Hilbert-Schmidt lower bounds for estimators on matrix lie groupsfor ATR
Grenander, U.; Miller, M.I.; Srivastava, A.
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Volume 20, Issue 8, Aug 1998 Page(s):790 - 802
Digital Object Identifier 10.1109/34.709572
Summary:Deformable template representations of observed imagery model the
variability of target pose via the actions of the matrix Lie groups on
rigid templates. In this paper, we study the construction of minimum
mean squared error estimators on the special orthogonal group, SO(n),
for pose estimation. Due to the nonflat geometry of SO(n), the standard
Bayesian formulation of optimal estimators and their characteristics
requires modifications. By utilizing Hilbert-Schmidt metric defined on
GL(n), a larger group containing SO(n), a mean squared criterion is
defined on SO(n). The Hilbert-Schmidt estimate (HSE) is defined to be a
minimum mean squared error estimator, restricted to SO(n). The expected
error associated with the HSE is shown to be a lower bound, called the
Hilbert-Schmidt bound (HSB), on the error incurred by any other
estimator. Analysis and algorithms are presented for evaluating the HSE
and the HSB in cases of both ground-based and airborne targets
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