I looked into it briefly, and while it may be easy at sea with a horizon reference, it becomes surprisingly hard without it (which also complicates testing). The article touches on this with the mention of the bubble sextant required at night, presumably because you can't see the horizon. You'd have the same problem over land.
The stars only give you the angle at which you're looking at the sky. If you know the angle to the center of the earth (or can relate the sky measurement to that) and the exact time, you know where you are, within the inaccuracy of your measurements. Being 1/60th of a degree (1 angular minute) off places you 1 nautical mile off.
The obvious solution that immediately springs to mind is a tilt sensor/accelerometer. However, once you get to a useful accuracy, those start getting expensive - several hundred dollars for a 0.01 degree system, which would give you an error of about 1 km.
You'd then need a sufficiently rigid mount for everything, proper calibration (remember, some angle on your mount being 0.05 degrees off completely destroys all usefulness of your system!), and then a camera and a plate solver (software that turns a photo into sky coordinates) should give you a useful fix. I think you could build a system that gets you within a few nautical miles for about $1000 (parts, not labor).
The stars only give you the angle at which you're looking at the sky. If you know the angle to the center of the earth (or can relate the sky measurement to that) and the exact time, you know where you are, within the inaccuracy of your measurements. Being 1/60th of a degree (1 angular minute) off places you 1 nautical mile off.
A bubble sextant solves this by including a literal 2D bubble level. "When properly used, the bubble sextant gives good results, by which we mean an accuracy to within 5 miles." (https://www.usni.org/magazines/proceedings/1939/june/averagi...).
The obvious solution that immediately springs to mind is a tilt sensor/accelerometer. However, once you get to a useful accuracy, those start getting expensive - several hundred dollars for a 0.01 degree system, which would give you an error of about 1 km.
You'd then need a sufficiently rigid mount for everything, proper calibration (remember, some angle on your mount being 0.05 degrees off completely destroys all usefulness of your system!), and then a camera and a plate solver (software that turns a photo into sky coordinates) should give you a useful fix. I think you could build a system that gets you within a few nautical miles for about $1000 (parts, not labor).