Approaches of FIR system identification with noisy data using higher order statistics

The problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is discussed. The system is driven by an independently identically distributed nonGaussian sequence that is not observed. The noise is additive and may be colored and nonGaussian. Following some existing linear parametric approaches to this problem, a linear method and a modification to an existing linear method are proposed for consistent parameter estimation in measurement noise under the assumption that the system order is known. Both recursive closed-form and batch least-squares versions of the parameter estimators are presented. The existing and the proposed linear methods utilize only a partial set of the relevant output statistics (this restriction being necessary to obtain a linear estimator), whereas there exist nonlinear method that exploit a much larger set of output statistics. A simulation example where two existing linear methods and the two new methods are compared to two existing nonlinear methods is presented