  SVOM is a Sino-French space mission targeting high-energy transient
astrophysical objects such as gamma-ray bursts. The soft X-ray part of the
spectrum is covered by the Micro-channel X-ray Telescope (MXT) which is a
narrow field telescope designed to precisely localize X-ray sources. This paper
presents the method implemented on-board to characterize and localize X-ray
sources with the MXT. A specific localization method was developed to
accommodate the optical system of the MXT, which is based on "Lobster-Eye"
grazing incidence micro-pore optics. For the first time, the algorithm takes
advantage of cross-correlation techniques to achieve a localization accuracy
down to 2 arcmin with less than 200 photons, which guarantees a rapid follow-up
for most of the gamma-ray bursts that SVOM will observe. In this paper, we also
study the limitations of the algorithm and characterize its performance.
