How to calculate Rotation Matrix in android from accelerometer and magnetometer sensor

Question

I found the rotation matrix returned by SensorManager.getRotationMatrix from link: https://math.stackexchange.com/questions/381649/whats-the-best-3d-angular-co-ordinate-system-for-working-with-smartphone-apps/382048#382048

The rotation matrix is:

But I cannot find the steps to reconstruct this matrix when I used the rotation matrix for each axis as specified in link: http://www.freescale.com/files/sensors/doc/app_note/AN3461.pdf

I really appreciate if anyone can show me the steps so that I can construct the above rotation matrix because I cannot find any document that shows me the steps to create this matrix.

And at the above link, there is also a matrix as following:

How can I calculate the matrix . What does it mean?

Answer 1

You almost got it!

Your general rotation matrix R can be constructed from the axis-specific rotation matrices R_x, R_y, R_z!

The axis-specific rotation matrices rotate around each of the major axes. If you combine them, you'll get the general rotation matrix R you are looking for.

So:

R = R_x * R_y * R_z.