Accurate procedure for deriving UT1 at a submilliarcsecond accuracy from Greenwich Sidereal Time or from the stellar angle

Present observations using modern astrometric techniques are supposed to provide the Earth orientation parameters, and therefore UT1, with an accuracy better than ± 1 mas. In practice, UT1 is determined through the intermediary of Greenwich Sidereal Time (GST), using both the conventional relationship between Greenwich Mean Sidereal Time (GMST) and UT1 (Aoki et al. 1982) and the so-called equation of the equinoxes limited to the first order terms with respect to the nutation quantities. This highly complex relation between sidereal time and UTI is not accurate at the milliarcsecond level which gives rise to spurious terms of milliarcsecond amplitude in the derived UT1