Accelerometer (on a rigid-body) readings, knowing its position and attitude in an inertial frame

Good morning,

I’m trying to simulate a rigid body with some accelerometers attached to it. The aim is to simulate accelerometers readings that will be later fed into a Kalman Filter (after being added biases, noise, sensor dynamics etc).

I’m considering 3 different reference frames:

1. Inertial NED reference frame, in which I simulated a trajectory through a fifth-order polynomial.
2. G frame (XYZ) that is centered in the center of mass of the rigid body and it is integral to it. I simulated its attitude again with a fifth-order polynomial (imposing initial and final conditions) using Euler angles (I’m aware of possible discontinuities etc…).
3. xyz frame centered in the sensor (whose position is identified by vector s). It is fixed on the rigid-body so it rotates with XYZ reference frame.

I know that accelerometers measure proper acceleration so I added a gravity contribution (going "upwards") and properly rotated with rotation matrices.

Unfortunately, I’m getting very confused on how to consider "non-inertial" contributions of acceleration due to the motion and rotation of the rigid-body.

I thought about using this formula:

where G is my NED frame and B is my G frame (XYZ). Then I would express it back into G frame. Could I apply something similar also for xyz (sensor frame)?

I’m currently stuck so your help could be providential! Just some hints would be enough.

Thank you very much in advance.

Have a good day!