基于小波分析的分形参数估计新方法
A New Parameter Estimation of (1/ f)-Type Fractal Signal Based on Wavelet Analysis
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摘要: 该文研究目的是估计1/f类分形随机过程参数矢量 (, 2,2w)。作者基于小波分析，对1/f过程观测值的小波系数方差进行一系列代数运算，并给出详尽的证明过程，最终求取了噪声中分数布朗运动(fBm)参数矢量的估计量。实验结果表明，与传统的极大似然估计(ML)相比，算法简洁，效果良好，估计参数范围广泛，同时对噪声也不再局限于高斯分布。Abstract: The research purpose of this paper is to estimate the parameter vector (, 2,2w)of (1/f)-type fractal stochastic processes. Using wavelets, the paper has performed a series of algebraic operation to the variance of the observation wavelet coefficients of process, and presented the elaborate theoretical analysis. As a result, the parameter vector of fractional Brownian motions (fBm) in noise is introduced. The experimental results demonstrate that the new estimator is far simpler and more effective than the traditional ML estimator and the range of estimate parameter is wider. Moreover the distribution of noise is not restricted within Gauss processes.
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