The paper concerns the use of satellites of the Galileo constellation for relativistic positioning and for measurements of the gravito-magnetic effects induced by the angular momentum both of the Earth and of the dark halo of the Milky Way. The experimental approach is based on the generalized Sagnac effect, induced both by the rotation of the device and the fact that the observer is located within the gravitational field of a spinning mass. Among the possible sources there is also the angular momentum of the dark halo of the Milky Way. Time modulation of the expected signal would facilitate its disentanglement from the other contributions. The modulation could be obtained using satellites located on different orbital planes.