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Abstract
We consider the inference of the drift velocity and the diffusion coefficient of a particle undergoing a directed random walk in the presence of static localization error. A weighted leastsquares fit to meansquare displacement (MSD) data is used to infer the parameters of the assumed driftdiffusion model. For experiments which cannot be repeated we show that the quality of the inferred parameters depends on the number of MSD points used in the fitting. An optimal number of fitting points popt is shown to exist which depends on the time interval between frames Δt and the unknown parameters. We therefore also present a simple iterative algorithm which converges rapidly toward popt. For repeatable experiments the quality depends crucially on the measurement time interval over which measurements are made, reflecting the different timescales associated with drift and diffusion. An optimal measurement time interval Topt exists, which depends on the number of measurement points and the unknown parameters, and so again we present an iterative algorithm which converges quickly toward Topt and is shown to be robust to initial parameter guesses.
Original language  English 

Article number  022134 
Number of pages  14 
Journal  Physical Review E 
Volume  100 
Issue number  2 
DOIs  
Publication status  Published  23 Aug 2019 
Keywords
 drift velocity
 diffusion coefficient
 static localization error
 driftdiffusion model
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Projects
 1 Finished

Understanding Cancer Metastasis by Combining Models, Numbers and Molecules
1/10/15 → 30/06/20
Project: Research