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

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. (c) 2005 Elsevier Ltd. All rights reserved.