Title :
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
fDate :
11/1/1996 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
