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تسجيل مستخدم جديدA conjugate gradient algorithm for the astrometric core solution of Gaia
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Alex Bombrun
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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.
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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 soluti
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Context. The Gaia ESA mission will estimate the astrometric and physical data of more than one billion objects, providing the largest and most precise catalog of absolute astrometry in the history of Astronomy. The core of this process, the so-called
global sphere reconstruction, is represented by the reduction of a subset of these objects which will be used to define the celestial reference frame. As the Hipparcos mission showed, and as is inherent to all kinds of absolute measurements, possible errors in the data reduction can hardly be identified from the catalog, thus potentially introducing systematic errors in all derived work. Aims. Following up on the lessons learned from Hipparcos, our aim is thus to develop an independent sphere reconstruction method that contributes to guarantee the quality of the astrometric results without fully reproducing the main processing chain. Methods. Indeed, given the unfeasibility of a complete replica of the data reduction pipeline, an astrometric verification unit (AVU) was instituted by the Gaia Data Processing and Analysis Consortium (DPAC). One of its jobs is to implement and operate an independent global sphere reconstruction (GSR), parallel to the baseline one (AGIS, namely Astrometric Global Iterative Solution) but limited to the primary stars and for validation purposes, to compare the two results, and to report on any significant differences. Results. Tests performed on simulated data show that GSR is able to reproduce at the sub-$mu$as level the results of the AGIS demonstration run presented in Lindegren et al. (2012). Conclusions. Further development is ongoing to improve on the treatment of real data and on the software modules that compare the AGIS and GSR solutions to identify possible discrepancies above the tolerance level set by the accuracy of the Gaia catalog.
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