The least square estimation of the basic frequency for periodically non-stationary random signals

Estimation of the basic frequency (non-stationarity period) of periodically correlated random processes (PCRPs) - the mathematical model of hidden periodicity - by the least squares (LS) method is considered. The properties of the basic frequency estimator are analyzed, on the basis of the nonlinear equations that represent a necessary condition for the existence of the minimum of the mean and covariance function statistics. Using the small parameter method, asymptotical unbiasedness and consistency of the estimators are proved, and the formulae for bias and variance are obtained in the first approximation. These formulae are concretized for particular PCRP cases. Finally, the method is verified using simulated sequences and a real-life vibration signal. (C)& nbsp;2021 Elsevier Inc. All rights reserved.

Automated summary

This article explores the estimation of the basic frequency of periodically correlated random processes using the least squares method. The properties of the estimator are analyzed, and bias and variance formulas are obtained based on nonlinear equations. The method is validated using simulated sequences and a real-life vibration signal.