  A reconstruction algorithm has been developed to capitalize on advances in
Cherenkov technology for reactor antineutrino detection.
  Large gadolinium-doped water (Gd-H$_2$O) Cherenkov detectors are a developing
technology which use Gd loading to increase the visibility of the neutrons
produced in inverse beta decay (IBD) interactions, which produce
positron-neutron pairs coincident in time and space. In this paper, we describe
the reconstruction which uses the combined light from both events in an IBD
pair to accurately reconstruct the interaction vertex.
  The algorithm has been applied to the reconstruction of reactor antineutrinos
in Gd-H$_2$O and in Gd-doped water-based liquid scintillator (Gd-WbLS), an
advanced detector medium which is also currently in development.
  Compared to a single-event reconstruction, the combined reconstruction
improves vertex resolution for reactor IBD positrons by up to a factor of 4.5
at the lowest energies. IBD-neutron vertex resolution was found to improve by
more than 30% in most instances.
  Powerful background rejection with the coincidence reconstruction can be
achieved by requiring a minimum quality of fit. This was found to reject up to
94% of accidental coincidences of uncorrelated background events, while
retaining at least 97.5% of the IBD signal pairs.
