Puzzle on how to rotate convariance

[Hypothesis-Z]

The following code is how this repository rotate covariance:

geometry2/tf2_geometry_msgs/src/tf2_geometry_msgs/tf2_geometry_msgs.py

Lines 101 to 104 in d1dc38b

	result_11 = R @ cov_11 @ R_transpose
	result_12 = R @ cov_12 @ R_transpose
	result_21 = R @ cov_21 @ R_transpose
	result_22 = R @ cov_22 @ R_transpose

This is how mrpt rotate covariance:
https://github.com/MRPT/mrpt/blob/4af6ea558bf75af9bc9798abfc3745fe7ce39c66/libs/poses/src/CPose3DPDF.cpp#L134-L158

Obviously different. It seems euler angles cannot be rorated via left-multipling a rotation matrix. Therefore, transforming a covariance matrix of euler angles is not the same as transforming translation's:

$$ Cov(RX)=R\cdot Cov(X)\cdot R^T $$

[roncapat]

Have a look at this one https://github.com/giafranchini/covariance_geometry_ros