On the Well-Posedness of a Parametric Spectral Estimation Problem and Its Numerical Solution

Bin Zhu

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arXiv · 1802.09330

On the Well-Posedness of a Parametric Spectral Estimation Problem and Its Numerical Solution

Bin Zhu

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Abstract

This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a solution can be based on prior functions. We show that the problem is well-posed when formulated in a parametric fashion, and that the solution parameter depends continuously on the prior function. In this way, we are able to obtain a smooth parametrization of admissible spectral densities. Based on this result, the problem is reparametrized via a bijective change of variables out of a numerical consideration, and then a continuation method is used to compute the unique solution parameter. Numerical aspects such as convergence of the proposed algorithm and certain computational procedures are addressed. A simple example is provided to show the effectiveness of the algorithm.

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Bin Zhu. 2018-02-26. On the Well-Posedness of a Parametric Spectral Estimation Problem and Its Numerical Solution. https://arxiv.org/abs/1802.09330

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