Maximum likelihood identification of correlation matrices for estimation of power spectra at arbitrary resolutions

In spectral estimation spectra are usually derived from an AR or MA model fitted to the data. An implicit step common to these methods is the estimation of the correlation matrix. In this paper our approach consists in doing maximum likelihood identification of structured correlation matrix. We have used two different structures corresponding to Toeplitz matrices and to matrices with DFT representation. Both structures are related to time invariant series. We have studied the performances of the spectral estimates obtained from our correlation matrix. In particular we show mean square error versus SNR plots for the frequency estimation of two noisy sinusoids.