  Inspired by the notion that environmental noise is in principle observable,
whilst fundamental noise due to spontaneous localisation would not be, we study
the estimation of the diffusion parameter induced by wave function collapse
models under continuous monitoring of the environment. We take into account
finite measurement efficiencies and, in order to quantify the advantage granted
by monitoring, we analyse the quantum Fisher information associated with such a
diffusion parameter, identify optimal measurements in limiting cases, and
assess the performance of such measurements in more realistic conditions.
