  One of the main pillars of the {\Lambda}CDM model is the Cosmological
Principle, which states that our Universe is statistically isotropic and
homogeneous on large scales. Here we test this hypothesis using the
Astrophysical Gravitational Wave Background (AGWB) expected to be measured by
the Einstein Telescope-Cosmic Explorer network; in particular we perform a
numerical computation of the AGWB dipole, evaluating the intrinsic contribution
due to clustering and the kinematic effect induced by the observer motion. We
apply a component separation technique in the GW context to disentangle the
kinematic dipole, the intrinsic dipole and the shot noise (SN), based on the
observation of the AGWB at different frequencies. We show how this technique
can also be implemented in matched-filtering to minimize the covariance which
accounts for both instrumental noise and SN. Since GW detectors are essentially
full-sky, we expect that this powerful tool can help in testing the isotropy of
our Universe in the next future.
