基于小波分析的分形參數(shù)估計(jì)新方法
A New Parameter Estimation of (1/ f)-Type Fractal Signal Based on Wavelet Analysis
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摘要: 該文研究目的是估計(jì)1/f類分形隨機(jī)過程參數(shù)矢量 (, 2,2w)。作者基于小波分析，對1/f過程觀測值的小波系數(shù)方差進(jìn)行一系列代數(shù)運(yùn)算，并給出詳盡的證明過程，最終求取了噪聲中分?jǐn)?shù)布朗運(yùn)動(dòng)(fBm)參數(shù)矢量的估計(jì)量。實(shí)驗(yàn)結(jié)果表明，與傳統(tǒng)的極大似然估計(jì)(ML)相比，算法簡潔，效果良好，估計(jì)參數(shù)范圍廣泛，同時(shí)對噪聲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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