The astrometric core solution for the Gaia mission. Overview of models, algorithms and software implementation

Details The astrometric core solution for the Gaia mission. Overview of models, algorithms and software implementation The astrometric core solution for the Gaia mission. Overview of models, algorithms and software implementation

2011-12-18

arxiv.org/abs/1112.4139v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

48 pages, 19 figures. Accepted for publication in Astronomy & Astrophysics

Scientific paper

10.1051/0004-6361/201117905

The Gaia satellite will observe about one billion stars and other point-like 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. We provide a comprehensive overview of the mathematical and physical models applicable to this solution, as well as its numerical and algorithmic framework. The astrometric core solution is a simultaneous least-squares estimation of about half a billion parameters, including the astrometric parameters for some 100 million well-behaved so-called 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 B-splines for the attitude representation, and a modified Cholesky algorithm for positive semidefinite problems) and discuss some complications expected in the real mission data.

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