Clarification on how prior uncertainty is parametrized in Pose3 and Velocity.

[Mike]

Reading the manifold tutorial and looking at the code, I interpreted Pose3 and Velocity priors as being computed by first transforming to local coordinates but after some thought I'm not sure that is correct, particularly for velocity since by itself velocity has no associated rotation transformation.

How are priors computed for Pose3 and Velocity? Are the translation and velocity components computed in global Cartesian frame or is something else done? How does the pose3 translation component uncertainty differ from a prior on velocity? 

Thanks