| Paper: | SS-4.5 | ||
| Session: | Algebra and Geometry: The Search for Structure in Signal Processing | ||
| Time: | Wednesday, May 17, 11:20 - 11:40 | ||
| Presentation: | Special Session Lecture | ||
| Topic: | Special Sessions: Algebra and geometry: the search for structure in Signal Processing | ||
| Title: | Intrinsic Quadratic Performance Bounds On Manifolds | ||
| Authors: | Steven Thomas Smith, MIT Lincoln Laboratory, United States; Louis L. Scharf, Colorado State University, United States; Todd McWhorter, Altius Research Associates, United States | ||
| Abstract: | Cramér-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 Cramér-Rao bounds, and more general quadratic bounds on manifold-valued parameters must be considered. | ||
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