Spectral Density Estimation for a Class of Spectrally Correlated Processes

Abstract

We study the estimation problem of the spectral density function for harmonizable non‐stationary processes. More precisely, we consider spectrally correlated processes whose spectral measure has the support contained in the union of unknown lines with possibly non‐unit slopes. We propose the frequency‐smoothed periodogram along the estimated support line as an estimator of the spectral density function. We show the mean‐square consistency of the proposed estimator. Additionally, we discuss the estimation of the support line in a specific model with its applications in locating a moving source. Finally, we present simulations confirming the proven results.