Estimation of fractional Brownian motion with multiresolution Kalman filter banks

Author

Hirchoren, G.A. ; D´Attellis, C.E.

Author_Institution

Dept. de Matematica, Buenos Aires Univ., Argentina

Volume

47

Issue

5

fYear

1999

fDate

5/1/1999 12:00:00 AM

Firstpage

1431

Lastpage

1434

Abstract

A filter bank design based on orthonormal wavelets and equipped with a multiscale Kalman filter was proposed for deconvolution of fractal signals. We use the same scheme for estimating fractional Brownian motion in noise considering (1) the effect of correlation in the sequence of wavelet coefficients; (2) the approximation term in the wavelet expansion; (3) aliasing effects; (4) the optimal number of scales in the filter bank. Considerations on the minimum number of filters in the bank are made, and comparisons between Wiener and Kalman filters are given. Explicit expressions of the mean-square error are given, and comparisons between theoretical and simulation results are shown

Keywords

Brownian motion; Kalman filters; channel bank filters; correlation methods; deconvolution; digital filters; fractals; mean square error methods; motion estimation; network synthesis; signal resolution; wavelet transforms; Wiener filters; aliasing effects; approximation term; correlation; deconvolution; explicit expressions; filter bank design; fractal signals; fractional Brownian motion estimation; mean-square error; multiresolution Kalman filter banks; multiscale Kalman filter; noise; orthonormal wavelets; scales; signal processing; simulation results; wavelet coefficients sequence; wavelet expansion; 1f noise; Brownian motion; Filter bank; Fractals; Motion estimation; Signal processing; Signal resolution; Wavelet analysis; Wavelet coefficients; Wiener filter;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.757238

Filename

757238