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.


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.


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