Robust spectral factor approximation of discrete-time frequency domain power spectras

Abstract

This paper presents a subspace-based identification algorithm for estimating the state-space quadruple [ A , B , C , D ] of a minimum-phase spectral factor from matrix-valued power spectrum data. For a given pair [ A , C ] with A stable, the minimum-phase property is guaranteed via the solution of a conic linear programming (CLP) problem. In comparison with the classical LMI-based solution, this results in a more efficient way to minimize the weighted 2-norm of the error between the estimated and given power spectrum. The conic linear programming problem can be solved in a globally optimal sense. This property is exploited in the derivation of a separable least-squares procedure for the (local) minimization of the above 2-norm with respect to the parameters of the minimal phase spectral factor. The advantages of the derived subspace algorithm and the iterative local minimization procedure are illustrated in a brief simulation study. In this study, the effect of dealing with short length data sets for computing the power spectrum, on the estimated spectral factor, is illustrated.