I've been working with MEMS gyroscopes in hobbyist projects for years—but it's recently come to my attention that I don't have any principled understanding of what rotation rate measurements mean, physically speaking, and now it's bugging me.
My immediate motivation for asking is that I want to understand the design decisions in Paul Riseborough's Kalman filter for UAVs (see my earlier attempt at this question). Now that I'm aware of my confusion, I have the same issue with interpreting output from the Portland State Aerospace Society's inertial measurement unit, which has a similar package of three-axis accelerometers/gyroscopes/etc.
Paul states (at the above link) that it's standard in the literature to interpret the three-axis rate-gyro measurements as a kind of axis-angle representation of rotation, where the direction of the 3-vector is the axis of rotation, and the magnitude of the vector is the angular rotation rate around that axis. I just don't understand why that would be true in general, although it's clearly true in the special case where rotation is exactly around one gyro axis.
I think that if someone can show me the derivation of what each MEMS gyro axis should read, given an arbitrary 3-D rotation rate, that may lead to a deeper understanding of how I should interpret these sensor readings.