2018/02/26 by Bin Zhu, Zhu, Bin
Engineering · Mathematics · #30E05 #47A57 #47A68 #65L05 #65L20 #93E12 #Control Systems and Identification #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1802.09330
openalex publication_date 2018/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.