An optimal control method for computation of the dynamical correction of the systematic errors in celestial reference frames

Abstract

The recent introduction of new star catalogues referred to the new ICRF reference frame gives special interest to the study of the orientation errors of this freferences frame with respect to the dynamical reference frame defined by means of planetary theory. Several methods can be used for this purpose. One of them is based in an optimal control method where the residuals given from the differences between the calculated and observated positions for a set of minor planets on a long time-span, and we use the residual function as cost function. This method requires a previous correction of the elements of the asteroids in order to consider the most precise calculated positions. For this purpose a set of observated positions asteroids in the time span 1836–1996 are taken. From this initial correction we compare the calculated and observated positions from a differential rotation with a linear correction in time around each axis an a model of correction is got.