ARMA parameter estimation using only output cumulants

The authors develop two algorithms to estimate the parameters of a nonminimum phase autoregressive moving average (ARMA) system which is excited by an unobservable i.i.d. nonGaussian process. AR parameters are obtained in the usual way-via the higher-order Yule-Walker equations based either on the autocorrelations or the cumulants. The first method uses q (where q is the MA order) one-dimensional slices of the output cumulant, whereas the second method uses only two such slices to compute the MA parameters. Neither method involves computation of the residual (i.e., AR compensated) time series of polynomial factorization. Extensions to 2D and multichannel systems, as well as to time-recursive versions, are also developed. Both methods handle Gaussian noise of unknown power spectral densities, at the input as well as the output