The multifractal spectrum of a sea clutter using a random walk model
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The multifractal spectrum of a sea clutter using a random walk model HE Jingbo1*, XU Jianghu1 1 Electronics Engineering College, Naval University of Engineering, Wuhan 430033, China
Received 7 August 2016; accepted 7 November 2016 ©The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2017
Abstract
The radar echo signal of a sea clutter is nonlinear, nonstationary and time varying. A multifractal measure analysis can describe the local singularity of a physics system. The random walk model of a sea clutter scattering is analysed to disclose the intrinsic physical characteristics and laws of the sea clutter. Stochastic differential _ equations are given for the physical quality of the sea clutter. A diffusion process model is established using Ito formula. The singularity of the random walk model is tested by a multifractal spectroscopy, and the accuracy of this model is proven by the multifractal spectroscopy of a real-life IPIX radar data set. Thus, the random walk model is effective for describing the dynamics mechanism of the sea clutter. Key words: random walk, sea clutter, multifractal Citation: He Jingbo, Xu Jianghu. 2017. The multifractal spectrum of a sea clutter using a random walk model. Acta Oceanologica Sinica, 36(9): 23–26, doi: 10.1007/s13131-017-1107-y
1 Introduction The sea clutter refers to the surface of a radar-scattering echo and is the most complicated form of a radar clutter. After years of testing, researchers have found that the probability distribution of the sea clutter is a Gaussian model. They have proposed a logarithmic normal distribution, Weibull distribution, K-distribution and other distribution models (Rosenberg and Bocquet, 2015; Velotto et al., 2014; Güntürkün, 2015; Jakeman and Pusey, 1976; Li et al., 2014). These models are close to the sea clutter probability distribution form to some extent, but they do not clearly describe the generating mechanism of the sea clutter. Only the statistical models for the first-order and second-order characteristics of the sea clutter are described. The time-varying characteristic of the sea clutter is not depicted (Granström et al., 2015; Suresh et al., 2015; Xing et al., 2014; Xiong et al., 2014). Consequently, precise modelling, analysis and processing of the nonlinear, nonstationary and time-varying characteristics of the sea clutter are difficult (Wu et al., 2014; Zhang et al., 2014; Xu et al., 2014). The multifractal measure analysis of different physical systems can completely describe the local singularity (Guan et al., 2010; Liu et al., 2012); the statistical properties of such singular measure in the characterisation can reveal complex heterogeneous structure system by determining the singularity spectrum. Jakeman and Tough (1987) proposed electromagnetic scattering of the random walk model to reveal the dynamics mechanism of the sea clutter. Considering the different parameters of the model, the evolution of the sea clutter can be all types of a statistical distribution model (e.g., Rayleigh distribution, Weibu
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