On estimation of the free core nutation parameters from analysis of the VLBI celestial pole offsets

The free core nutation (FCN) resonance influences Earth rotation in two different ways: 1) through resonant enhancement of the amplitudes of those forced nutation components which are close to the FCN frequency (indirect effect); 2) it gives rise to the free oscillation of the pole in response to the irregular nearly-diurnal geophysical forcing (direct effect). It is commonly believed that the best estimate of the FCN parameters, the space-referred period T and the quality factor Q, is that from the VLBI determination of the nutation amplitudes. The estimated values corresponding to the MHB2000 precession-nutatin model are T=-430 days and Q=20 000 with quite narrow uncertainty limits (429.93,430.48) and (18 870,21 280), respectively. Here we focus attention on determination of T and Q from analysis of the FCN signal observed by VLBI since 1984. The underlying stochastic model is similar to that applied since decades for analysis of the Chandler wobble, the so-called "pea-shooter" model proposed by Jeffreys (1940). We discuss here different ways of implementation of such model based on the methods of time series analysis. We also show and compare the FCN parameters derived from various available VLBI nutation data sets.