So that's a lot of questions, that I all can't answer in full.

> Would you mind sharing some more of the why it is still an open problem?

Because for train sensors, there is a small drift which accumulates too much, hence it is synchronized by magnetic position markers in the tracks.

> I understand satellite positioning isn't definitive

Yes, and the point is it might be some solution if we would have the safety systems from 1860. But we do not and hence it needs to be more accurate than the current system, and it is not and in addition also more expensive (and subject to remote influence and reliance on potentially adversary nation states).

> Sorry for the bleak introduction of economics

No, economics is basically the primary constraint for safety. We could pay million people to make sure a single person does not stumble if we want total safety, but that's completely pointless, and also these million people would starve, because no one is producing food anymore.

> But even as a tertiary or lower risk mitigating factor

But for that it's too expensive and still unreliable. There is RCAS[1], which I already linked elsewhere in the thread. That's basically cutting edge and too expensive to introduce everywhere. Also previous safety systems are already not rolled out enough, which is causing these accidents, so rolling out yet another expensive system is not going to improve much.

> But what track you are on, isn't that obvious to the human in the cabin?

Yes, but if it is already known, why use GPS to calculate the same information with more error?

> So could a vision based solution help count tracks from left to right?

If the train driver or dispatcher makes use of vision to assess the train position, the error will be higher than the current sensor/electric-resistance based system.

> Assistant: "US PTC [...]

BTW, that seems to be a verbatim quote from https://www.railwayage.com/cs/the-way-forward/

> US PTC

According to Wikipedia, ASFA being introduced in 1975 is rolled out in the entire Spain network. ETCS which is the European standardization seems to be rolled out on all high-speed lines or currently being rolled out.

> So you use the dimension that matters most in crashes (forwards / backwards) from satellite, augmented with vision or human based left-right positioning.

Duh, that just sounds like trains would be operating blindly in space currently and need to assess their approximate position.

> Perhaps I am read as suggesting that the problem is easy, and that is not my intention.

No, the issue is that you are suggesting far more complicated solutions to already solved problems, with simpler systems in operation for decades. The current system is that nobody in the train even has a say on where the train goes, so the problem you are trying to prevent doesn't even exist. This IS why it's way more safer than a car. There are movement authorities, that define from where you are allowed (and have to) drive with your train. The problem is not, that the train driver isn't able to know where he is and hence drives wrong or too far (that would be prevented by the on-board safety system), but that the movement authority itself is faulty.

On an up-to-date signaling box (withing the past 6 decades), even the train dispatcher is no say in safety questions. You could put a monkey in charge of it. There would be chaos, but they would not cause a crash. The current job of a dispatcher in normal operation is to assign resources to prevent deadlocks and to implement vaguely defined priorities. (Basically the equivalent of the public thinking a programmer is a code monkey, while the actual point is clarifying stakeholder interests.)

The actual issue here is, that while these safety system have a very small false positive rate, they do have a too large false negative rate for there to be an acceptable availability. Hence in the latter case, the human needs to take over and then you are back to a much higher false positive rate. The issue would be alleviated by relaxing the constraints on cost per availability. Either by allowing for less availability or by reintroducing more humans, so that the system situation can be assessed by humans directly.

These accidents are caused as follows: the automatic system fails, because the internal state of the system does not match the actual state of the world. Hence the human needs to take over. But the human also needs to rely on some system to know the world state. Which systems can he trust, given that the whole situation is that the systems report that he can't trust them? So he needs to make some decision and in most cases, that decision is still correct. But there is still an error rate to that, and then something like what we are discussing happens.

> But for cars this was solved decades ago for routing and years ago for self-driving.

This is absolutely not solved for the cars, and to the sense that it is, it was solved and rolled out from the 1870s onward for railways using mechanical computing systems, the switch to using electricity happened in the 1910s.

> Flying is organised with a very clear 6 sigma approach.

You are correct, that aircraft safety systems need to be designed to a higher reliability than railways, because on a rail you can always stop in case of an error, while in the air such a choice doesn't lead to a safe state. But if you compare these safety systems, basically aircraft is operated like railways used to be operated in the 1920s. (My peers actually had a task to compare them and find ideas from one that can be applied to the other. While there is a lot of automation to be taken from rail that can be applied to the aerial industry, there is not really much that can be applied the other way.) It is also operated with the amount of personal than 1920s railways. That's because there is a lot of money in aircraft, while railways are mass-transit and need to be cheap. If you would operate today's railway with the amount of human oversight than in the past, it would be a lot safer than aircraft.

> there is clearly something lacking for trains, when compared to other types of transport.

What are you talking about? Railways are so much safer than cars. https://news.ycombinator.com/item?id=50288518 Yes, there are less accidents in planes than in trains, but this is due to what I already explained.

   [1]  https://www.dlr.de/en/kn/research-transfer/projects/next-generation-train/rcas-railway-collision-avoidance-system