  We present improved relative astrometry for stars within the central half
parsec of our Galactic Center based on data obtained with the 10 m W. M. Keck
Observatory from 1995 to 2017. The new methods used to improve the astrometric
precision and accuracy include correcting for local astrometric distortions,
applying a magnitude dependent additive error, and more carefully removing
instances of stellar confusion. Additionally, we adopt jackknife methods to
calculate velocity and acceleration uncertainties. The resulting median proper
motion uncertainty is 0.05 mas/yr for our complete sample of 1184 stars in the
central 10'' (0.4 pc). We have detected 24 accelerating sources, 2.6 times more
than the number of previously published accelerating sources, which extend out
to 4'' (0.16 pc) from the black hole. Based on S0-2's orbit, our new
astrometric analysis has reduced the systematic error of the supermassive black
hole (SMBH) by a factor of 2. The linear drift in our astrometric reference
frame is also reduced in the North-South direction by a factor of 4. We also
find the first potential astrometric binary candidate S0-27 in the Galactic
center. These astrometric improvements provide a foundation for future studies
of the origin and dynamics of the young stars around the SMBH, the structure
and dynamics of the old nuclear star cluster, the SMBH's properties derived
from orbits, and tests of General Relativity (GR) in a strong gravitational
field.
