  The Next Generation Transit Survey (NGTS), operating in Paranal since 2016,
is a wide-field survey to detect Neptunes and super-Earths transiting bright
stars, which are suitable for precise radial velocity follow-up and
characterisation. Thereby, its sub-mmag photometric precision and ability to
identify false positives are crucial. Particularly, variable background objects
blended in the photometric aperture frequently mimic Neptune-sized transits and
are costly in follow-up time. These objects can best be identified with the
centroiding technique: if the photometric flux is lost off-centre during an
eclipse, the flux centroid shifts towards the centre of the target star.
Although this method has successfully been employed by the Kepler mission, it
has previously not been implemented from the ground. We present a
fully-automated centroid vetting algorithm developed for NGTS, enabled by our
high-precision auto-guiding. Our method allows detecting centroid shifts with
an average precision of 0.75 milli-pixel, and down to 0.25 milli-pixel for
specific targets, for a pixel size of 4.97 arcsec. The algorithm is now part of
the NGTS candidate vetting pipeline and automatically employed for all detected
signals. Further, we develop a joint Bayesian fitting model for all photometric
and centroid data, allowing to disentangle which object (target or background)
is causing the signal, and what its astrophysical parameters are. We
demonstrate our method on two NGTS objects of interest. These achievements make
NGTS the first ground-based wide-field transit survey ever to successfully
apply the centroiding technique for automated candidate vetting, enabling the
production of a robust candidate list before follow-up.
