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

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**The astrometric core solution for the Gaia mission Overview of models, algorithms, and software implementation.** / Lindegren, Lennart; Lammers, U.; Hobbs, David; O'Mullane, W.; Bastian, U.; Hernandez, J.

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*Astronomy & Astrophysics*, vol. 538, A78. https://doi.org/10.1051/0004-6361/201117905

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*Astronomy & Astrophysics*,

*538*, [A78]. https://doi.org/10.1051/0004-6361/201117905

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*Astronomy & Astrophysics*. 2012. 538. https://doi.org/10.1051/0004-6361/201117905

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TY - JOUR

T1 - The astrometric core solution for the Gaia mission Overview of models, algorithms, and software implementation

AU - Lindegren, Lennart

AU - Lammers, U.

AU - Hobbs, David

AU - O'Mullane, W.

AU - Bastian, U.

AU - Hernandez, J.

PY - 2012

Y1 - 2012

N2 - Context. 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. 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 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. 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.

AB - Context. 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. 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 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. 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.

KW - instruments

KW - space vehicles:

KW - methods: numerical

KW - methods: data analysis

KW - astrometry

U2 - 10.1051/0004-6361/201117905

DO - 10.1051/0004-6361/201117905

M3 - Article

VL - 538

JO - Astronomy & Astrophysics

JF - Astronomy & Astrophysics

SN - 1432-0746

M1 - A78

ER -