Power-spectrum identification in terms of rational models

A technique is described for the identification of unknown power-spectral densities from sampled data in terms of a rational function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> . The problem is reduced to the minimization of a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> parameters, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> is the order of the numerator of the model. This criterion, called the "minimum residual" criterion, reduces to the maximum likelihood criterion when the observed signal is Gaussian. A computational technique is described for minimizing this function which uses filtering and correlation to obtain the gradient and an iterative descent method due to M. J. D. Powell for minimization. Some computational results are given in which the method is compared with all-pole and conventional spectrum estimation techniques.