The motion of Earth's spin axis in space is monitored by Very Long-Baseline Interferometry (VLBI), and since 1994 also its rate is measured by Global Positioning System (GPS). The method of "combined smoothing", developed recently at the Astronomical Institute in Prague enables one to combine both series. The solution, based on observations in 1979.6-2004.7, is compared with the recently adopted IAU2000 model of precession-nutation. The analysis reveals substantial residual offsets from the model. The dominant peak in frequency domain can be identified with Retrograde Free Core Nutation (RFCN), and we find also statistically significant deviations of several forced nutation terms. From the direct analysis of VLBI observations of celestial pole offsets from IAU2000 model of precession-nutation, it follows that the dominant period apparently grew from the average 435 days (VLBI observations in 1983(VLBI observations in .7-2004.7) to 460 days (VLBI/GPS combination in 1994.3-2004. A study of indirect determination of the RFCN period from the observed forced nutation terms through the resonance effects is presented, and the difference from the value found by direct analysis is discussed. It is demonstrated that the resonance approach does not confirm the apparent change of the period obtained from the direct analysis of observed celestial pole offsets; the resonance value is close to 430 solar days, and it seems to be very stable in time. The different value found from the direct analysis of observations can be probably ascribed to a small additional excitation by the atmosphere and/or ocean with retrograde terrestrial period around 23h 53min mean solar time.

The optical astrometry observations of latitude/universal time variations made with 48 instruments at 31 observatories are used to determine the Earth orientation parameters (EOP) since the beginning of the century. The Hipparcos Catalogue is used to bring more than four million individual observations, made in the interval 1899.7-1992.0, into the International Celestial Reference System. The Earth orientation parameters (polar motion, celestial pole offsets and, since 1956.0, also universal time UT1) are determined at 5-day intervals, with average uncertainties ranging from 8 mas (in the eighties) to about 40 mas (in the forties). Making use of very long series of ground-based observations, the solution also leads to the improvement of proper motions of about ten per cent of the observed Hipparcos stars, with precision of ±0.2 — 0.5 mas/yr. In addition, 474 auxiliary parameters, describing the rheological properties of the Earth and seasonal deviations of the observations at contributing observatories, are found. The new solution provides the EOP series suitable for further analyses, e.g., for studying long-periodic polar motion, length-of-day changes or precession/nutation.

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Context. In addition to the torques exerted by the Moon, Sun, and planets, changes of precession-nutation are known to be caused also by geophysical excitations. Recently studies suggest that geomagnetic jerks (GMJ) might be associated with sudden changes of phase and amplitude of free core nutation. We showed that using atmospheric and oceanic excitations with those by GMJ improves substantially the agreement with observed celestial pole offsets. Aims. Traditionally, the period T f and quality factor Q f of the free core nutation (FCN) are derived from VLBI-based celestial pole offsets (CPO). Either direct analysis of the observed CPO, or indirect method using resonant effects of nutation terms with frequencies close to FCN, are used. The latter method is usually preferred, since it yields more accurate results. Our aim is to combine both approaches to better derive FCN parameters. Methods. We numerically integrated the part of CPO that is due to geophysical excitations for different combinations of T f , Q f , using Brzeziński's broadband Liouville equations (Brzeziński 1994, Manuscripta geodaetica, 19, 157), and compared the results with the observed values of CPO. The values yielding the best fit were then estimated. The observed CPO, however, must be corrected for the change of nutation that is caused by the T f , Q f values different from those used to calculate IAU 2000 model of nutation. To this end, we have used the Mathews-Herring-Buffet transfer function and applied it to the five most affected terms of nutation (with periods 365.26, 182.62, 121.75, 27.55 and 13.66 days). Results. The results, based on the CPO data in the interval 1986.0-2016.0 and excitations with three different models, are presented. We demonstrate that better results are obtained if the influence of additional excitations at GMJ epochs is added to excitations by the atmosphere and oceans. Our preferred values are T f = 430.28 ± 0.04 mean solar days and Q f = 19 500 ± 200.

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