Maximum-likelihood estimation of complex sinusoids and Toeplitz covariances

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Abstract
In an extension of previous methods for maximum-likelihood (ML) Toeplitz covariance estimation, new iterative algorithms for computing joint ML estimates of complex sinusoids in unknown stationary Gaussian noise are proposed. The number of sinusoids is assumed known, but their frequencies and amplitudes are not. The iterative algorithm, an adaptation of the expectation-maximization (EM) technique, proceeds from an initial estimate of the mean and Toeplitz covariance, and iterates between estimating the mean given the current covariance and vice versa, with likelihood increasing at each step. The resulting ML covariance estimates are compared to conventional estimators and Cramer-Rao bounds. An analysis of the Kay and Marple (1981) data set is also presented. The effectiveness of the new algorithm for estimating means in unknown noise is investigated, and the usefulness of simultaneously estimating the covariance and the mean is demonstrated