Identification of linear stochastic systems via second- and fourth-order cumulant matching

The identification problem for time-invariant single-input single-output linear stochastic systems driven by non-Gaussian white noise is considered. The system is not restricted to be minimum phase, and it is allowed to contain all-pass components. A least-squares criterion that involves matching the second- and the fourth-order cumulant functions of the noisy observations is proposed. Knowledge of the probability distribution of the driving noise is not required. An order determination criterion that is a modification of the Akaike information criterion is also proposed. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are presented to illustrate the method.