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Error characterization of the Gaia astrometric solution II. Validating the covariance expansion model

Holl, Berry LU ; Lindegren, Lennart LU and Hobbs, David LU (2012) In Astronomy & Astrophysics 543.
Abstract
Context. To use the data in the future Gaia catalogue it is important to have accurate estimates of the statistical uncertainties and correlations of the errors in the astrometric data given in the catalogue. Aims. In a previous paper we derived a mathematical model for computing the covariances of the astrometric data based on series expansions and a simplified attitude description. The aim of the present paper is to determine to what extent this model provides an accurate representation of the expected random errors in the astrometric solution for Gaia. Methods. We simulate the astrometric core solution by making least-squares solutions of the astrometric parameters for one million stars and the attitude parameters for a five-year... (More)
Context. To use the data in the future Gaia catalogue it is important to have accurate estimates of the statistical uncertainties and correlations of the errors in the astrometric data given in the catalogue. Aims. In a previous paper we derived a mathematical model for computing the covariances of the astrometric data based on series expansions and a simplified attitude description. The aim of the present paper is to determine to what extent this model provides an accurate representation of the expected random errors in the astrometric solution for Gaia. Methods. We simulate the astrometric core solution by making least-squares solutions of the astrometric parameters for one million stars and the attitude parameters for a five-year mission, using nearly one billion simulated elementary observations for a total of 26 million unknowns. Two cases are considered: one in which all stars have the same magnitude, and another with 30% brighter and 70% fainter stars. The resulting astrometric errors are statistically compared with the model predictions. Results. In all cases considered, and within the statistical uncertainties of the numerical experiments (typically below 0.4%), the theoretically calculated variances and covariances are consistent with the simulations. To achieve this it is however necessary to expand the covariances to at least third or fourth order, and to apply a (theoretically motivated and derived) "fudge factor" in the kinematographic model. Conclusions. The model provides a feasible method to estimate the covariance of arbitrary astrometric data, accurate enough for most applications, and as such it should be available as part of the user's interface to the Gaia catalogue. A main assumption in the current model is that the observational errors are uncorrelated (e.g., photon noise), and further studies are needed on how correlated modelling errors, in particular in the attitude, can be taken into account. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
astrometry, catalogs, methods: data analysis, methods: statistical, space vehicles: instruments
in
Astronomy & Astrophysics
volume
543
publisher
EDP Sciences
external identifiers
  • wos:000306597200015
  • scopus:84862676331
ISSN
0004-6361
DOI
10.1051/0004-6361/201218808
language
English
LU publication?
yes
id
d98a846f-005f-46a3-b115-3c2d2fefe7c0 (old id 3069995)
date added to LUP
2012-09-26 15:57:29
date last changed
2017-07-23 04:19:32
@article{d98a846f-005f-46a3-b115-3c2d2fefe7c0,
  abstract     = {Context. To use the data in the future Gaia catalogue it is important to have accurate estimates of the statistical uncertainties and correlations of the errors in the astrometric data given in the catalogue. Aims. In a previous paper we derived a mathematical model for computing the covariances of the astrometric data based on series expansions and a simplified attitude description. The aim of the present paper is to determine to what extent this model provides an accurate representation of the expected random errors in the astrometric solution for Gaia. Methods. We simulate the astrometric core solution by making least-squares solutions of the astrometric parameters for one million stars and the attitude parameters for a five-year mission, using nearly one billion simulated elementary observations for a total of 26 million unknowns. Two cases are considered: one in which all stars have the same magnitude, and another with 30% brighter and 70% fainter stars. The resulting astrometric errors are statistically compared with the model predictions. Results. In all cases considered, and within the statistical uncertainties of the numerical experiments (typically below 0.4%), the theoretically calculated variances and covariances are consistent with the simulations. To achieve this it is however necessary to expand the covariances to at least third or fourth order, and to apply a (theoretically motivated and derived) "fudge factor" in the kinematographic model. Conclusions. The model provides a feasible method to estimate the covariance of arbitrary astrometric data, accurate enough for most applications, and as such it should be available as part of the user's interface to the Gaia catalogue. A main assumption in the current model is that the observational errors are uncorrelated (e.g., photon noise), and further studies are needed on how correlated modelling errors, in particular in the attitude, can be taken into account.},
  articleno    = {A15},
  author       = {Holl, Berry and Lindegren, Lennart and Hobbs, David},
  issn         = {0004-6361},
  keyword      = {astrometry,catalogs,methods: data analysis,methods: statistical,space vehicles: instruments},
  language     = {eng},
  publisher    = {EDP Sciences},
  series       = {Astronomy & Astrophysics},
  title        = {Error characterization of the Gaia astrometric solution II. Validating the covariance expansion model},
  url          = {http://dx.doi.org/10.1051/0004-6361/201218808},
  volume       = {543},
  year         = {2012},
}