Estimation of the parameters of a random amplitude sinusoid by correlation fitting

Author

Besson, Olivier ; Stoica, Petre

Author_Institution

Dept. of Avionics & Syst., Ecole Nat. Superieure d´´Ingenieurs de Constr. Aeronaut., Toulouse, France

Volume

44

Issue

11

fYear

1996

fDate

11/1/1996 12:00:00 AM

Firstpage

2911

Lastpage

2916

Abstract

We consider the best asymptotic accuracy that can be achieved when estimating the parameters of a random-amplitude sinusoid from its sample covariances. An estimator based on matching in a weighted least-squares sense the sample correlation sequence to the theoretical sequence is presented. The asymptotic properties of the estimator are analyzed. A lower bound on the estimation of the parameters from sample covariances is derived. This bound is shown to be attainable by appropriately choosing the weighting matrix. However, the unweighted nonlinear least-squares estimate performance is shown to come close to the lower bound. The influence of the number of samples, the number of correlation samples, and the lowpass envelope characteristics are studied. Finally, a comparison with Yule-Walker (YW) methods is given

Keywords

amplitude estimation; correlation methods; covariance matrices; estimation theory; least squares approximations; random processes; signal sampling; Yule-Walker methods; asymptotic accuracy; asymptotic properties; correlation fitting; correlation matching algorithm; correlation samples; covariance matrix; lower bound; lowpass envelope characteristics; parameter estimation; random amplitude sinusoid; sample correlation sequence; sample covariances; theoretical sequence; unweighted nonlinear least-squares estimate; weighted least-squares; weighting matrix; Amplitude estimation; Convergence of numerical methods; Covariance matrix; Least squares approximation; Least squares methods; Parameter estimation; Signal processing; Signal processing algorithms; Speech processing; Vectors;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.542455

Filename

542455