Identification of nonminimum phase linear stochastic systems

We consider the identification of time-invariant, nonminimum phase, stochastic systems driven by non-Gaussian white noise, given only the noisy observations of the system output. A two-step procedure is proposed. In the first step a spectrally equivalent minimum phase (SEMP) system is estimated using a standard technique that exploits only the second order statistics of the measurements. In the second step partial, 4th order cumulants of the measurements are 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 mild sufficient conditions. Simulation results are also presented in support of the theory.