Identification of Linear Stochastic Systems via Cumulant Matching

The problem of identification of 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 moreover, 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 well known Akaike information criterion is also proposed. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are also presented to illustrate the method.