  The release of Gaia catalog is revolutionary to the astronomy of solar system
objects. After some effects such as atmospheric refraction and CCD geometric
distortion have been taken into account, the astrometric precision for
ground-based telescopes can reach the level of tens of milli-arcseconds. If an
object approaches a reference star in a small relative angular distance (less
than 100 arcseconds), which is called close approach event in this work, the
relative positional precision between the object and reference star will be
further improved since the systematic effects of atmospheric turbulence and
local telescope optics can be reduced. To obtain the precise position of a
main-belt asteroid in an close approach event, a second-order angular velocity
model with time is supposed in the sky plane. By fitting the relationship
between the relative angular distance and observed time, we can derive the time
of maximum approximation and calculate the corresponding position of the
asteroid. In practice, 5 nights' CCD observations including 15 close approach
events of main-belt asteroid (702) Alauda are taken for testing by the 1m
telescope at Yunnan Observatory, China. Compared with conventional solutions,
our results show that the positional precision significantly improves, which
reaches better than 4 milli-arcseconds, and 1 milli-arcsecond in the best case
when referenced for JPL ephemeris in both right ascension and declination.
