  We analyse a class of estimators of the generalized diffusion coefficient for
fractional Brownian motion $B_t$ of known Hurst index $H$, based on weighted
functionals of the single time square displacement. We show that for a certain
choice of the weight function these functionals possess an ergodic property and
thus provide the true, ensemble-averaged, generalized diffusion coefficient to
any necessary precision from a single trajectory data, but at expense of a
progressively higher experimental resolution. Convergence is fastest around
$H\simeq0.30$, a value in the subdiffusive regime.
