publication . Article . 2005

Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds

S.T. Smith;
Open Access
  • Published: 01 Jun 2005 Journal: IEEE Transactions on Signal Processing, volume 53, pages 1,610-1,630 (issn: 1053-587X, Copyright policy)
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Abstract
Crame/spl acute/r-Rao bounds on estimation accuracy are established for estimation problems on arbitrary manifolds in which no set of intrinsic coordinates exists. The frequently encountered examples of estimating either an unknown subspace or a covariance matrix are examined in detail. The set of subspaces, called the Grassmann manifold, and the set of covariance (positive-definite Hermitian) matrices have no fixed coordinate system associated with them and do not possess a vector space structure, both of which are required for deriving classical Crame/spl acute/r-Rao bounds. Intrinsic versions of the Crame/spl acute/r-Rao bound on manifolds utilizing an arbitr...
Subjects
free text keywords: Signal Processing, Electrical and Electronic Engineering, Estimation theory, Combinatorics, Subspace topology, Linear subspace, Estimation of covariance matrices, Mathematics, Covariance matrix, Estimator, Invariant subspace, Covariance
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