# What is the proper way to obtain the fixed-axis covariance matrix from quaternions?

REP 103 defines the standard for rotation representation as quaternions, but the covariance matrix associated to it is given in terms of fixed axis rotations. In my work, I use quaternions directly for attitude estimation and obtain covariances in terms of the quaternion parameters.

How can I convert these covariances to the convention used by ROS, so they can be published appropriately?

PS: I have searched ROS Answers and found a few discussions briefly addressing this topic, but usually referring to external documents or additional packages. I think it would be useful to have a single definitive reference for this here, so that implementations don't depend on the reader's interpretation of what is expected.

@tfoote@William, any chance you guys could help me out with this one?