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Improved estimators for fractional Brownian motion via the expectation-maximization algorithm.

Russell Fischer·Metin Akay
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Abstract

Fractional Brownian motion (FBM) provides a useful model for many physical and biological phenomena demonstrating long-term dependencies and 1/f-type spectral behavior. In this model, only one parameter is necessary to describe the complexity of the data, the Hurst exponent (H). The development of accurate estimators for H is a topic of interest in areas such as radiographic image processing and heart rate variability (HRV) analysis. The development of a 1D estimator utilizing the Expectation-Maximization (EM) algorithm is explained; the estimator is designed for a signal model consisting of FBM and additive white noise. The performance of this estimator is tested on simulated noisy FBM data sets, and found to provide more accurate estimates of H than a maximum likelihood estimator for FBM and the detrended fluctuation analysis (DFA) method.

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AlgorithmsBiophysical PhenomenaBiophysicsHeart RateLikelihood FunctionsNormal DistributionJournal ArticleResearch Support, U.S. Gov't, P.H.S.

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Russell Fischer, Metin Akay. 2002. Improved estimators for fractional Brownian motion via the expectation-maximization algorithm.. https://doi.org/10.1016/s1350-4533(01)00115-1

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