Markov-based eigenanalysis method for frequency estimation

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Abstract
This paper proposes an eigenanalysis-based method for estimating the frequencies of complex-valued sine waves. The basic idea behind this method consists of using a set of linearly independent vectors that are orthogonal to the signal subspace spanned by the principal eigenvectors of the data covariance matrix. Exploiting that orthogonality condition gives an overdetermined system of linear equations, the unknown parameters of which are uniquely related to the frequencies. Analytical expressions are derived for the covariances of the equation errors in the sample version of the aforementioned linear system of equations. Based on these expressions a Markov-like estimate of the unknown parameters is introduced, which asymptotically (with respect to either the number of data samples or the signal-to-noise ratio) provides the minimum variance frequency estimates in a fairly large class of consistent estimators. The paper includes Monte-Carlo simulations that support the theoretical analysis results and show that those results may apply to scenarios with rather low values of the number of data samples and the signal-to-noise ratio

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