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Lie groups were well understood for estimation problems, which also are very concerned with observability. In fact, applying standard control theory 'through' a

Lie groups were well understood for estimation problems, which also are very concerned with observability. In fact, applying standard control theory 'through' an observable system is no giant achievement. In 2010-2015 a hit topic was 'consistency' which was shown to be related to observability by using something that seems to be quite similar (based on keyword matching alone). Roumeliotis and Gao did a lot of work here. It's old news. I'm surprised it didn't translate back to control theory, but it probably did. The writing of the abstract actually treats observability in that context, with monocular cameras on drones and all that. And it wouldn't suprise me if there was a little bit of XKCD factor going on. https://xkcd.com/793 https://xkcd.com/793. I mean, 'developed by the author' might be a bit strong. But I haven't read the article yet so those are first impressions.

goldbattle 5y ago
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 https://arxiv.org/abs/1805.10410 [2] https://scholar.google.com/citations?user=c5HeXxsAAAAJ&hl=en&oi=sra https://scholar.google.com/citations?user=c5HeXxsAAAAJ&hl=en...

goldbattle 5y ago

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 https://arxiv.org/abs/1805.10410 [2] https://scholar.google.com/citations?user=c5HeXxsAAAAJ&hl=en&oi=sra https://scholar.google.com/citations?user=c5HeXxsAAAAJ&hl=en...