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One dimensional cumulant and auto-correlation output statistics are combined to form an overdetermined system of equations whose least-squares solution yields the coefficients of an ARMA model. The driving input noise is assumed to be non-Gaussian and white. The ARMA model is allowed to be non-minimum phase and even to contain all-pass factors. The special cases of AR and MA models are also included. The overdetermined nature of the method makes the solution practical for moderate output data lengths, when additive white Gaussian noise is considered. Simulations illustrate that our approach performs very well even at low signal-to-noise ratios.