Automated Astrometric Calibration of Astronomical Images with Gaia DR3 and Residual Error Decomposition

Abstract Precise astrometric validation requires residuals between catalog-predicted positions and measured stellar locations, not between a prediction and its nearest integer pixel. This work presents a deterministic Flexible Image Transport System (FITS) calibration and residual-analysis pipeline that combines median-background suppression, blind plate solving with Astrometry.net, Gaia Data Release 3 (DR3) reference-star projection, Astrometry.net source-list association, bounded two-dimensional Gaussian centroid refinement, robust outlier rejection, and an affine decomposition of systematic and random residual components. Four satellite-tracking FITS frames (GAOFEN 11 − 3, NIGERIASAT-2, THEOS, and YAOGAN-50) were processed independently in raw and background-suppressed branches. Astrometry.net solved all eight branches. The raw images, however, produced only 3, 6, 1, and 4 validated Gaussian matches, leaving three of four raw branches below the six-match statistical threshold. Background suppression increased the corresponding match counts to 14, 43, 30, and 53; all four suppressed branches therefore supported full residual analysis. Suppressed-branch Gaia matching completeness ranged from 42.4% to 75.0% (median 43.2%). Measured total root-mean-square (RMS) residuals were 1.589–3.932 arcsec (median 3.153 arcsec), while post-affine random RMS ranged from 0.447 to 3.196 arcsec (median 2.731 arcsec). The former nearest-pixel metric yielded a much narrower 1.555–1.704 arcsec range and underestimated measured RMS in three of four fields, demonstrating why it cannot serve as an astrometric-accuracy estimator. The results show that background suppression primarily improves usable source-measurement yield in this data set, while the systematic–random decomposition provides a more defensible characterization of calibration quality. Because the local Gaia mirror lacks proper-motion and formal-error columns and the demonstration contains only four frames, the reported values are treated as a pilot validation rather than a population-wide accuracy claim.