Forbes article - https://www.forbes.com/sites/jasonevangelho/2018/06/12/sources-amd-created-navi-for-sonys-playstation-5-vega-suffered/#a16310d24fda
The vast majority of AMD and Sony's Navi collaboration took place while Raja Koduri -- Radeon Technologies Group boss and chief architect -- was at AMD.
On a related note, a new rumor emerged recently about Navi for desktop being merely a midrange part
and not competing with Nvidia's high-end GeForce cards. That makes perfect sense if it was developed primarily for a console first.
Navi 10, the small Navi, manufactured on 7nm, is set to arrive at some point in 2019. There will be a big gaming GPU called Navi 20, but this one won’t come until 2020.
When we say 2020, you should not be thinking on the first few months of the year, as traditionally with AMD, you can expect it later, rather than sooner. It could be as late as the tail end of the year with the possibility it might slip to the following year. The Navi 20 is based on 7nm architecture and will share the DNA with Navi 10.
My take, if all that lines up Nvidia launches there next gen cards (20xx / 11xx series) within the next 4 months. A "Ti" version comes maybe a 8-12 months later. AMD has a GPU Navi solution for PS5 that IMO comes Fall 2019 holidays with the potential for an AMD consumer mid range Navi then. That won't be able to compete (I feel) gaming high end wise, with either of Nvidia's launches, also gives time for Nvidia to revise their 2018 offerings too. The larger gaming Navi comes in 2020 speculating towards the end, if sooner though great. However, that could be just in time for Nvidia's next cycle. Speculation for another 2 years for a high end AMD gaming card.