Fig 1.
Fitting a time averaged MSD with various maximum time lags.
A trajectory with α = 0.7, L = 29, σ = 0.5 was simulated (black squares) and fitted for various τM values. While the small τM fitting (red τM = 10 and blue τM = 50) underestimated α, the large τM (green τM = 150) gives an overestimation. Clearly, selecting the optimal τM value is not trivial as both small and large values may lead to erroneous results. Graphically assessing the quality of the fit does not help select the best τM either.
Fig 2.
Performance of the time averaged MSD estimator for various trajectory lengths L and maximal time lags τM.
Color bar gives the precision Φ and black lines give representative bias values, B. Rows give various anomalous exponents with (a–c) strong subdiffusion α = 0.3, (d–f) weak subdiffusion α = 0.7, (g–i) weak superdiffusion α = 1.3 and (j–l) strong superdiffusion α = 1.7. Measurement error changes between columns with (left) small error σ = 0.1, (middle) medium error σ = 0.5 and large error σ = 1. The optimal τM is selected as the area where Φ is maximal and ∣B∣ is minimal for a given trajectory length L.
Table 1.
Recommended τM values.