Despite all that, maps are still produced of the leveled and normalized ground field (see geomagnetic maps).

Using the geomagnetic as an assist / backup to navigation reduces to something similar to the use of a DTM as an assist - not much use in flat areas, useful in areas with distinct features, easily confused if one valley looks much like another.

The daily flux is an issue, of course, but your software, hypothetically, would be looking at the preserved shape of waves on the ocean despite the fact that the tide is rising and falling all around.

>The system deduces the strength of Earth’s gravity in every given point of the journey from the motion of the atoms illuminated by laser beams inside a vacuum chamber and compares that data with gravity maps compiled from satellite measurements.

BPS depends on terrestrial stations instead of satellites, like Loran, which was used in the past.

BPS is at least as easily jammed or disabled as GPS.

With the gravimeter discussed in the article, and with adequate maps, one can navigate autonomously, without depending on any external help.

Moreover, BPS appears to be intended to cover only continental USA. There are no plans to use radio frequencies that would allow global coverage, like Loran had in the past.

That's how ships navigated for centuries. The instruments are simple by modern standards. You don't need a computer, although it's nice to have. The fixes aren't (normally) as precise as you get from GPS, but they're much better than you'll ever get from gravimetry. It can take time to get one, though.

Celestial navigation was a huge driver for the development of timekeeping and supporting technologies. They still teach it in "ship school". It was big news when the US Naval Academy stopped requiring it, and I think they've now backed off and brought it back because of the GPS jamming. It can be and has been automated, although the resulting instrument is a lot bigger, touchier, and more expensive than a GPS receiver.

If you need a lot of accuracy, you normally use more than one object and don't trust the compass. Individual stars are fair game and have a lot of advantages over extended objects.

But, yeah, clouds. I assume clouds are the reason people are building these big complicated expensive devices. It also gets harder to do it, at least manually, if the ship is rolling around a lot.

"I must go down to the seas again, to the lonely sea and the sky And all I ask is a tall ship and a star to steer her by."

It's 'locked' to the tidal surface (meaning an internal tide model and a mean global ocean surface model are onboarded) and perturbed by wave action, the heaving pitch and yaw presaging a decent chunder (it's being trialed on an Australian Navy ship)

Likely single channel gravity signal and three axis inertial measures .. as outlined in this abstract:

Software Ruggedized Atom Interferometry for Strapdown Mobile Quantum Inertial Sensing

  Here, we report world-first demonstrations of a dual quantum gravimeter operating in a relevant maritime environment, with an unattended uptime of >144 hours, ...

  In addition, we present a compact 3-axis quantum inertial sensor capable of high repetition rate operation in extremely harsh environments.

gamma radiation would be harder to block or deny

gamma radiation jamming could be more easily compensated for due to directionality of the line of gamma sight from jammer to receiver. its not even necessary to fully block the jammer (one could modulate different paths by rotating lead plates, or do other types of source separation)