  The Gaia Early Data Release 3 (Gaia EDR3) contains results derived from 78
billion individual field-of-view transits of 2.5 billion sources collected by
the European Space Agency's Gaia mission during its first 34 months of
continuous scanning of the sky. We describe the input data, which have the form
of onboard detections, and the modeling and processing that is involved in
cross-matching these detections to sources. For the cross-match, we formed
clusters of detections that were all linked to the same physical light source
on the sky. As a first step, onboard detections that were deemed spurious were
discarded. The remaining detections were then preliminarily associated with one
or more sources in the existing source list in an observation-to-source match.
All candidate matches that directly or indirectly were associated with the same
source form a match candidate group. The detections from the same group were
then subject to a cluster analysis. Each cluster was assigned a source
identifier that normally was the same as the identifiers from Gaia DR2. Because
the number of individual detections is very high, we also describe the
efficient organising of the processing. We present results and statistics for
the final cross-match with particular emphasis on the more complicated cases
that are relevant for the users of the Gaia catalogue. We describe the
improvements over the earlier Gaia data releases, in particular for stars of
high proper motion, for the brightest sources, for variable sources, and for
close source pairs.
