I have a scenario where a camera is mounted to an aircraft. For this camera, I have the attitude correction values i.e. misalignment angles, namely, yaw, pitch, and roll. Also, I have the yaw, pitch, roll, of the aircraft at the time of aerial photos are taken. In addition, I have the camera position, and the position of the aircraft for each image. I'd like to know how can I obtain the effective rotation angle, so that I can apply the pinhole camera model for my images in determining the geocoordinates of my images.
Working formulas as well as theories around this problem is also highly appreciated.
Use Euler angles to rotation matrices and then multiply them together
$$ R_\text{air} \mathrm{rot}(\alpha,\beta,\gamma) $$
and
$$ R_\text{cam} = \mathrm{rot}(u,v,r) $$
and then combine them to get
$$ R_\text{combined} = R_{\rm air} R_{\rm cam} $$
Here ${}^\intercal$ is the matrix transpose which inverts the rotation.
to get the relative position of the aircraft to the camera. Finally convert from rotation matrix back to Euler angles.
$$ (a,b,c) = \mathrm{rot}^{-1} ( R_{\rm combined} ) $$