  We present a study of the HD 165054 astrometric calibration field that has
been periodically observed with the Gemini Planet Imager. HD 165054 is a bright
star within Baade's Window, a region of the galactic plane with relatively low
extinction from interstellar dust. HD 165054 was selected as a calibrator
target due to the high number density of stars within this region ($\sim 3$
stars per square arcsecond with $H<22$), necessary because of the small
field-of-view of the Gemini Planet Imager. Using nine epochs spanning over five
years, we have fit a standard five-parameter astrometric model to the
astrometry of seven background stars within close proximity to HD 165054
(angular separation $< 2$ arcsec). We achieved a proper motion precision of
$\sim 0.3$ mas/yr, and constrained the parallax of each star to be $\lesssim 1$
mas. Our measured proper motions and parallax limits are consistent with the
background stars being a part of the galactic bulge. Using these measurements
we find no evidence of any systematic trend of either the plate scale or the
north angle offset of GPI between 2014 and 2019. We compared our model
describing the motions of the seven background stars to observations of the
same field in 2014 and 2018 obtained with Keck/NIRC2, an instrument with an
excellent astrometric calibration. We find that predicted position of the
background sources is consistent with that measured by NIRC2, within the
uncertainties of the calibration of the two instruments. In the future, we will
use this field as a standard astrometric calibrator for the upgrade of GPI and
potentially for other high-contrast imagers.
