A Bayesian framework for astrometry in a sparse star field and its application to Triton observations

¹ Department of Computer Science, Jinan University, Guangzhou 510632, China
² School of Mathematics and Computer, Guangdong Ocean University, Zhanjiang 524088, China
³ Department of Physics, College of Physics and Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
⁴ Sino-French Joint Laboratory for Astrometry, Dynamics and Space Science, Jinan University, Guangzhou 510632, China

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 January 2026
Accepted: 13 February 2026

Abstract

Context. The Gaia DR3 catalog significantly improves ground-based astrometric precision for natural satellites, largely because sufficient reference stars with high-precision positions are typically available within an object’s field. These stars enable the determination of a high-order plate model (e.g., a fourth-degree polynomial) that can fully absorb the geometric distortion (GD) in the CCD field. However, accurate calibration is still challenging when a natural satellite moves into a small sparse star field (about 12×12 arcmin²) containing only a dozen or so reference stars.

Aims. This study aims to improve natural satellite astrometry in sparse star fields without requiring the calibration observations that are needed for currently well-established GD solutions. Additionally, our previously published observations of Neptune’s largest satellite, Triton, from 2014 to 2016 show a significant positive systematic offset in right ascension, and the underlying reason will be clarified.

Methods. We present a Bayesian framework that models the GD effect using the CCD frames of the science object itself. This approach is self-calibrating and does not require additional calibration observations of dense star fields. The model parameters and their distributions are optimized using the Markov chain Monte Carlo algorithm, and the positional O–C (observed minus computed) values are derived by sampling from these posterior distributions, rather than employing point estimates.

Results. The effectiveness of the proposed approach was evaluated using 985 CCD frames of Triton. The results demonstrate a significant improvement in astrometric precision over the commonly used least-squares (LS) method, and show comparable or even better performance relative to the well-established GD correction method, particularly in the absence of suitable calibration observations. Additionally, we find that the systematic offsets in our previous work on Triton are due to differences in Earth’s precession-nutation theory adopted by the Jet Propulsion Laboratory ephemeris for Triton and adopted by the NOVAS library for reference stars.