Third-order cumulant RLS algorithm for nonminimum ARMA systems identification

Abstract As higher-order cumulants preserve both the magnitude and the phase information of received signals, higher-order statistics have been considered as powerful signal processing tools for identifying nonminimum phase systems. A third-order cumulant-based recursive least-squares (CRLS) algorithm for the identification of time-invariant as well as time-variant nonminimum phase ARMA systems has been successfully developed in this paper. A cost function based on the third-order cumulant and/or the third-order cross cumulant is defined for the development of the CRLS system identification algorithm. The CRLS algorithm are then applied to different MA and ARMA models. In the case of identifying the parameters of an MA model, a direct application of the CRLS algorithm is adequate. When dealing with an ARMA model, the poles and the zeroes are estimated separately. In estimating the zeroes of the ARMA model, the construction of a residual time-series sequence for the MA part is required. In the present investigation, the strong convergency and consistency of the CRLS algorithm are analyzed and simulations on the time-invariant and time-variant nonminimum phase systems show that the results of applying the proposed CRLS approach are quite satisfactory. In addition, because of the third-order cumulant properties, the CRLS algorithm can also suppress the Gaussian noise and is capable of providing an unbiased estimate under a noisy environment.