Blind deconvolution based criteria for parameter estimation with noisy data

The author considers the problem of estimating the parameters of a stable, scalar ARMA(p,q) signal model (causal or noncausal, minimum phase or mixed phase), driven by an independent and identically distributed nonGaussian sequence. The driving noise sequence is not observed. A class of criteria that involve explicit higher order whitening, where higher order cumulants of deconvolved data are exploited at a finite number of lags excluding the zero lag, is proposed. In the presence of a class of measurement noise of unknown covariance/cumulant function, the criteria are shown to yield strongly consistent parameter estimators. Computer simulations illustrate the approach