Characterization and analysis of the astrometric errors in the global astrometric solution for Gaia

The space astrometry mission Gaia, planned for launch in 2013 by the European Space Agency (ESA), will provide the most comprehensive and accurate catalogue of astrometric data for galactic and astrophysical research in the coming decades. It will observe roughly one billion stars, quasars and other point like objects for which the five astrometric parameters (position, parallax and proper motion) will be determined. The resulting catalogue will become available to the scientific community around 2020. The self-calibrating nature of Gaia requires that both the ~5 billion astrometric and ~50 million additional 'nuisance' parameters are estimated from 1000 billion observations. The interconnectivity of the parameters requires them to be estimated together using a global astrometric solution. The high connectivity together with the sheer number of parameters makes a direct solution computationally infeasible and therefore an iterative approach is adopted using the Astrometric Global Iterative Solution (AGIS). The main part of this thesis discusses the estimation and characterization of the astrometric errors that result from observations containing random errors. Because the observations will be dominated by photon noise this is a good approximation of reality. Using Monte-Carlo experiments we find that the astrometric parameters of sources with angular separation within roughly the field of view size of Gaia will be correlated due to observations that are affected by common (random) attitude errors, and that this correlation scales inversely with the number of sources per attitude parameter. We derive a covariance series expansion model that allows the efficient and accurate estimation of the covariance between any pair of astrometric parameters using only a limited amount of input data. This estimation was not possible before, but is now proposed as a tool in the Gaia catalogue. Additionally the identification and calibration of systematic errors due to radiation damage is studied. We use electron-level Monte-Carlo simulations of the observation process to characterize the biases and standard errors that result from radiation induced traps in the CCDs. Subsequently these standard errors and biases are rigorously propagated through the astrometric solution in numerical experiments. We find that the resulting biases in the astrometric parameters can easily be identified in the data, and that it is likely that they can be calibrated by the methods foreseen in the Gaia data processing. The resulting standard errors in the astrometric parameters are expected to increase by about 10% due to radiation damage, in which case Gaia can still reach its required scientific performance