Improved parameter estimation with noisy data for linear models using higher order statistics and inverse filter criteria

The problem of estimating the parameters of a non-Gaussian ARMA signal model using higher order statistics is considered. We propose and analyze a novel class of criteria involving explicit higher order whitening, where higher order cumulants of deconvolved data are exploited at a finite number of lags excluding the zero lag. In the presence of a class of measurement noise of unknown covariance/cumulant function, the proposed criteria are shown to yield strongly consistent parameter estimators unlike the Wiggins-Donoho-Shalvi-Weinstein class involving implicit higher order whitening, where higher order cumulants of deconvolved data are exploited only at zero lag.<>