Lower bounds for the divergence of orientational estimators

This paper is concerned with the properties of estimators in O(n,p),the n/spl times/p orthogonal matrices. It is shown that it is natural to introduce the notion of a parallel estimator where the expected value of the estimator must lie in normal space (orthogonal complement of tangent space) of O(n...

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Bibliographic Details
Published in:IEEE transactions on information theory 2001-09, Vol.47 (6), p.2490-2504
Main Authors: Valkenburg, R.J., Kakarala, R.
Format: Article
Language:English
Subjects:
Complement
Computer simulation
Divergence
Estimating techniques
Estimators
Information systems
Mathematical analysis
Mathematical models
Matrices
Maximum likelihood estimation
Statistics
Tangents
Theory
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Summary:This paper is concerned with the properties of estimators in O(n,p),the n/spl times/p orthogonal matrices. It is shown that it is natural to introduce the notion of a parallel estimator where the expected value of the estimator must lie in normal space (orthogonal complement of tangent space) of O(n,p) at the true value. An appropriate measure of variance, referred to as divergence, is introduced for a parallel estimator and a Cramer-Rao (CR) type bound is then established for the divergence. The well-known Fisher-von Mises matrix distribution is often used to model random behavior on O(n,p) and depends on parameters /spl Theta//spl isin/O(n,p) and H a p/spl times/p symmetric matrix. The bound for this distribution is calculated for the case n=p=3 and the divergence of the maximum-likelihood estimator (MLE) of /spl Theta/ is estimated by simulation. The bound is shown to be tight over a wide range of H.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.945260