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An analysis of the source position differences between VLBI-based ICRF and$Gaia$-CRF catalogues is a key step in assessing their systematic errors anddetermining their mutual orientation. One of the main factors that limits theaccuracy of determination of the orientation parameters between two frames isthe impact of outliers. To mitigate this effect, a new method is proposed basedon pixelization data over the equal-area cells, followed by median filtering ofthe data in each cell. After this, a new data set is formed, consisting of datapoints near-uniformly distributed over the sphere. The vector sphericalharmonics (VSH) decomposition is then applied to this data to finally computethe orientation parameters between ICRF and $Gaia$ frames. To validate theproposed approach, a comparison was made of the ICRF3-SX and $Gaia$~DR2catalogues using several methods for outliers removal. The results of this workshowed that the proposed method is practically insensitive to outliers and thusprovides much more robust results of catalogues comparison than the methodsused so far. This conclusion was confirmed by analogous test comparison of the$Gaia$~DR2 and OCARS catalogues.

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