  Optomechanical devices are being harnessed as sensors of ultraweak forces for
applications ranging from inertial sensing to the search for the elusive dark
matter. For the latter, there is a focus on detection of either higher energy
single recoils or ultralight, narrowband sources; a directional signal is
expected. However, the possibility of searching for a stochastic stream of weak
impulses, or more generally a directional broadband signal, need not be
excluded; with this and other applications in mind, we investigate the
experimental signature of Gaussian white noise impulses with a well defined
direction $\Psi$ on a levitated nanosphere, trapped and 3D cooled in an optical
tweezer. We find that cross-correlation power spectra offer a calibration-free
distinctive signature of the presence of a directional but stochastic
microscopic force and its orientation quadrant, unlike normal power spectral
densities (PSDs). We obtain excellent agreement between theoretical and
experimental results. With calibration we are able to measure the angle $\Psi$,
akin to a force compass in a plane. We discuss prospects for extending this
technique into quantum regime and compare the expected behaviour of quantum
baths and classical baths.
