  Light has shown up an incredibe capability in precision measurement based on
opto-mechanic interaction in high vacuum by isolating environment noises.
However, there are still obstructions, such as displacement and mass estimation
error, highly hampering the improvement of absolute accuracy at the nanoscale.
Here, we present a nonlinearity based metrology to precisely measure the
position and mass of a nanoparticle with optical levitation under $10^{-5}$
mbar, 6-order of magnitude lower than the electrostatic-force and
stochastic-force-based counterparts. By precisely controlling the amplitude of
the levitated nanoparticle at the nonlinear regime, we realized a feasible
sub-picometer-level position measurement with an uncertainty of $1.0\%$ without
the prior information of mass, which can be further applied to weigh the
femtogram-level mass with an uncertainty of $2.2\%$. It will also pave the way
to construct a well-calibrated opto-mechanic platform in high vacuum for high
sensitivity and accuracy measurement in force and acceleration at the nanoscale
and the study in quantum superposition at the mesoscopic scale.
