I want to simulate the readings of an accelerometer that is arbitrarily moved through 3D space. In an inertial reference frame $W$, the motion of the accelerometer is described by it's linear acceleration $\vec{a}_{A/W}(t)$ and it's angular velocity $\vec{\omega}_{A/W}(t)$. Let's assume that there's no gravity and at $t=0$ the reference frame of the accelerometer $A$ is equal to $W$.
The question is, how do I compute the acceleration measured by the accelerometer? I know that $\vec{a}_{A/W}(t) = \vec{a}_{A/A}(t) + \vec{\omega}_{A/W}(t) \times \vec{v}_{A/A}(t)$, but the acceleration and velocity of a reference frame with respect to itself should be zero, correct? What am I missing? What does the accelerometer actually measure and in which reference frame?