Estimation of fractional Brownian motion with multiresolution Kalman filter banks

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.