Accurately characterizing the anomalous diffusion of a tracer particle has become a central issue in biophysics. However, measurement errors raise difficulty in the characterization of single trajectories, which is usually performed through the time-averaged mean square displacement (TAMSD). In this paper, we study a fractionally integrated moving average (FIMA) process as an appropriate model for anomalous diffusion data with measurement errors. We compare FIMA and traditional TAMSD estimators for the anomalous diffusion exponent. The ability of the FIMA framework to characterize dynamics in a wide range of anomalous exponents and noise levels through the simulation of a toy model (fractional Brownian motion disturbed by Gaussian white noise) is discussed. Comparison to the TAMSD technique, shows that FIMA estimation is superior in many scenarios. This is expected to enable new measurement regimes for single particle tracking (SPT) experiments even in the presence of high measurement errors.
|State||Published - 11 Jun 2015|
Bibliographical noteFunding Information:
K. Burnecki, G. Sikora and A. Weron would like to acknowledge a support of NCN Maestro Grant No. 2012/06/A/ST1/00258. E. Kepten and Y. Garini where supported, in part, by the Israel Centers of Research Excellence (ICORE) No. 1902/12, and Israel Science Foundation No. 51/12. E. Kepten also thanks A.W. and K.B. for the warm hospitality.