  Comparison of stellar catalogues with position and proper motion components
using a decomposition on a set of orthogonal vector spherical harmonics. We
show the theoretical and practical advantages of this technique as a result of
invariance properties and the independence of the decomposition from a prior
model. We describe the mathematical principles used to perform the spectral
decomposition, evaluate the level of significance of the multipolar components
and examine the transformation properties under space rotation. The principles
are illustrated with a characterisation of the systematic effects in the FK5
catalogue compared to Hipparcos and with an application to the extraction of
the rotation and dipole acceleration in the astrometric solution of QSOs
expected from Gaia.
