<div>The wet tropospheric component and clock phase variations are the most important factors that limit the accuracy of the geodetic VLBI products. These fast fluctuations can be introduced into the parametric model as a correlated stochastic noise and treated in a special way using the least square collocation method (LSCM). An a-priori covariance function is used to construct the non-diagonal covariance matrix. We have developed a procedure to calculate the wet troposphere delay and the clock offset for each observation epoch. The wet troposphere delays calculated by the LSCM are in perfect agreement with the water vapour radiometer (WVR) data, within the uncertainty of 2-3 mm. This information is then incorporated into the NGS data file and used in the second iteration. As a result, the procedure for analysing the VLBI data becomes simpler and faster, since the remaining observational error is Gaussian, and the matrix of the observational covariance can be treated as diagonal. For the calibrated VLBI data, the simple least squares method (without breaking the 24-hour experiment into small bins) is applied, followed by a reduction in the number of estimated parameters. All VLBI data between 1993 and 2023 were processed with pre-calibrated tropospheric and clock delays. The result was tested with two independent software packages, OCCAM and VieVS, and showed a good efficiency with respect to the traditional approach. The accuracy of the estimates reaches: 1 mm for VLBI site positions, 3 µas for UT1-UTC values, 40 mas for X- and Y-pole components. The formal error of the most observed ICRF reference radio source positions drops to 1-2 µas, and the ”floor” (or ”inflated”) error for the future ICRF realization would also be reduced. This paper shows that the new data analysis procedure produces results which align with the announced VGOS goals for the S/X VLBI data. Finally we report a detection of the negative parallax effect with an amplitude of −15.8(±0.5) µas. Abstract presented at the 2024 13th General Meeting of the International VLBI Service for Geodesy and Astrometry (IVS), Tsukuba, Japan

The Gaia optical astrometric mission has measured the precise positions of millions of objects in the sky, including extragalactic sources also observed by Very Long Baseline Interferometry (VLBI). In the recent Gaia EDR3 release, an effect of negative parallax with a magnitude of approximately −17 μas was reported, presumably due to technical reasons related to the relativistic delay model. A recent analysis of a 30-yr set of geodetic VLBI data (1993–2023) revealed a similar negative parallax with an amplitude of −15.8 ± 0.5 μas. Since both astrometric techniques, optical and radio, provide consistent estimates of this negative parallax, it is necessary to investigate the potential origin of this effect. We developed the extended group relativistic delay model to incorporate the additional parallactic effect for radio sources at distances less than 1 Mpc and found that the apparent annual signal might appear due the non-orthogonality of the fundamental axes, which are defined by the positions of the reference radio sources themselves. Unlike the conventional parallactic ellipse, the apparent annual effect in this case appears as a circular motion for all objects independently of their ecliptic latitude. The measured amplitude of this circular effect is within a range of 10–15 μas that is consistent with the ICRF3 stability of the fundamental axis. This annual circular effect could also arise if a Gödel-type cosmological metric were applied, suggesting that, in the future, this phenomenon could be used to indicate global cosmic rotation. <b>Citation:</b> Titov O, Osetrova A. Parallactic delay for geodetic VLBI and non-orthogonality of the fundamental axes. <i>Publications of the Astronomical Society of Australia</i>. 2024;41:e111. doi:10.1017/pasa.2024.111