Higher-order statistics-based input/output system identification and application to noise cancellation

Higher-than-second-order statistics-based input/output identification algorithms are proposed for linear and nonlinear system identification. The higher-than-second-order cumulant-based linear identification algorithm is shown to be insensitive to contamination of the input data by a general class of noise including additive Gaussian noise of unknown covariance, unlike its second-order counterpart. The nonlinear identification is at least as optimal as any linear identification scheme. Recursive-least-squares-type algorithms are derived for linear/nonlinear adaptive identification. As applications, the problems of adaptive noise cancellation and time-delay estimation are discussed and simulated. Consistency of the adaptive estimator is shown. Simulations are performed and compared with the second-order design.Part of the results of this paper were presented at the workshop on HOSA, Vail, CO, June 1989, and at the International Conference on ASSP, Albuquerque, NM, April 1990. The work of G. B. Giannakis in this paper was supported by LabCom Contract 5-25254.