The PlayStation 3 emulator being worked on is RPCS3 and is an open-source, community-driven emulator written in C++. The project has been in the works since 2011 and is working with some PS3 titles -- reportedly over 500 commercial games, but many of the demanding AAA titles do not yet work. RPC3 has Vulkan and OpenGL support along with DirectX.
Shared today in a post on Patreon, Nekotekina has mentioned that the Linux support is seeing improved stability, a ALSA audio back-end has been implemented, and automatic Linux builds may be ready soon. This is great to hear that RPCS3's Linux support is coming together.
In other work, he's also been improving support for the PRX dynamic link libraries and also the project's LLVM-based recompiler.
Those wishing to learn more about RPCS3 can visit GitHub for the code or the project's informational site at rpcs3.net.