### 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 least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion 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.

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 |

### Fingerprint

### Keywords

- drift velocity
- diffusion coefficient
- static localization error
- drift-diffusion model

### Cite this

}

*Physical Review E*, vol. 100, no. 2, 022134. https://doi.org/10.1103/PhysRevE.100.022134

**Optimal estimation of drift and diffusion coefficients in the presence of static localization error.** / Devlin, J.; Husmeier, D.; MacKenzie, J. A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimal estimation of drift and diffusion coefficients in the presence of static localization error

AU - Devlin, J.

AU - Husmeier, D.

AU - MacKenzie, J. A.

PY - 2019/8/23

Y1 - 2019/8/23

N2 - 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 least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion 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.

AB - 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 least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion 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.

KW - drift velocity

KW - diffusion coefficient

KW - static localization error

KW - drift-diffusion model

U2 - 10.1103/PhysRevE.100.022134

DO - 10.1103/PhysRevE.100.022134

M3 - Article

VL - 100

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 2

M1 - 022134

ER -