  The signature of free core nutation (FCN) is found in the motion of the
celestial intermediate pole in the celestial reference frame and in the
resonance behaviour of the frequency-dependent Earth tidal displacement in its
diurnal band. We focus on estimation of the FCN parameters, i.e. the period and
amplitude. We run several global adjustments of 27 years of very long baseline
interferometry (VLBI) data (1984.0 - 2011.0) to determine the FCN period from
partial derivatives of the VLBI observables with respect to the FCN as
contained in the nutation of the celestial intermediate pole and in the solid
Earth tidal displacement in the diurnal band. Finally, we estimate the FCN
period by a global adjustment from both phenomena simultaneously, which has not
been done before. We find that our estimate of the FCN period of -431.18 +/-
0.10 sidereal days slightly deviates from the conventional value of -431.39
sidereal days. Additionally, we present our empirical model of the FCN with
variable amplitude and phase compatible with the estimated period.
