  We report a factor of $\sim$3 improvement in Keck Laser Guide Star Adaptive
Optics (LGSAO) astrometric measurements of stars near the Galaxy's supermassive
black hole (SMBH). By carrying out a systematic study of M92, we have produced
a more accurate model for the camera's optical distortion. Updating our
measurements with this model, and accounting for differential atmospheric
refraction, we obtain estimates of the SMBH properties that are a factor of
$\sim$2 more precise, and most notably, increase the likelihood that the black
hole is at rest with respect to the nuclear star cluster. These improvements
have also allowed us to extend the radius to which stellar orbital parameter
estimates are possible by a factor of 2.
