Algorithm of comparison


The algorithm of comparison is the one currently used at the ICRS Centre; the coordinate difference between two frames is modelled by a global rotation of the axes, represented by the angles A1, A2, A3, and by a deformation represented by three parameters: one is a slope in right ascension as a function of the declination (Da), another is a slope in declination as a function of the declination (Dd), and the third one is a bias of the principal plane of the frame relative to that of the ICRF-Ext.1 (Bd).


A1 tg d cos a + A2 tg d sin a - A3 + Da (d - d0)


a1 - a2

-A1 sin a + A2 cos a + Dd (d - d0) + Bd


d1 - d2


Only defining sources common to each individual frame and the ICRF-Ext.1 have been used for the comparison. The parameters have been evaluated by a weighted least squares fit; the equations have been weighted using the inverse of the variance of the coordinate differences.

Formal uncertainties in radio source positions listed in the individual frames smaller than 0.01 mas were set to this value for the assignation of weights. The six fitted parameters allow to transform coordinates in the individual frames into ICRS.