[chris_va]

Solution (2) as written seems to imply that the camera can only use the gyroscope signal while the camera is pointed at the subject, but I cannot see why that is a strong limitation.

In theory, you can take the last N seconds of data from the gyroscope (I assume it is running while the camera is active) to get the overall drift, even if it is tumbling around for a while before being pointed at the subject... Assuming the tumbling has enough periods of time that are correlated with the earth's rotation (e.g. someone carrying it, not pointing it an an aircraft or something moving EW for the window duration that is anticorrelated with the rotation).

[felixhandte]

That would only work in the case that the camera is fixed on a tripod and has a long period of stable / rigid pointing before the exposure during which to collect this data. This is sometimes the situation in which image stabilization is used. (But if you can be that stable for that long on a tripod, you may not actually need image stabilization.)

By far the more common case for image stabilization is one in which the photographer is hand-holding the camera and may not frame the subject until the moment before the exposure begins. The camera movement will likely be several orders of magnitude (~4 to 7) larger than the drift that you want to measure. A low pass filter will tell you nothing at all.

At a certain point we can just start using guide stars [0].

[0] https://en.wikipedia.org/wiki/Guide_star