In this contribution we give a brief account of the problem of the Global Astrometric Sphere Reconstruction in Astrometry, with particular reference to the Gaia and Gaia-like astrometric missions, namely those adopting a scanning strategy with observations in TDI mode. We sketch the design of the Gaia mission, the mathematical modelling that comes naturally from its observing strategy, and how the problem of the global sphere reconstruction translates into that of the solution of large, sparse, and overdetermined system of linearized equations. After a short description of the two approaches to this problem implemented in the Gaia data reduction pipelines, we list the main known problems of the current approaches, with specific reference to the calibration and the correlation issues. Finally, we suggest how an arc-based solution could help to alleviate some of these problems, how it would be possible to devise a mathematical model for such an observable despite the TDI observing mode, and the main difficulty that a parallel implementation of this model would have to solve.
@article{arxiv.2503.23843,
title = {The Problem of the Global Astrometric Sphere Reconstruction in Astrometry -- Issues and Approaches},
author = {Alberto Vecchiato and Alexey Butkevich and Mario Gai and Valentina Cesare and Beatrice Bucciarelli and Mario Gilberto Lattanzi},
journal= {arXiv preprint arXiv:2503.23843},
year = {2025}
}