IEEE Transactions on Pattern Analysis and Machine IntelligenceHilbert - Schmidt

In a deformable template representation of observed images fundamental to mod-eling the variability of target pose is the action of the matrix Lie groups (such as SO(n)) on rigid templates. For the problem of target identiication using remote sensors , a Bayesian approach constructs a posterior distribution on the rotation group from which the conditional expectations can be generated. Due to the non-at geometry of the matrix Lie-groups, the usual Bayesian setups need modiications for target pose estimation. We present a Bayesian optimality criterion for pose estimation from multi-sensor data using the Hilbert-Schmidt metric on SO(n). This leads to a lower bound, the Hilbert-Schmidt Bound (HSB), on the expected variation of any Lie-group valued estimator. The analysis and algorithms are presented for evaluating HSB in estimating pose of both the ground-based and airborne targets. The fundamental role of these bounds on pose estimation in analyzing the target identiication performance is also demonstrated.