 # Velocity conversion to global coordinates

After predicting the velocities (Vx, Vy, Vz) in camera sensor coordinates, we convert them to global coordinates using:
(Vx_glob, Vy_glob, Vz_glob)^T = ego_to_world * cam_to_ego * (Vx, Vy, Vz)^T

However, if the ego vehicle is turning, it has angular velocity, and the rotation matrix changes: The derivative of the rotation matrix is not 0 (https://arxiv.org/pdf/1311.6010.pdf).
If the ego vehicle is not turning, we can convert the velocity from one coordinate system to another using the relevant rotation matrix. However, when the ego vehicle is turning, we need to consider also the angular velocity in the rotation matrix derivative.

How do you propose to convert velocity vectors between different coordinates when the ego vehicle is turning?

Thanks.

Hi. I suppose you could estimate the angular velocity.
I am not very familiar with the math in the above paper, but it does not make sense to me intuitively. If we model a vehicle with a velocity vector (and no angular velocity), we can convert that to any other coordinate frame and it should still be valid.