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AR Spectrum analysis based on a noisy autocovariance sequence

This paper presents two methods for AR spectrum analysis based on a noisy autocovariance sequence. Unlike most of the traditional spectrum analysis methods, we assume that there is an observed autocovariance sequence, possibly with errors. Such a situation occurs in the Fourier spectroscopy. We fit AR models to this autocovariance sequence by two methods. The one is based on the least squares fit of the autocovariances to the Yule-Walker equations and the other is based on the maximum likelihood estimation of partial autocorrelation coefficients by nonlinear optimization techniques. We apply these two methods to simulated and real plasma data and compare their results.