Astronomy Department, St.-Petersburg University,
198904, St.-Petersburg, Petrodvorets, Bibliotechnaya pl.2, Russia
E-mail vityazev@venvi.usr.pu.ru
In astrometry, there are several important tasks that may be reduced to the problem of deriving the parameters of mutual orientation of reference frames. They are: orientation of an astrometric instrument in space and time; determination of the Earth rotation parameters from VLBI observations; determination of precession and nutation; deriving of the mutual rotation between the axes of two astrometric catalogs, etc.
At present, astrometry deals with three types of reference frames. The first one, based on meridian observations of stars, is represented by the FK5 at the accuracy level of 0.02 ÷ 0.03 arcsec. The second one, resulted from VLBI observations of radio sources, reached the accuracy of the order 0.0005 arcsec. The third type of reference frames can be produced by observations from outer space. Data reductions for the project HIPPARCOS are now near completion and the accuracy of the resulting catalogue is expected to be 0.001 ÷ 0.002 arcsec. According to inner logics of astrometry, all the reference frames are to be connected. A lot of observational programs aiming at the connection is now in progress: observations of radio stars and extra-galactic radio sources in optical and radio regions of the spectrum, the Hubble Space Telescope measurements of the HIPPARCOS stars with respect to quasars, etc.
Very often the problem of connection between two catalogues is reduced to determination of their mutual rotation. In this paper the theoretical study of determination of rotation is made. Two approaches are considered. The first technique is the Standard Method based on the least squares procedure and the second one is a new method based on the representation of the systematic differences in terms of orthogonal functions -- henceforth the ROTOR ( ROTation by Orthogonal Representation). It is shown that the ROTOR is preferable over the Standard Method since it
Due to these properties the ROTOR yields realistic results even in the case when the observational data contain not only noise but other systematic terms that have nothing to do with rotation. Numerical experiments with the 1535 basic stars of the FK5 showed that the ROTOR can be used to obtain rotation of any reference frame with respect to the FK5. The special emphasis is made on the ROTOR's application to the catalogs characterized by small number of the objects of comparison (such are the catalogs of radio sources).