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The all-sky survey of Gaia will generate vast amounts of astrometric data, in which there are expected to be thousands of planets found. Finding a system of $n_\textup{p}$ planets requires fitting of a total $5+7n_\textup{p}$ parameters: five astrometric and seven Keplerian parameters for every planet. The problem is thus highly non-linear and computationally prohibitive. After exploiting the line
