The first car navigator, the Etak, came out in 1985 and used dead reckoning and quantization to tell where the car was on the map; see this excellent article from 2017:
Today dead reckoning is used in aerial navigation, and commercial planes (and others) are equipped with Inertial Navigation systems to supplement GPS information; they are getting more and more precise but can still go wrong and need frequent re-calibration.
The next step is "Quantum Positioning System" that promises to detect infinitely small movements and produce perfect dead reckoning at all times, with a precision of the order of one centimeter. It has already been tested successfully. For now the machines are heavy and extremely expensive, but it's imaginable that in some not-so-distant future the technology will be much more available.
But dead reckoning for train travel should be massively easier. Train movement is constrained to tracks so you only need to resolve how far along track train has moved + possible junctions, which should already make the problem much simpler than e.g. airplane ins where you are resolving full 3d position. To make things even more easier, you only need to reckon between individual stops which prevents error accumulation over the whole trip. Lastly you have schedule information, so you know roughly where the train should be at any given moment.
There is a very good set of podcasts[0] by Cautionary Tales about the German V2 rockets in WW2 which tried to use this. It was so hard the Allies allowed them to continue wasting money on it during the war. Well worth a listen to if you're into that.
https://en.wikipedia.org/wiki/Dead_reckoning
The first car navigator, the Etak, came out in 1985 and used dead reckoning and quantization to tell where the car was on the map; see this excellent article from 2017:
https://www.fastcompany.com/3047828/who-needs-gps-the-forgot...
Today dead reckoning is used in aerial navigation, and commercial planes (and others) are equipped with Inertial Navigation systems to supplement GPS information; they are getting more and more precise but can still go wrong and need frequent re-calibration.
The next step is "Quantum Positioning System" that promises to detect infinitely small movements and produce perfect dead reckoning at all times, with a precision of the order of one centimeter. It has already been tested successfully. For now the machines are heavy and extremely expensive, but it's imaginable that in some not-so-distant future the technology will be much more available.
https://newatlas.com/aircraft/quantum-navigation-infleqtion-...