Error characterization of the Gaia astrometric solution I. Mathematical basis of the covariance expansion model
(2012) In Astronomy & Astrophysics 543. Abstract
 Context. Accurate characterization of the astrometric errors in the forthcoming Gaia Catalogue will be essential for making optimal use of the data. This includes the correlations among the estimated astrometric parameters of the stars as well as their standard uncertainties, i.e., the complete (variance)covariance matrix of the relevant astrometric parameters. Aims. Because a direct computation of the covariance matrix is infeasible due to the large number of parameters, approximate methods must be used. The aim of this paper is to provide a mathematical basis for estimating the variancecovariance of any pair of astrometric parameters, and more generally the covariance matrix for multidimensional functions of the astrometric parameters.... (More)
 Context. Accurate characterization of the astrometric errors in the forthcoming Gaia Catalogue will be essential for making optimal use of the data. This includes the correlations among the estimated astrometric parameters of the stars as well as their standard uncertainties, i.e., the complete (variance)covariance matrix of the relevant astrometric parameters. Aims. Because a direct computation of the covariance matrix is infeasible due to the large number of parameters, approximate methods must be used. The aim of this paper is to provide a mathematical basis for estimating the variancecovariance of any pair of astrometric parameters, and more generally the covariance matrix for multidimensional functions of the astrometric parameters. The validation of this model by means of numerical simulations will be considered in a forthcoming paper. Methods. Based on simplifying assumptions (in particular that calibration errors can be neglected), we derive and analyse a series expansion of the covariance matrix of the leastsquares solution. A recursive relation for successive terms is derived and interpreted in terms of the propagation of errors from the stars to the attitude and back. We argue that the expansion should converge rapidly to useful precision. The recursion is vastly simplified by using a kinematographic (stepwise) approximation of the attitude model. Results. Loworder approximations of arbitrary elements from the covariance matrix can be computed efficiently in terms of a limited amount of precomputed data representing compressed observations and the structural relationships among them. It is proposed that the user interface to the Gaia Catalogue should provide the tools necessary for such computations. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3069991
 author
 Holl, Berry ^{LU} and Lindegren, Lennart ^{LU}
 organization
 publishing date
 2012
 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:000306597200014
 scopus:84862678904
 ISSN
 00046361
 DOI
 10.1051/00046361/201218807
 language
 English
 LU publication?
 yes
 id
 e066e0a644994f5fafda9e6a799cd8d1 (old id 3069991)
 date added to LUP
 20120926 15:56:11
 date last changed
 20180107 07:40:17
@article{e066e0a644994f5fafda9e6a799cd8d1, abstract = {Context. Accurate characterization of the astrometric errors in the forthcoming Gaia Catalogue will be essential for making optimal use of the data. This includes the correlations among the estimated astrometric parameters of the stars as well as their standard uncertainties, i.e., the complete (variance)covariance matrix of the relevant astrometric parameters. Aims. Because a direct computation of the covariance matrix is infeasible due to the large number of parameters, approximate methods must be used. The aim of this paper is to provide a mathematical basis for estimating the variancecovariance of any pair of astrometric parameters, and more generally the covariance matrix for multidimensional functions of the astrometric parameters. The validation of this model by means of numerical simulations will be considered in a forthcoming paper. Methods. Based on simplifying assumptions (in particular that calibration errors can be neglected), we derive and analyse a series expansion of the covariance matrix of the leastsquares solution. A recursive relation for successive terms is derived and interpreted in terms of the propagation of errors from the stars to the attitude and back. We argue that the expansion should converge rapidly to useful precision. The recursion is vastly simplified by using a kinematographic (stepwise) approximation of the attitude model. Results. Loworder approximations of arbitrary elements from the covariance matrix can be computed efficiently in terms of a limited amount of precomputed data representing compressed observations and the structural relationships among them. It is proposed that the user interface to the Gaia Catalogue should provide the tools necessary for such computations.}, articleno = {A14}, author = {Holl, Berry and Lindegren, Lennart}, issn = {00046361}, 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 I. Mathematical basis of the covariance expansion model}, url = {http://dx.doi.org/10.1051/00046361/201218807}, volume = {543}, year = {2012}, }