Lennart Lindegren, Uwe Lammers, David Hobbs, William O'Mullane, Ulrich Bastian, José Hernández
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.
View original:
http://arxiv.org/abs/1112.4139
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