海杂波AR谱多重分形特性及微弱目标检测方法

第38卷第2期电子与信息学报 Vol.38No.2 2016年2月 Journal of Electronics & Information Technology Feb. 2016

范一飞罗丰*李明胡冲陈帅霖

(西安电子科技大学雷达信号处理国家重点实验室西安710071)

摘要：该文研究了海杂波功率谱的多重分形特性。为了克服频谱傅里叶分析的缺点，用现代谱估计的方法来计算海杂波的功率谱。AR模型是一个线性预测模型，它通过序列的自相关函数矩阵来估计功率谱，并且具有更精确的频谱分辨率。该文主要分析基于AR谱估计的海杂波功率谱的多重分形特性，以及在微弱目标检测中的应用。首先，以分数布朗运动(FBM)模型为例，证明其功率谱具有多重分形特性。其次，根据X波段雷达的实测海杂波数据，通过多重去趋势分析法(MF-DFA)验证了海杂波AR谱的多重分形特性。最后，分析了海杂波AR谱的广义Hurst 指数以及影响参数，并提出一种基于局部AR谱广义Hurst指数的目标检测方法。实验结果表明，该种检测方法具有海杂波背景下微弱目标检测的能力。与现有的分形检测方法和传统的CFAR检测方法对比，该算法在低信杂比情况下具有较好的检测性能。

关键词：目标检测；海杂波；多重分形；AR谱估计

中图分类号：TN959.72 文献标识码：A 文章编号：1009-5896(2016)02-0455-09 DOI: 10.11999/JEIT150581

The Multifractal Properties of AR Spectrum and Weak

Target Detection in Sea Clutter Background

FAN Yifei LUO Feng LI Ming HU Chong CHEN Shuailin

(National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China)

Abstract: This paper focuses on the multifractal properties of sea clutter in power spectrum domain. To overcome the deficiencies of Fourier transform analysis, the power spectrum of the sea clutter is obtained by AutoRegressive (AR) spectrum estimation. The AR model is a linear predictive model, which estimates the power spectrum of sea clutter from its autocorrelation matrix and has a higher frequency resolution than Fourier analysis. This paper concentrates on analyzing the multifractal property of the power spectrum based on AR spectral estimation and its application to weak target detection. Firstly, Fractional Brownian Motion (FBM) is taken as an example to prove the multifractal property of the power spectrum. Then, real measured X-band data is used to verify the multifractal property of the AR spectrum of sea clutter by MultiFractal Detrended Fluctuation Analysis (MF-DF A) method. Finally, the generalized Hurst exponent of AR spectrum and its influence factors are analyzed, and a novel detection method based on local AR generalized Hurst exponent is proposed. The results show that the proposed method is effective for weak target detection in sea clutter background. Compared to the existing fractal method and the traditional CFAR method, the proposed method has a better detection performance in low SCR condition.

Key words: Target detection; Sea clutter; Multifractal; AR spectral estimation

1 引言

20世纪70年代文献[1]首次提出了用分形理论来描述自然界中不光滑和不规则的复杂结构，它解释了随机信号中普遍存在的尺度不变性和自相似性。分形理论在雷达信号处理领域有着重要的应用，文献[2]首次计算了海杂波的单一分形维数，并应用

收稿日期：2015-05-15；改回日期：2015-10-13；网络出版：2015-11-19 *通信作者：罗丰luofeng@https://www.360docs.net/doc/b518370746.html,

基金项目：国家部委基金(4010101030101)

Foundation Item: The National Ministries Fund (4010101030101) 分形维数来检测海杂波背景中的目标，随后分形理论在雷达信号处理领域开始有了较快的发展[3]。然而单一分形忽略了无标度区间以外的海杂波信息，在高海情下，单一的分形维数难以有效地区分海杂波与目标。由于单一分形的局限性，研究人员提出了多重分形理论，并且在微弱目标检测领域有了较好的应用和发展。文献[4]通过多重分形分析，提出了多重分形谱维数的概念，并应用于海面中弱小目标检测。文献[5]分析了X波段雷达的实测海杂波数据，结果表明海杂波在时域具有长时相关特性，并且在一定范围内具有尺度不变特性，提出了一种基于小