  Astrometric detection involves a precise measurement of stellar positions,
and is widely regarded as the leading concept presently ready to find
earth-mass planets in temperate orbits around nearby sun-like stars. The
TOLIMAN space telescope[39] is a low-cost, agile mission concept dedicated to
narrow-angle astrometric monitoring of bright binary stars. In particular the
mission will be optimised to search for habitable-zone planets around Alpha
Centauri AB. If the separation between these two stars can be monitored with
sufficient precision, tiny perturbations due to the gravitational tug from an
unseen planet can be witnessed and, given the configuration of the optical
system, the scale of the shifts in the image plane are about one millionth of a
pixel. Image registration at this level of precision has never been
demonstrated (to our knowledge) in any setting within science. In this paper we
demonstrate that a Deep Convolutional Auto-Encoder is able to retrieve such a
signal from simplified simulations of the TOLIMAN data and we present the full
experimental pipeline to recreate out experiments from the simulations to the
signal analysis. In future works, all the more realistic sources of noise and
systematic effects present in the real-world system will be injected into the
simulations.
