I have understood that the accelerometer measures acceleration indirectly due to the force acting on it. So the physical vector it measures is force. Now this force which is also called inertial force may be due to two things, 1. The force which is actually causing an acceleration of the body on which the accelerometer is mounted, and 2. The gravity. So essentially an accelerometer measures indirectly the acceleration due to Applied Force + Acceleration due to gravity.
But a gyroscope measures the angular velocity of itself around the frame defined on itself, i.e., the body frame. This angular velocity will be caused by a force applied to it. This force would also show up on the accelerometer. But gyroscope is not sensitive to gravity. So the physical vector whose angular velocity the gyroscope measures is only the Force vector causing the angular rotation and NOT gravity.
If this is the case then how are accelerometer data and gyroscope data used in composite filters, complimentary filters, Direction Cosine Matrix algorithms and what not to get optimum results by using each other to cancel out errors caused in each other?
Aren't we doing an apples to oranges comparison here?