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.

中文翻译：

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关于参数谱估计问题的适定性及其数值解

本文涉及一个谱估计问题，我们希望找到与估计的二阶统计量一致的谱密度函数。它是一个允许多个解的逆问题，可以根据先验函数来选择一个解。我们表明，当以参数方式制定时，问题是适定的，并且解决方案参数持续依赖于先验函数。通过这种方式，我们能够获得可容许光谱密度的平滑参数化。基于这个结果，从数值考虑，通过变量的双射变化对问题进行重新参数化，然后使用延拓法计算唯一解参数。数值方面，例如所提出的算法的收敛性和某些计算程序得到解决。