Fractional Brownian motion: a maximum-likelihood estimator for blurred data

Rachid Harba, Universite d'Orleans
William J. Ohley, Universite d'Orleans
Stephan Hoefer, Universite d'Orleans


Fractional Brownian motion is a useful tool to describe many objects and phenomena. But in the case of real data, the estimation of the H parameter is corrupted by noise and sometimes blur. The maximum likelihood estimation of H can take into account these perturbations. This communication deals with the problem of the blur which is modeled by a low pass filter. It is then possible to rewrite the autocorrelation function of the data and the estimation of H is performed. The Cramer-Rao lower bound (CRLB) is stated. Finally, synthetic data permit the proof that the estimation of H is possible even if the signal is blurred. The variance of the estimates is compared with the CRLB and shows the quality of the results.