PCSX ReARMed is a Playstation one emulator with enhanced support for ARM devices. Thanks to libretro team one of that supported devices is now Playstation Vita / PSTV. Here you can download standalone core, but you should try also nighlies from libretro buildbot. Buildbot is updated daily so will have freshest version included.
Latest nightlies download: https://buildbot.libretro.com/nightly/playstation/vita/
Use this link to get latest nightly build that also including PCSX ReARMed core.
VITA / PS TV PCSX ReARMed (libretro standalone core) 02-10-2016 nightly
Playstation 1 emulator for PS Vita and PSTV