A modified version of the Pisarenko method to estimate the power spectral density of any asymptotically wide sense stationary vector process

摘要

The Pisarenko method estimates the power spectral density (PSD) of Gaussian wide sense stationary (WSS) 1-dimensional (scalar) processes when the PSD is Lipschitz. In this paper we modify the Pisarenko method to estimate the generating function of a sequence of block Toeplitz matrices from another sequence of matrices when both sequences are asymptotically equivalent. This modified version of the Pisarenko method allows us to estimate the PSD of any asymptotically WSS (AWSS) multidimensional (vector) process even if the process is not Gaussian and even if the PSD is continuous, but not Lipschitz.