An Intrinsic McAulay-Seidman Bound for Parameters Evolving on Matrix Lie Groups

Lower bounds on the mean square error (MSE) are of fundamental importance to know the ultimate achievable estimation performance of any unbiased estimator. Even if the Cramér-Rae bound (CRB) is the most popular one, mainly due to its simplicity of calculation, other bounds are of interest in several applications. In this communication,
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e derive a new intrinsic McAulay-Seidman bound (IMSB) for the estimation of unknown deterministic parameters lying on Lie groups, which generalize known results on the intrinsic CRB. The validity of the proposed IMSB is shown for the Gaussian observation model with unknown deterministic parameters belonging to SO(3) by comparing the IMSB with the intrinsic MSE.