Abstract
In this paper, we address the problem of determining maximum-likelihood estimates of sinusoid parameters from a signal that consists of sinusoids and additive noise. We present three algorithms that integrate interval methods for global optimization with procedures that decompose the problem into smaller ones. Interval methods represent a global optimization technique that is based upon the branch and bound principle. More specifically, we decompose the problems via the expectation-maximization algorithm and variations of the coordinate descent algorithm. Although, we have not proven that the proposed algorithms converge to the global optimum, their performance in our simulation example was much superior to that of the popular iterative quadratic maximum likelihood (IQML) method.
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Edmonson, W.W., Lee, W.H. & Anderson, J.M.M. Interval Methods for Sinusoidal Parameter Estimation: A Comparative Analysis. Reliable Computing 6, 321–336 (2000). https://doi.org/10.1023/A:1009986615302
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DOI: https://doi.org/10.1023/A:1009986615302