  Hidden within the Gaia satellite's multiple data releases lies a valuable
cache of dark companions. To facilitate the efficient and reliable detection of
these companions via combined analyses involving Gaia, Hipparcos, and Tycho-2
catalogs, we introduce an astrometric modeling framework. This method
incorporates analytical least square minimization and nonlinear parameter
optimization techniques to a set of common calibration sources across the
different space-based astrometric catalogues. This enables us to discern the
error inflation, astrometric jitter, differential parallax zero-point, and
frame rotation of various catalogues relative to Gaia DR3. Our findings yield
the most precise Gaia DR2 calibration parameters to date, revealing notable
dependencies on magnitude and color. Intriguingly, we identify sub-mas frame
rotation between Gaia DR1 and DR3, along with an estimated astrometric jitter
of 2.16 mas for the revised Hipparcos catalog. In a thorough comparative
analysis with previous studies, we offer recommendations on calibrating and
utilizing different catalogs for companion detection. Furthermore, we provide a
user-friendly pipeline (https://github.com/ruiyicheng/Download_HIP_Gaia_GOST)
for catalog download and bias correction, enhancing accessibility and usability
within the scientific community.
