The astrometric core solution for the Gaia mission. Overview of models, algorithms, and software implementation
Abstract
Context. The Gaia satellite will observe about one billion stars and other pointlike sources. The astrometric core solution will determine the astrometric parameters (position, parallax, and proper motion) for a subset of these sources, using a global solution approach which must also include a large number of parameters for the satellite attitude and optical instrument. The accurate and efficient implementation of this solution is an extremely demanding task, but crucial for the outcome of the mission.
Aims: We aim to provide a comprehensive overview of the mathematical and physical models applicable to this solution, as well as its numerical and algorithmic framework.
Methods: The astrometric core solution is a simultaneous leastsquares estimation of about half a billion parameters, including the astrometric parameters for some 100 million wellbehaved socalled primary sources. The global nature of the solution requires an iterative approach, which can be broken down into a small number of distinct processing blocks (source, attitude, calibration and global updating) and auxiliary processes (including the frame rotator and selection of primary sources). We describe each of these processes in some detail, formulate the underlying models, from which the observation equations are derived, and outline the adopted numerical solution methods with due consideration of robustness and the structure of the resulting system of equations. Appendices provide brief introductions to some important mathematical tools (quaternions and Bsplines for the attitude representation, and a modified Cholesky algorithm for positive semidefinite problems) and discuss some complications expected in the real mission data.
Results: A complete software system called AGIS (Astrometric Global Iterative Solution) is being built according to the methods described in the paper. Based on simulated data for 2 million primary sources we present some initial results, demonstrating the basic mathematical and numerical validity of the approach and, by a reasonable extrapolation, its practical feasibility in terms of data management and computations for the real mission.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 February 2012
 DOI:
 10.1051/00046361/201117905
 arXiv:
 arXiv:1112.4139
 Bibcode:
 2012A&A...538A..78L
 Keywords:

 astrometry;
 methods: data analysis;
 methods: numerical;
 space vehicles: instruments;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 48 pages, 19 figures. Accepted for publication in Astronomy &