proper motion errors (of order the size of the proper motions themselves!), with large enough samples distributed over the sky, the rotation signal can still be recovered provided that the errors are largely random rather than systematic.\
The details of the creation of the recalibrated SDSS astrometric catalogue and measurement of SDSS-[*Gaia*]{} proper motions will be described in a separate paper (Koposov 2017 in preparation), but here we give a brief summary of the procedure.

In the original calibration of the astrometry of SDSS sources, exposed in detail by [@pier03], there are two key ingredients. The first is the mapping between pixel coordinates on the CCD $(x,y)$ and the coordinates corrected for the differential chromatic refraction and distortion of the camera $(x',y')$ (see Eqn. 5-10 in @pier03). The second is the mapping between $(x',y')$ and the great circle coordinates on the sky $(\mu, \nu)$ aligned with the SDSS stripe (Eqn. 9, 10, 13, 14 of @pier03). The first transformation does not change strongly with time, requires only a few free parameters and is well determined in SDSS. However, the second transformation that describes the scanning of the telescope, how non-uniform it is and how it deviates from a great circle, 