基于海杂波随机游走模型的多重分形谱分析

海杂波具有非线性、非平稳和时变特性，多重分形测度分析是对物理系统局部奇异性的一个完整描述。本文根据海杂波电磁散射的经典模型——随机游走模型，利用随机微分理论对海杂波的物理特性进行了系统地建模分析。建立了描述海杂波电磁散射时变特性的随机微分方程，利用Itô公式得到了海杂波散射信号幅度和相位的扩散过程模型，并利用多重分形谱分析了该模型的奇异性。为了验证其准确性，与加拿大McMaster大学IPIX雷达实测海杂波数据的多重分形谱进行对比，实验结果表明两者完全一致，从而表明基于随机游走的随机微分模型是描述海杂波动力学机理的有效算法。

The multifractal spectrum of a sea clutter using a random walk model

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 Itô 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.