Cramér-Rao bound on Lie groups with observations on Lie groups: application to $SE(2)$
Samy LABSIR (IPSA); Alexandre Renaux (Université Paris Saclay); Jordi Vilà-Valls (ISAE-SUPAERO); Eric Chaumette (ISAE-SUPAERO)
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06 Jun 2023
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 $SE(2)$. To support the discussion, the proposed bound is numerically validated for a Lie group Gaussian model on $SE(2)$.
