An Intrinsic CramérRao Bound on Lie Groups  Silvere Bonnabel, Axel Barrau

Author: Silvere Bonnabel, Axel Barrau
DIO URL: http://dx.doi.org/10.1007/9783319250403_71
Video: http://www.youtube.com/watch?v=w7nIx16lIYA
Slides: Bonnabel_Intrinsic KramerRao bound on Lie group.pdf
Presentation: https://www.see.asso.fr/en/node/14594
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
In his 2005 paper, S.T. Smith proposed an intrinsic Cramér Rao bound on the variance of estimators of a parameter defined on a Riemannian manifold. In the present technical note, we consider the special case where the parameter lives in a Lie group. In this case, by choosing, e.g., the right invariant metric, parallel transport becomes very simple, which allows a more straightforward and natural derivation of the bound in terms of Lie bracket, albeit for a slightly different definition of the estimation error. For biinvariant metrics, the Lie group exponential map we use to define the estimation error, and the Riemannian exponential map used by S.T. Smith coincide, and we prove in this case that both results are identical indeed.