Approximate realization and model reduction of non-minimum phase stochastic systems

This paper deals with the stochastic realization and reduction of non-minimum phase, linear time-invariant systems. Assuming that the input is non-Gaussian, stationary and white, we propose the use of 2nd- and higher-order output statistics to identify a finite-dimensional ARMA model. Both the input/output, and state space approaches are considered. We show that higher-order output cumulants are useful in estimating the AR coefficients of the minimum-phase (MP) part, and in providing us with a means for model order determination. Higher-order cumulants of the innovations are exploited to realize the all-pass (AP) part of the ARMA model.