<p dir="ltr">Optical observations provide a cost-effective means of tracking satellites and space debris with high angular accuracy, and many amateur, academic, and professional observers use them extensively. Optical images can be accumulated quickly, and automation is important to rapidly produce accurate measurements of objects found in them. Effects like atmospheric refraction, atmospheric scattering of incoming light, aberration due to the motion of the observer, image distortions from the optics of the telescope, scintillation due to atmospheric turbulence, limited resolution, and various sources of noise create challenges for observers. An image processing pipeline has been developed from scratch for the purpose of automating the collection of data with the Purdue Optical Ground Station telescope. Effects that are deterministic are mathematically modeled and corrected, and all steps of the pipeline are described. A novel method is presented for detecting and optimally estimating the centroids of faint, streaked objects in astronomical images with several-second-long exposure times. The ability to accurately determine the pointing direction of a telescope from the stars in the image is demonstrated with a series of images of a GPS satellite. The resulting orbit is compared with the broadcast ephemeris, with an average positional error of 22.1 meters over the observation period.</p>