Maximum-likelihood estimation of complex sinusoids and Toeplitzcovariances
Turmon, M.J.; Miller, M.I.
Signal Processing, IEEE Transactions on
Volume 42, Issue 5, May 1994 Page(s):1074 - 1086
Digital Object Identifier 10.1109/78.295210
Summary: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
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