We present initial results of a study that has more than doubled the time baseline for astrometric measurements of faint stars orbiting the supermassive black hole (SMBH) at the Galactic center. The advent of adaptive optics has enabled stars as faint as K = 19 mag to be tracked at 50 mas resolution for the last decade. While similar resolution images exist from the prior decade, they were obtained from speckle imaging data analyzed with the technique of shift-and-add, which limited detections to stars brighter than K = 16 mag. By improving the speckle data analysis technique with speckle holography and using prior orbital knowledge, we are now able to track stars as faint as ∼18 mag at 50 mas resolution through the early Keck speckle data sets (1995-2005). This methodology has already led to the detection of two short-period stars never previously seen in speckle images, such that our data now spans their full orbits. We can now better constrain the orbital parameters of all stars in the intriguing “S-star cluster,” which will ultimately give us insight into the origin of these stars and be used to probe the curvature of space-time in the unexplored regime near a SMBH.