal property of the clutter from natural rough surface is studied on both the
real-life data and the generation mechanism. On the one hand the analysis on
fractal properties of the real-life clutter data is proceeded, and the conclusion that
the clutter from natural rough surface has random fractal characteristic is obtained.
On the other hand the mechanism of the fractal property is discussed by means of
study on Kirchoff solution to the electromagnetic scattering field from both time-
variant fractal surface and natural rough surface, and the random fractal model for
the clutter from natural rough surface is proposed further. The conclusion that both
experimental analysis and theoretically deduction demonstrate that the clutter from
natural rough surface do have random fractal feature provides a new way to study
the property of the clutter.
3 .The statistic and fractal characteristic of the parameters in the random fractal
model for the clutter from natural rough surface is advanced. By applying the
either radix orthogonal wavelet transform, not only the validity of the random
fractal model for the clutter is proved, but also the mathematic expressions for the
parameters in the model is provided. Combining the traditional idea and method
for clutter simulation, the simulation method based on random fractal model is
proposed by using X radix wavelet and random Weierstrass function respectively,
which is the entia of the statistic property and the fractal property.
4.Combining the theory on model matching and correlation detection, the methods
for radar target detection based on the fractal model are proposed in three aspects
of multi-fractal spectrum, iterated function system and wavelet whitening filter
according to the fact that the clutter from natural rough surface has random fractal
feature. Experiment results demonstrate the detection ability of all proposed
methods is better. All that has been done provide new idea and method for target
detection with strong clutter.
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