I have a drifted LiDAR odometry $^w \textbf{T}_{1:k}\in SE(3)$ and a drift corrected LiDAR odometry $^w \textbf{T}'_{1:k}\in SE(3)$ by a loop closure where w represents the reference world frame.
Given an uncertainty or noise level $\Sigma_{6\times6}$, we can predict the possible range of the current location by propagating this uncertainty.
My question is how to calculate the uncertainty $\Sigma_{6\times6}$.
Currently I am just calculating the error of frame to frame motion in $se(3)$ and calculating a 6 by 6 covaraince from it.
$e_n=log((^n\textbf{T}_{n+1})^{-1}\textbf{T}'_{n+1})$
For the pose propabation I will use on se3 pose compounding method by Timothy Barfoot (according to his state estimation book chapter 7.3.3 Compounding Poses). The book is here.
I guess this topic is well established in EKF localization problem. Any idea and thoughts will be appreciated.
