  We show that the position of a dark matter-wave soliton can be determined
with a precision that scales with the atomic density as $n^{-3/4}$. This
surpasses the standard shot-noise detection limit for independent particles,
without use of squeezing and entanglement, and it suggests that interactions
among particles may present new advantages in high-precision metrology. We also
take into account quantum density fluctuations due to phonon and Goldstone
modes and we show that they, somewhat unexpectedly, actually improve the
resolution. This happens because the fluctuations depend on the soliton
position and make a larger amount of information available.
