Comment by Animats
> They are called resolvers which are rotary transformers which output a sine and cosine signal. You input an AC sine wave and compare the phase offsets of the outputs to determine the rotor angle.
Right. Syncro resolvers are the classic way to do it. Modern versions use a permanent magnet and two Hall-effect sensors.
How accurate can you get with Hall-effect sensors? Back in the day when I was in the field (30-40 years ago), we used to get 20 bits of resolution out of a course+fine rotary inductosyn pair.