APPROACHES TO FIR SYSTEM-IDENTIFICATION WITH NOISY DATA USING HIGHER-ORDER STATISTICS

In this paper we address the problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output. The system is driven by an independent and identically distributed (i.i.d.) non-Gaussian sequence that is not observed. The noise is additive and may be colored and non-Gaussian. Following some existing linear parametric approaches to this problem, we propose a new linear method, and a modification to an existing linear method, 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 methods that exploit a much larger set of output statistics. We conclude by presenting a simulation example where two existing linear methods and the two new methods are compared to two existing nonlinear methods. © 1990 IEEE