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.

PTC is a performance standard, not a concrete system. Some PTC systems do seem to use GPS for train positioning, which does seem surprising from a European train protection system perspective which all seem to completely avoid reliance on GNSS so far.

I guess a much less dense and largely overground network, mainly used by fairly slow moving freight trains as opposed to highspeed passenger connections, changes requirements somewhat.