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A conjugate gradient algorithm for the astrometric core solution of Gaia

Bombrun, A.; Lindegren, Lennart LU ; Hobbs, David LU ; Holl, Berry LU ; Lammers, U. and Bastian, U. (2012) In Astronomy & Astrophysics 538.
Abstract
Context. 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. Aims. Our aim is to find a computationally efficient and numerically accurate iteration scheme for the astrometric solution, compatible with the AGIS framework, and a... (More)
Context. 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. Aims. Our aim is to find a computationally efficient and numerically accurate iteration scheme for the astrometric solution, compatible with the AGIS framework, and a convergence criterion for deciding when to stop the iterations. Methods. 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. This allows to define, simulate and study scaled astrometric core solutions with a much smaller number of unknowns than in AGIS, and therefore to perform a large number of numerical experiments in a reasonable time. After successful testing in AGISLab, the CG scheme has been implemented also in AGIS. Results. 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 moreover 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. While it appears to be difficult to define a strict and robust convergence criterion, we have found that the sizes of the updates, and possibly the correlations between the updates in successive iterations, provide useful clues. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
astrometry, methods: data analysis, space vehicles: instruments, methods: numerical
in
Astronomy & Astrophysics
volume
538
publisher
EDP Sciences
external identifiers
  • wos:000300614100077
  • scopus:84856976138
ISSN
0004-6361
DOI
10.1051/0004-6361/201117904
language
English
LU publication?
yes
id
2209e595-21d6-4442-b331-f564ea6daea8 (old id 2517378)
date added to LUP
2012-05-08 12:53:38
date last changed
2017-01-01 05:29:42
@article{2209e595-21d6-4442-b331-f564ea6daea8,
  abstract     = {Context. 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. Aims. Our aim is to find a computationally efficient and numerically accurate iteration scheme for the astrometric solution, compatible with the AGIS framework, and a convergence criterion for deciding when to stop the iterations. Methods. 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. This allows to define, simulate and study scaled astrometric core solutions with a much smaller number of unknowns than in AGIS, and therefore to perform a large number of numerical experiments in a reasonable time. After successful testing in AGISLab, the CG scheme has been implemented also in AGIS. Results. 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 moreover 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. While it appears to be difficult to define a strict and robust convergence criterion, we have found that the sizes of the updates, and possibly the correlations between the updates in successive iterations, provide useful clues.},
  articleno    = {A77},
  author       = {Bombrun, A. and Lindegren, Lennart and Hobbs, David and Holl, Berry and Lammers, U. and Bastian, U.},
  issn         = {0004-6361},
  keyword      = {astrometry,methods: data analysis,space vehicles: instruments,methods: numerical},
  language     = {eng},
  publisher    = {EDP Sciences},
  series       = {Astronomy & Astrophysics},
  title        = {A conjugate gradient algorithm for the astrometric core solution of Gaia},
  url          = {http://dx.doi.org/10.1051/0004-6361/201117904},
  volume       = {538},
  year         = {2012},
}