We run numerical simulations of the disruption of satellite galaxies in a Galactic potential to build up the entire stellar halo, in order to investigate what the next generation of astrometric satellites will reveal by observing the halo of the Milky Way. We generate artificial DIVA, FAME and GAIA halo catalogues, in which we look for the signatures left by the accreted satellites. We develop a method based on the standard Friends-of-Friends algorithm applied to the space of integrals of motion. We find this simple method can recover about 50 per cent of the different accretion events, when the observational uncertainties expected for GAIA are taken into account, even when the exact form of the Galactic potential is unknown. The recovery rate for DIVA and FAME is much smaller, but these missions, like GAIA, should be able to test the hierarchical formation paradigm on our Galaxy by measuring the amount of halo substructure in the form of nearby kinematically cold streams with, for example, a two-point correlation function in velocity space.