By default, sigma is the asymptote of the variogram and tau is an array of autocorrelation timescales. The position timescale is roughly the time lag it takes of the variogram to reach 63% of its asymptote. The velocity autocorrelation timescale visually corresponds to width of the concave bowl shape at the beginning of the variogram. If CTMM=ctmm(range=FALSE), sigma is the asymptotic slope of the variogram and only the velocity timescale is finite.
By default, parameter values are estimated from the shape of the variogram. If this fails, the CTMM option can provide alternative initial guesstimates.
variogram.fit is called by ctmm.guess, and there is usually no reason to call variogram.fit directly.