Title :
Cramer-Rao bounds for deterministic modal analysis
Author :
McWhorter, Todd ; Scharf, Louis L.
Author_Institution :
Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA
fDate :
5/1/1993 12:00:00 AM
Abstract :
The accuracy with which deterministic modes can be identified from a finite record of noisy data is determined 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 influence of mode locations on the 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
Keywords :
parameter estimation; poles and zeros; spectral analysis; Cramer-Rao bounds; asymptotic frequency-domain; autoregressive parameters; deterministic modal analysis; energy spectrum; error covariance matrix; finite record; fourth-order systems; mode locations; mode parameters; moving-average parameters; noisy data; parameter estimation; parametric descriptions; poles; residues; spectral peaks resolution; unbiased estimator; zeros; Chromium; Covariance matrix; Energy resolution; Frequency domain analysis; Least squares methods; Modal analysis; Noise measurement; Parameter estimation; Poles and zeros; Signal processing;
Journal_Title :
Signal Processing, IEEE Transactions on