Cartesian catalog of 30 million Gaia sources

We aim to create a Cartesian catalog from Gaia DR3 to serve as a high-precision database for further research using stellar coordinates and velocities. To avoid the negative parallax values, we select 31129169 sources in Gaia DR3 with radial velocity, where the fractional parallax error is less than 20% (0<{sigma}_{varpi}_/{varpi}<0.2).

To select the most accurate and efficient method of propagating mean and covariance, we use the Monte Carlo results with 107 samples (MC7) as the benchmark, and compare the precision of linear, second-order, and Monte Carlo error propagation methods. By assessing the accuracy of propagated mean and covariance, we observe that second-order error propagation exhibits mean deviations of at most 0.5% compared to MC7, with variance deviations of up to 10%.