Cramer-Rao bounds for deterministic modal analysis McWhorter, L. Todd ; Scharf, Louis L. "This work was supported by Bonneville Power Administration under Contract DEB17990BP07346 and by the Office of Naval Research under Contract N00014-89-J-1070." How accurately can deterministic modes be identified from a finite record of noisy data? In this paper we answer this question by computing the Cramer-Rao bound on the error covariance matrix of any unbiased estimator of mode parameters. The bound is computed for many of the standard parametric descriptions of a mode, including autoregressive and moving average parameters, poles and residues, and poles and zeros. Asymptotic, frequency domain versions of the Cramer-Rao bound bring insight into the role played by poles and zeros. Application of the bound to second- and fourth-order systems illustrates the coupling between estimator errors and illuminates the influence of mode locations on our ability to identify them. Application of the bound to the estimation of an energy spectrum illuminates the accuracy of estimators that presume to resolve spectral peaks. Colorado State University. Libraries 1993 text ; image application/pdf ECElls00005.pdf FACFECEN100394ARTI eng c1993 IEEE
Cramer-Rao bounds for deterministic modal analysis
McWhorter, L. Todd ; Scharf, Louis L.
"This work was supported by Bonneville Power Administration under Contract DEB17990BP07346 and by the Office of Naval Research under Contract N00014-89-J-1070."
How accurately can deterministic modes be identified from a finite record of noisy data? In this paper we answer this question by computing the Cramer-Rao bound on the error covariance matrix of any unbiased estimator of mode parameters. The bound is computed for many of the standard parametric descriptions of a mode, including autoregressive and moving average parameters, poles and residues, and poles and zeros. Asymptotic, frequency domain versions of the Cramer-Rao bound bring insight into the role played by poles and zeros. Application of the bound to second- and fourth-order systems illustrates the coupling between estimator errors and illuminates the influence of mode locations on our ability to identify them. Application of the bound to the estimation of an energy spectrum illuminates the accuracy of estimators that presume to resolve spectral peaks.
Colorado State University. Libraries
1993
text ; image
application/pdf
ECElls00005.pdf
FACFECEN100394ARTI
eng
c1993 IEEE