GPS-based PTC absolutely does what you describe. It has long been solved.

No, it does not do, what I described. I was talking about solely determining it inside the train. At least Wikipedia indicates it is similar to LZB or ETCS. I am not familiar with PTC itself.

That's a research topic, because the infrastructure companies would like to not pay as much for maintenance and still have a high sequence of trains. Also with track based train control systems you can only have very high resolution in specific places, where you place your track-side infrastructure, but it would be nice to have that resolution anywhere you like.