Optimal parameters for anomalous diffusion exponent estimation from noisy data

TL;DR

This paper evaluates methods for estimating the anomalous diffusion exponent from noisy single-particle trajectories, highlighting the limitations of conventional linear fitting and proposing more robust alternatives.

Contribution

The study compares three estimation approaches for anomalous diffusion exponents under noise, identifying the least optimal method and suggesting improvements.

Findings

Conventional linear fitting performs poorly with noisy data.

Alternative estimation methods show improved accuracy.

Gaussian noise significantly biases traditional estimation techniques.

Abstract

The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However, various measurement noises that are unavoidably present in experimental data, can strongly deteriorate the quality of this estimation procedure and bias the estimated exponent. To investigate the impact of noises and to improve the estimation quality, we compare three approaches for estimating the anomalous diffusion exponent and check their efficiency on fractional Brownian motion corrupted by Gaussian noise. We discuss how the parameters of this anomalous diffusion model and the parameters of the estimation techniques influence the estimated exponent. We show that the conventional linear fitting is the least optimal method for the analysis of noisy data.