Accurate characterization of the errors in the global astrometric solution for Gaia is essential for making optimal use of the catalogue data. We investigate the structure of the covariance between the estimated astrometric parameters by studying the properties of the astrometric least squares solution. We find that astrometric errors can be separated in a star and an attitude part, due to the estimation of the star and attitude parameters respectively. Hence the covariances can be separated in a star, an attitude and a cross term. This is demonstrated using our scalable simulation tool AGISLab, where the covariances are estimated statistically using Monte Carlo techniques.