Hello, @constructionworker. You've asked a good, but pretty complex, question, and have also "left out" the (to my mind) more interesting one about gyros vs. accelerometers. They all measure different things, make different assumptions about what is going on, have different uses, and use different coordinate systems.
- Accelerometers, as the name implies, measure linear acceleration along a single axis. They are often combined into a "tri-axial accelerometer", which (as the name implies) measures linear acceleration along three mutually-perpendicular axes. By doing this, they can resolve a (for-the-moment-assumed) constant linear acceleration into a unique 3-D vector of acceleration.
- It is tricky to describe what a single gyroscope measures, but a tri-axial gyroscope (where you have three gyros whose spinning axes are mutually perpendicular, not that modern gyros use spinning axes) measures angular velocity in 3-D space.
- A magnetometer "points toward magnetic North" (whatever that means). If you confine yourself to the surface of the Earth, Magnetic North lies in the vicinity of (but not at) the North Pole. So this gives you a position reading, but one that is to a point on a 2-D curved space (the surface of the Earth).
You ask about Roll, Pitch, and Yaw, which are components of rotations of a gimbal system (of which there are several, giving different final orientations -- look up Fick vs Helmholtz Gimbals). Suppose you are in an airplane flying True North. Your Magnetic Compass will probably not read "North" (unless you are at the longitude of Magnetic North), but never mind. You Roll the Airplane -- you are still flying North, and until you get (more-or-less) "upside down", the Magnetic bearing won't change, but then will "flip" by 180°. Now suppose you Pitch the Airplane -- same thing, you are still going "North". But now you yaw (my coordinate system says if I yaw 10°, I'll be pointing slightly to the West of North), and the Magnetic compass should also change by (approximately) 10°, telling me Magnetic North has moved 10° Eastward, therefore I've moved 10° Westward.
What does the Gyro do during all these rotations? It tells me my angular velocity about the Roll, Pitch, and Yaw axes, axes fixed to the Airplane. If I want to know my final position, I need to integrate this velocity to get position, and worry about drift. Or I can use an Accelerometer to tell me "which way is down" (unless I've jumped out of the plane without a parachute and am in "free fall" (and ignoring wind resistance, but this is getting much too complicated).
Combine Linear Accelerometers, Gyros, and Magnetic Compass + moving at moderate speeds on the surface of the Earth and you can get a pretty good position/velocity indicator. The Magnetic Compass gives you a (relatively) stable position reading for orientation about an Earth-vertical "Yaw" axis, you can use magnetic and Gyros to give you heading, and you can use the Accelerometers to give you (surprise) accelerations (such as how hard you are pressing the "accelerometer" or the "brakes" on your car). Speaking of a car, think about what each of these sensors tells you as you "make a left turn" ...
Bob Schor
