Cramér-Rao Bound on Lie Groups with Observations on Lie Groups: Application to SE(2)

In this communication, we derive a new intrinsic Cramér-Rao bound for both parameters and observations lying on Lie groups. The expression is obtained by using the intrinsic properties of Lie groups. An exact expression is obtained for the case where parameters and observations are in SE(2), the semi-direct Lie group of 2D rotation and 2D translation. To support the discussion, the proposed bound is numerically validated for a Lie group Gaussian model on SE(2).