Power Spectral Density Estimation Using Statistical Smoothing of the Linear Difference Model Parameters of the Random Time Series

Abstract

The parametric estimation problem of a power spectral density for a random process is considered. A linear difference equation with constant parameters as a discrete model of a random process time series is used. An approach that allows simultaneous parameters estimation of the model numerator and denominator is proposed. Such an approach made it possible to increase the computational efficiency of parametric estimation procedures of spectral density power. For a stable estimation of linear difference model parameters, an overdetermined system of equations is used. An increase in the equations number provides a statistical smoothing of the calculated estimates of the definable model parameters. In order to find the best estimates of the model parameters, the least squares method is used. The problem of choosing the model order is reviewed. As the simplest criterion for choosing the linear difference model order, we use the minimum of the residuals square sum. The scheme of the algorithm for the parameters estimating of a linear difference model is given.