@ysong Thank you for you reply.
I'm aware of the math. My easy approach would be to use the rotationmatrix form the quatanionsystem and tranform the acceleration to the world frame acceleration. Then I would simply remove the gravity and retransform it to body frame by using the inverse.
However I just wanted to make sure, that I'm not missing something.
Is it possible to install the INS app without gps and use the linear acceleration?