Improved Astrometry in a Sparse Star Field and New Positions of Triton and Nereid (2018–2020)

High-precision astrometry of Neptunian satellites is fundamental for determining their orbital parameters and can provide clues to the origin and evolution of the Neptunian system. During 2018–2020, Neptune passed through a region at a high galactic latitude (about −58 ∘ ), where background Gaia reference stars are relatively sparse. Compounding this sparsity, pronounced geometric distortion is evident even within small CCD fields of view (e.g., 1 0 ′ × 1 0 ′ ), necessitating modeling with a high-order polynomial. However, applying standard high-order plate models independently to each CCD frame in sparse star fields can lead to overfitting, thereby limiting the astrometric precision of Neptunian satellites. To address this, we propose the PlateOne method, which combines all images taken in a single night to determine a common high-order polynomial. We also investigate the minimum number of stars required for a high-order plate model to avoid overfitting, a crucial yet currently unresolved question. The proposed method has been successfully applied to the astrometry of Triton and Nereid, significantly improving their positional precision. We obtained 451 new CCD positions for Triton, with precisions of 13 mas in right ascension and 18 mas in declination. For Nereid, we obtained eight positions, with a precision of approximately 40–50 mas.