These pages refer to the annual analysis run at the ICRS Center in order to assess the consistency of new VLBI radio source catalogs provided through the IVS with the current ICRF. These analyses are regularly published in the IERS Annual Reports.
We evaluate the consistency of catalogs submitted to the IERS by modeling the coordinate difference with the ICRF2 (in the sense catalog minus ICRF2) by a 6-parameter transformation:
A1 tan δ cos α + A2 tan δ sin α - A3 + Dα (δ-δ0) = α2 - α1,
-A1 sin α + A2 cos α + Dδ (δ-δ0) + Bδ = δ2 - δ1,
where A1, A2, and A3 are rotation angles around the X, Y, and Z axes of the celestial reference frame, respectively, Dα and Dδ represent linear variations with the declination (which origin δ0 can be arbitrarily chosen but is generally set to zero, Bδ is a bias in declination, and α2 - α1 and δ2 - δ1 are coordinate differences between the studied and the ICRF2 catalogs. The 6 parameters can be fitted by weighted least squares to the coordinate difference of the defining sources or of all ICRF2 sources found in the catalog.
After alignment of the considered frame to the ICRF2, one can assess the consistency of the remaning (nonsystematic) offsets to ICRF2 with respect to formal errors. This test is motivated by the consideration that, although the ICRF2 is not the truth, it nevertheless provides accurate values of well-observed sources. As a consequence, for most of the sources, the addition of new observations after 2009 should not perturb significantly the estimated position but only improve the formal error. If one displays the scatter around the ICRF2 position computed for bins of increasing formal error, the signature of a white noise corresponds to values close to the first diagonal (i.e., the formal error fully explains the offset to ICRF2). Deviations from the diagonal may be caused by the existence of a noise floor, and/or a scale factor. One can therefore look for a relation like
σr = ((σ s)2 + f2)-0.5
where σ is the error, s a scale factor and f a noise floor. The superscript r in the LHS means ``realistic."
Last item to be addressed in the consistency analysis is how the formal error varies with the number N of observations (or, in other terms, how the error on delays is propagated to the estimated source coordinates). A deviation from a white noise regime can occur for large N as the signature of non-Gaussian correlated errors: as N increases, thermal baseline-dependent error tends to zero and the station-dependent error arising from time- and space-correlated parameters becomes dominant (see, e.g., Gipson 2006 or Romero-Wolf et al. 2012; see also Lambert 2014).