Closed loop linear model validation and order estimation using polyspectral analysis

Previously, various techniques have been proposed for closed loop system identification using polyspectral analysis. Having obtained a model, how do we know if the fitted model is “good?” This paper is devoted to the problem of model validation using polyspectral analysis. We propose simple statistical tests based upon the estimated polyspectrum (integrated bispectrum and/or integrated trispectrum) of an output error signal or the estimated cross-polyspectrum between the external reference and the output error signal. Model order estimation is a by-product of the model validation procedure. Illustrative computer simulation examples are presented