[labcomputer]

> Was it essentially doing the high-tech equivalent of dangling a rock on a string with some dampening (in a gyroscopic cage to avoid being affected by the airplane's rotation), or something smarter?

Yes, that is essentially how a gyroscopic artificial horizon works.

Consider that the local horizon changes relative to an inertial frame (the stars) as you travel across the surface of a sphere, so even if you could build a perfect gyro that remained stationary in the inertial frame you would need to update the local down as you move. The solution is to slightly weight the gyro cage to bias it to the local down.

Now, consider that, in a properly-coordinated turn, the passengers (and gyro) will feel that gravity points straight to the floor :) So the time-constant of the damping is important.

[tgsovlerkhgsel]

I assume the constant is usually chosen short enough that the system will "forget" turns quickly, in exchange for becoming useless while turning?

Still, getting this whole thing accurate to probably one minute of arc is insane, especially with the gyro and star tracker linked only via motors and synchros. So the total error is the sum of any deviation of the gyroscope from the actual down direction, the error in measuring the gyro angle, the error in setting the star tracker to that exact angle, and then all other errors the system introduces. Then you need to take multiple separate measurements at different times and compensate for the movement, and a one-degree difference means you're over the wrong city (or in Europe, country) so the end-to-end accuracy must be much better than that.

And sailors supposedly did that with a sextant to something like 0.01° on a moving ship.