Variance of least squares estimators for a damped sinusoidal process

Author

Yao, Ying-Xian ; Pandit, Sudhakar M.

Author_Institution

PTPD, Ford Motor Co., Redford, MI, USA

Volume

42

Issue

11

fYear

1994

fDate

11/1/1994 12:00:00 AM

Firstpage

3016

Lastpage

3025

Abstract

The variance of least squares estimators for the parameter estimation of a damped sinusoidal process is analyzed, based on first-order perturbation. Analytical expressions for the variances of the frequency, damping factor, amplitude, and phase estimators are derived. Explicit expressions are given for both damped and undamped single-mode cases. The effect of mode separation on the accuracy is investigated through the two-mode case. The dependence of the variances on number of data points, model order, signal-to-noise ratio, and mode separation is investigated, both analytically and numerically, for practical applications. Extensive Monte Carlo simulation results are given to verify, enhance, and illustrate the analytical expressions

Keywords

Monte Carlo methods; amplitude estimation; digital simulation; frequency estimation; least squares approximations; phase estimation; signal processing; Monte Carlo simulation; amplitude; damped sinusoidal process; damping factor; data points; first-order perturbation; frequency; least squares estimators; mode separation; model order; parameter estimation; phase estimator; signal-to-noise ratio; single-mode cases; Amplitude estimation; Analysis of variance; Damping; Frequency estimation; Least squares approximation; Parameter estimation; Phase estimation; Sampling methods; Signal analysis; Signal to noise ratio;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.330362

Filename

330362