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Variance of least squares estimators for a damped sinusoidal process

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2 Author(s)
Ying-Xian Yao ; PTPD, Ford Motor Co., Redford, MI, USA ; S. M. Pandit

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

Published in:

IEEE Transactions on Signal Processing  (Volume:42 ,  Issue: 11 )