This paper presents a variant of the "Third-Order Recursion (TOR)" method for bispectral estimation of transfer-function parameters of a non-minimum-phase all-poles system. The modification is based on the segmentation of system-output data into coupled records, instead of independent records. It consists of considering the available data at the left and the right of each record as not null and taking them as the data corresponding to the preceding and succeeding record respectively. The proposed variant can also be interpreted as a "Constrained Third-Order Mean (CTOM)" method with a new segmentation in overlap records. Simulation results show that this new segmentation procedure gives more precise system parameters than the TOR and CTOM methods, to be obtained. Finally, in order to justify the use of bispectral techniques, the influence of added white and colored Gaussian noise on the parameter estimation is also considered.

This paper addresses the problem of estimating the parameters of multivariate ARMA processes by using higher-order statistics called cumulants. The main objective in this paper is to extend the idea of the q-slice algorithm in univariate ARMA processes to multivariate ARMA processes. It is shown for a multivariate ARMA process that the MA coefficient matrices can be estimated up to postmultiplication of a permutation matrix by using the third-order cumulants and of an extended permutation matrix by using the fourth-order cumulants. Simulation examples are included to demonstrate the effectiveness of the proposed method.