  The ESA space astrometry mission Gaia, planned to be launched in 2013, has
been designed to make angular measurements on a global scale with
micro-arcsecond accuracy. A key component of the data processing for Gaia is
the astrometric core solution, which must implement an efficient and accurate
numerical algorithm to solve the resulting, extremely large least-squares
problem. The Astrometric Global Iterative Solution (AGIS) is a framework that
allows to implement a range of different iterative solution schemes suitable
for a scanning astrometric satellite. In order to find a computationally
efficient and numerically accurate iteration scheme for the astrometric
solution, compatible with the AGIS framework, we study an adaptation of the
classical conjugate gradient (CG) algorithm, and compare it to the so-called
simple iteration (SI) scheme that was previously known to converge for this
problem, although very slowly. The different schemes are implemented within a
software test bed for AGIS known as AGISLab, which allows to define, simulate
and study scaled astrometric core solutions. After successful testing in
AGISLab, the CG scheme has been implemented also in AGIS. The two algorithms CG
and SI eventually converge to identical solutions, to within the numerical
noise (of the order of 0.00001 micro-arcsec). These solutions are independent
of the starting values (initial star catalogue), and we conclude that they are
equivalent to a rigorous least-squares estimation of the astrometric
parameters. The CG scheme converges up to a factor four faster than SI in the
tested cases, and in particular spatially correlated truncation errors are much
more efficiently damped out with the CG scheme.

Instrumentation and Methods for Astrophysics