噪声中1/f类分形参数估计的新方法

A New Method for Estimation of Parameters of 1/f-Type Fractal Signal in Noise

噪声中1/f类分形信号参数β、σ2和σ2w通常用极大似然(ML)法予以估计,然而ML迭代算法极为繁复,且受到谱指数γ范围(γ∈(0,1))的影响,故该方法并不适合于分数布朗运动(FBM)这种分形信号的优良模型,而文中基于小波分析求取了噪声中FBM参数β、σ2和σ2w的估计值.理论分析和实验结果表明,与ML估计相比,该估计算法既简洁且效果良好,而且噪声不局限于高斯分布.

The maximum likelihood (ML) estimation is usually used to estimate the parameters of β、σ~2 and σ~2_w of 1/f-type fractal signal embedded in noise. However, the iteration algorithm of the ML estimation is very complicated. The ML estimation is also influenced by the range of the spectral exponent γ(γ∈(0,1)).Therefore, these estimators are not suitable to the parameters of fractional Brownian motions (FBM) as a good model of 1/f-type fractal signal. In this paper, based on wavelet analysis,the estimator of the parameters β,σ~2 and σ~2_w of FBM in noise is introduced. Both theoretical analysis and experimental results demonstrate that the new estimators are much more simple and effective than the ML estimator. The distribution of noise is not restricted within Gauss processes.