Identification of non-minimum phase linear stochastic systems

The identification of time-invariant, non-minimum phase, stochastic systems driven by non-Gaussian white noise is considered, given only (the noisy observations of the system output. A two-step procedure is proposed. In the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements. In the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros. Knowledge of the probability distribution of the driving noise is not required. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are also presented in support of the theory.