Variance of least squares estimators for a damped sinusoidal process

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