A note on the intrinsic Cramer-Rao bound

Axel Barrau (1) , Silvère Bonnabel (1)

1 CAOR - Centre de Robotique

We consider the intrinsic version of the Cramer-Rao lower bound (CRLB) as introduced by S.T. Smith in 2005. In the concerned paper, the derived lower bound on the intrinsic root-mean-square error (RMSE) of any sample covariance matrix (SCM) estimator is shown not to depend on the underlying parameter, and the author claims the result stems from the invariances of the Fisher Information Metric (FIM). But it also stems from the use of special coordinates used to derive the result. The goal of this paper is to address the following questions: 1- to what extent is the intrinsic CRLB bound independent of a specific choice of coordinates ? 2- when can the intrinsic CRLB be expected not to depend on the underlying parameter ? The paper is essentially tutorial and can be considered as an introduction to the intrinsic CRLB.

Domaines: Automatique / Robotique

Axel Barrau, Silvère Bonnabel. A note on the intrinsic Cramer-Rao bound. 2013. ⟨hal-00828037v1⟩