Clarification needed. Left box plus used in Right Invariance filter. about kalmanif HOT 1 OPEN

@slovak194,

First of all I have to point that the UKFM examples in manif are wrong and listed on my todo list for a fix. You should therefore refer the kalmanif implementation as the most up to date.

To answer your question clearly, the covariance P is expressed in the global frame at the group origin.
Note that the README states: Both the IEKF and UKFM filters are implemented in their 'right invariant' flavor. However they are able to handle both 'right' and 'left' measurements.
The conditional invariance you've linked to is only related to the measurement model used.

This being said, this topic isn't trivial and a little far in my memories. That's why I have just added some old and partial notes on the invariance topic. They are based on [1] and other publications from the same authors/group.

Mind that the right/left invariance definition comes from this line of work and may be a little confusing with respect to our definition of right/left box-plus. Indeed they are somewhat inversed in that the right invariance is naturally associated with the left box-minus and the left invariance goes in pair with the right box-minus. This is all detailed in eqs (7-10) in the notes.

Let me know if those notes are any useful and if you have any further question.

[1] “The Invariant Extended Kalman Filter as a Stable Observer” A. Barrau and S. Bonnabel.

from kalmanif.