The extended Gaia-PS1-SDSS (GPS1+) proper motion catalog

The GPS1 catalog was released in 2017. It delivered precise proper motions for around 350 million sources across three-fourths of the sky down to a magnitude of \(r\sim20\)\,mag. In this study, we present GPS1+ the extension GPS1 catalog down to \(r\sim22.5\)\,mag, based on {\it Gaia} DR2, PS1, SDSS and 2MASS astrometry. The GPS1+ totally provides proper motions for \(\sim\)400 million sources with a characteristic systematic error of less than 0.1\masyr. This catalog is divided into two sub-samples, i.e., the primary and secondary parts. The primary \(\sim\)264 million sources have either or both of the {\it Gaia} and SDSS astrometry, with a typical precision of 2.0-5.0 \masyr. In this part, \(\sim\)160 million sources have {\it Gaia} proper motions, we provide another new proper motion for each of them by building a Bayesian model. Relative to {\it Gaia}'s values, the precision is improved by \(\sim\)0.1\,dex on average at the faint end; \(\sim\)50 million sources are the objects whose proper motions are missing in {\it Gaia} DR2, we provide their proper motion with a precision of \(\sim\)4.5\masyr; the remaining \(\sim\)54 million faint sources are beyond {\it Gaia} detecting capability, we provide their proper motions for the first time with a precision of 7.0 \masyr. However, the secondary \(\sim\)136 million sources only have PS1 astrometry, the average precision is worse than 15.0 \masyr. All the proper motions have been validated using QSOs and the existing {\it Gaia} proper motions. The catalog will be released on-line and available via the VO-TAP Service, or via the National Astronomical Data Center serviced by China-VO: https://nadc.china-vo.org/data/data/gps1p/f.