[goldbattle]

My understanding is is that group invariance is just another perspective to look at the original non-linear system transformations as compared to the more traditional "on-manifold".

Really it seems like an easier way to derive a system which the observable properties of the system are well defined as compared to worrying about ensuring observability (and unobservability) properties hold through the non-linear linearization process.

There are quite a few groups that use "invariant filters" in robotics (eg [1]), but I always wonder if this could not be addressed through more traditional means (i.e. designing a better state representations or correcting gains in unobservable directions).

Roumeliotis is referring to Stergios [2] or another scholar? Could you provide full names?

[1] https://arxiv.org/abs/1805.10410

[2] https://scholar.google.com/citations?user=c5HeXxsAAAAJ&hl=en...