Parameter estimation of a fractional Brownian motion in a white noise using wavelets

Author

Hwang, Wen-Liang

Author_Institution

California Univ., Irvine, CA, USA

fYear

1994

fDate

13-16 Apr 1994

Firstpage

646

Abstract

To discriminate the fractal parameter of a fractional Brownian motion (fBm) embedded in a white noise is equivalent to discriminating the composite singularity formed by superimposing a peak singularity upon a Dirac singularity. We use the autocorrelation of the wavelet transform coefficients to characterize the composite singularity, by formalizing this problem as a nonlinear optimization problem. We modify the internal penalty function method to efficiently estimate the parameters of the fBm in the white noise

Keywords

Brownian motion; correlation theory; functions; optimisation; parameter estimation; stochastic processes; wavelet transforms; white noise; Dirac singularity; Gaussian process; autocorrelation; composite singularity; fractal parameter; fractional Brownian motion; internal penalty function method; nonlinear optimization problem; parameter estimation; peak singularity; signal processing; wavelet transform coefficients; white noise; 1f noise; Autocorrelation; Brownian motion; Computer vision; Fractals; Maximum likelihood estimation; Nonlinear equations; Parameter estimation; Wavelet transforms; White noise;

fLanguage

English

Publisher

ieee

Conference_Titel

Speech, Image Processing and Neural Networks, 1994. Proceedings, ISSIPNN '94., 1994 International Symposium on

Print_ISBN

0-7803-1865-X

Type

conf

DOI

10.1109/SIPNN.1994.344828

Filename

344828