It's not dead reckoning, it's continually fixing to a map.

Let's use a magnetometer as an example. Inertial navigation system (INS) is just using the magnetometer as a compass, so errors in bearing accumulate over time. Instead, if you built a map of magnetic field strength, the slight spatial variation of field strength would let you precisely localize on the map.

In robotics parlance, this is the difference between dead reckoning versus SLAM (simultaneous localization and mapping).

Then it looks like underwater landslides, volcanoes and earthquakes could throw things off from time to time.

Traditional dead reckoning is reasonably accurate over moderate timescales in the mostly empty ocean as subs are big and relatively slow. Thus the existing approach of only occasionally surfaces for GPS. This is therefore more a supplement as being able to regularly recenter even a few times a day is good enough.

I would assume that you'd use that data in conjunction with others (sensor fusion / kalman filter).

Wenn you know you were at location X 10 minutes ago and now one sensor tells you you are at Y ... You can reasonably assume that that sensor is wrong.

Doesn't matter just take into account what didn't move. you don't have to recalibrate at each instant.

The earths magnetic field is not constant. I don't know how much it changes, but I know magnetic north drifts a bit every year. And every once in a while the field reverses (IIRC we are like 10k years overdue for a reversal if we read the history of them right - a lot of guesses go into that of cousre)

Right, but it seems it is constant enough in the near term for practical purposes.

I didn't mean to imply that it wasn't useful for practical purposes. That is what the article is about. I just meant to point out that there are limits and disadvantages to work around. I'm expecting to make this useful they will have to have a team to constantly remap the earth, and send those updates to whoever needs the information.

There’s nothing saying that you can’t do a re-localization or remapping path with basically infinite frequency, or any frequency that we know that there is variance around. At a minimum then, it becomes a better standard for which other things can bear on.

Can you talk more about this source of error? When I google this, your post is the main thing that comes up for the term…

A long, long time ago I used to work as a technician in a shop that aligned INS for aircraft (although I didn't work on them myself). I think what the OP is referring to is that during the alignment process, the assumption is that the acceleration due to gravity is always perpendicular to the surface. So if there are any errors in the INS leveling during alignment, they can cause errors in the INS calibration. I assume this is what the OP means by "tilt error" (although this is the first time hearing of the term). These errors then get compounded during use. You can look up INS alignment processes for more information.

The accuracy of the reading determines the error. If today's error is so large that you have to resurface for GPS several times a day to reset it, maybe this can lower that error so you only have to resurface several times a month.

Huge game changer if true.

Especially if it means you can go into enemy territory for days or even weeks before exiting to friendly or international waters to surface and reset.