VARIANCE OF LEAST-SQUARES ESTIMATORS FOR A DAMPED SINUSOIDAL PROCESS

In this paper, the variance of least squares estimators for the parame ter estimation of a damped sinusoidal process is analyzed, based on fi rst-order perturbation. Analytical expressions for the variances of th e frequency, damping factor, amplitude, and phase estimators are deriv ed. Explicit expressions are given for both damped and undamped single -made cases. The effect of mode separation on the accuracy is investig ated through the two-mode case. The dependence of the variances on num ber of data points, model order, signal-to-noise ratio, and mode separ ation is investigated, both analytically and numerically, for practica l applications. Extensive Monte Carlo simulation results are given to verify, enhance, and illustrate the analytical expressions.