Identification of linear systems with noisy input using fourth-order cumulants

An identification method is presented for estimating the parameters of a discrete-time linear dynamic system excited by non-Gaussian input signals using the fourth-order cumulants of the input and output signals, both of which are contaminated by additive Gaussian noise. Two types of estimators of the fourth-order cumulants of the input and output signals are proposed for this method. The first one is conventional. The second one, which is new, only allows the use of a recursive algorithm for computing the parameter estimators. The parameter estimators obtained by this algorithm are shown to be strongly consistent under certain weak conditions.