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 \sim 20 mag .
In this study , we present GPS1+ the extension GPS1 catalog down to r \sim 22.5 mag , based on 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 mas yr ^ { -1 } .
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 Gaia and SDSS astrometry , with a typical precision of 2.0-5.0 mas yr ^ { -1 } .
In this part , \sim 160 million sources have Gaia proper motions , we provide another new proper motion for each of them by building a Bayesian model .
Relative to 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 Gaia DR2 , we provide their proper motion with a precision of \sim 4.5 mas yr ^ { -1 } ; the remaining \sim 54 million faint sources are beyond Gaia detecting capability , we provide their proper motions for the first time with a precision of 7.0 mas yr ^ { -1 } .
However , the secondary \sim 136 million sources only have PS1 astrometry , the average precision is worse than 15.0 mas yr ^ { -1 } .
All the proper motions have been validated using QSOs and the existing Gaia proper motions .
The catalog will be released on-line and available via the TAP Service .