The trouble is that GPS was designed for use out in the open; like in the middle of the sea or in a desert. It constantly under-performs on the railway because of steel infrastructure, tunnels, and built up areas. The satellite antenna needs to see a large part of the sky in order to perform well, and this frequently doesn't happen on a train.
If you look at the 377 fleet, which use GPS in the Selective Door Opening process, they are constantly having problems. When a train arrives at a station where the on-board GPS doesn't have a satisfactory fix it will inhibit the door release. The train then sits there for an eternity while the the driver has to manually override the system and put up a manual release. It's farcical to have a safety system that needs to be bypassed.
I believe that one day we'll be extensively using a system like ERTMS with trackside beacons and in-cab signalling, but the investment will be so large that I wouldn't hold my breath.
ERTMS website..
.http://www.ertms.com/2007v2/what.html