Towards a robust estimation of orientation parameters between ICRF and $Gaia$ celestial reference frames

An analysis of the source position differences between VLBI-based ICRF and $Gaia$-CRF catalogues is a key step in assessing their systematic errors and determining their mutual orientation. One of the main factors that limits the accuracy of determination of the orientation parameters between two frames is the impact of outliers. To mitigate this effect, a new method is proposed based on pixelization data over the equal-area cells, followed by median filtering of the data in each cell. After this, a new data set is formed, consisting of data points near-uniformly distributed over the sphere. The vector spherical harmonics (VSH) decomposition is then applied to this data to finally compute the orientation parameters between ICRF and $Gaia$ frames. To validate the proposed approach, a comparison was made of the ICRF3-SX and $Gaia$~DR2 catalogues using several methods for outliers removal. The results of this work showed that the proposed method is practically insensitive to outliers and thus provides much more robust results of catalogues comparison than the methods used so far. This conclusion was confirmed by analogous test comparison of the $Gaia$~DR2 and OCARS catalogues.