  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.
