  For Brownian motion of a single particle subject to a tilted periodic
potential on a ring, we propose a formula for experimentally determining the
cumulant generating function of time-averaged current without measurements of
current fluctuations. We first derive this formula phenomenologically on the
basis of two key relations: a fluctuation relation associated with Onsager's
principle of the least energy dissipation in a sufficiently local region and an
additivity relation by which spatially inhomogeneous fluctuations can be
properly considered. We then derive the formula without any phenomenological
assumptions. We also demonstrate its practical advantage by numerical
experiments.
