Spectral estimation by least-squares optimization based on rational covariance extension

This paper proposes a new spectral estimation technique based on rational covariance extension with degree constraint. The technique finds a rational spectral density function that approximates given spectral density data under constraint on a covariance sequence. Spectral density approximation problems are formulated as nonconvex optimization problems with respect to a Schur polynomial. To formulate the approximation problems, the least-squares sum is considered as a distance. Properties of optimization problems and numerical algorithms to solve them are explained. Numerical examples illustrate how the methods discussed in this paper are useful in stochastic model reduction and stochastic process modeling.