System identification using a linear combination of cumulant slices

A linear approach to identifying the parameters of a moving-average (MA) model from the statistics of the output is presented. First, it is shown that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. Then, this result is used to obtain a well-conditioned linear method for estimating the MA parameters of a nonGaussian process. The linear combination of slices used to compute the MA parameters can be constructed from different sets of cumulants of different orders, provided a general framework in which all the statistics can be combined. It is not necessary to use second-order statistics (autocorrelation slice), and therefore the proposed algorithm still provides consistent estimates in the presence of colored Gaussian noise. Another advantage of the method is that while most linear methods give totally erroneous estimates if the order is overestimated, the proposed approach does not require a previous estimation of the filter order. The simulation results confirm the good numerical conditioning of the algorithm and its improvement in performance in comparison to existing methods