Intrinsic Quadratic Performance Bounds on Manifolds

Cramer-Rao bounds have been previously generalized to the class of nonlinear estimation problems on manifolds. This new approach can be used to derive a broad class of quadratic error performance bounds. A generalized intrinsic score function on the manifold-valued parameter space is introduced that distinguishes one bound from another. The derivation itself is invariant to transformations of the parameter space and score space. The resulting generalized Weiss-Weinstein bounds are shown to be invariant to certain transformations of the score. Applications of this work include cases where ambiguities, low signal-to-noise, or low sample support limit the utility of Cramer-Rao bounds, and more general quadratic bounds on manifold-valued parameters must be considered