Let us assume we have a gyro that is perfectly aligned to a global frame ($X,Y,Z$).
From what I know the gyro data give me the angular rate with respect to the gyro axis ($x,y,z$). So let's say I got $\omega_x,\omega_y,\omega_z$. Since I know that the 2 frames are perfectly aligned I perform the following operations:
- $\theta_X = dt * \omega_x$
- $\theta_Y = dt * \omega_y$
- $\theta_Z = dt * \omega_z$
where $\theta_X$ is the rotation angle around $X$ and so on.
My question is: what is this update like in the following steps? Because this time the measurement that I get are no more directly related to the global frame (rotated with respect to the gyro frame).