Identification of nonminimum phase systems using higher order statistics

A method is presented for identification of linear, time-variant, nonminimum phase systems when only output data are available. The input sequence need not be independent, but it must be non-Gaussian, with some special properties described in the test. The authors model a finite-dimensional system as an ARMA (autoregressive moving-average) rational function of known orders, but the special cases of AR, MA, and all-pass models are also considered. To estimate the parameters of their model, the authors utilize both second- and higher-order statistics of the output, which may be contaminated by additive, zero-mean, Gaussian white noise of unknown variance. The parameter estimators obtained are proved, under mild conditions, to be consistent. Simulations verify the performance of the proposed method in the case of relatively low signal-to-noise ratios, and when there is a model-order mismatch