'Calculate Rotation of IMU by using the acceleration

I have an IMU with 9 degrees of freedom. Now I would like to get the vertical acceleration (as marked red in the image) from an IMU that I assume is not aligned perfectly but has a slight tilt.

Reading other StackOverflow entries and further articles I got to the point to calculate the Roll and Pitch angle only by using the acceleration data and adapt my data with this information. The results I get with this approach seem to be correct but as far as I understand it, it is not possible to differentiate between the acceleration of the earth and the acceleration of movement.

Does that mean that this approach of calculating Pitch and Roll from accelerometer data is not working as soon as the IMU is moving? How else can I get to the vertical acceleration when the device is not standing still and calculate the angles of rotation?

enter image description here

rotationsensorseuler-anglesimu


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