Parameter estimation problems with singular information matrices

Author

Stoica, Petre ; Marzetta, Thomas L.

Author_Institution

Dept. of Syst. & Control, Uppsala Univ., Sweden

Volume

49

Issue

1

fYear

2001

fDate

1/1/2001 12:00:00 AM

Firstpage

87

Lastpage

90

Abstract

The case of a singular Fisher information matrix (FIM) represents a significant complication for the theory of the Cramer-Rao lower bound (CRB) that is usually handled by resorting to the pseudoinverse of the Fisher matrix. We take a different approach in which the CRB is derived as the solution to an unconstrained quadratic maximization problem, which enables us to handle the singular case in a simple yet rigorous manner. When the Fisher matrix is singular, except under unusual circumstances, any estimator having the specified bias derivatives that figure in the CRB must have infinite variance

Keywords

information theory; matrix inversion; parameter estimation; CRB; Cramer-Rao lower bound; infinite variance; parameter estimation problems; pseudoinverse Fisher matrix; singular Fisher information matrix; singular information matrices; unconstrained quadratic maximization problem; Blind equalizers; Control systems; Covariance matrix; Density functional theory; Information technology; Neural networks; Parameter estimation; Positron emission tomography; Symmetric matrices; System identification;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.890346

Filename

890346