Calculate the least-squares estimate of (alpha, D)
.
Matrix of trajectory positions, where each row is an observation and each column is a measurement coordinate. The trajectory is assumed to be sampled at a constant frequency.
Interobservation time \(\Delta t\) = 1/fps (positive scalar).
Integer vector of lags to use in the fit, such that the timepoints used in the fit are tau = dt * lags
.
Either "standard" for the usual LS estimator, or "improved" for the version of Zhang et al (2018).
If TRUE
, returns an estimate of the variance matrix of (alpha, logD)
.
Vector of empirical MSD estimates computed by msd_fit()
at the values of lags
.
Length of the particle trajectory.
Number of dimensions of the particle trajectory.
If vcov = FALSE
, vector of length 2 with estimates of (alpha, logD)
. Otherwise, a list with elements coef
and vcov
, where the former is the estimate and the latter is the corresponding variance estimator.
ls_fit()
first computes the MSD using msd_fit(Xt, dt, demean = TRUE)
then passes this on to ls_msd_fit()
. For finer control over the MSD or if it has been precomputed, one may interact with ls_msd_fit()
directly.
Uses the subdiff convention for D
.
Zhang, K., Crizer, K.P.R., Schoenfisch, M.H., Hill, B.D., Didier, G. (2018) "Fluid heterogeneity detection based on the asymptotic distribution of the time-averaged mean squared displacement in single particle tracking experiments". Journal of Physics A: Mathematical and Theoretical, 51, pp 445601(44).