Nonlinear system identification using autoregressive quadratic models

Abstract

In this paper, we study the identification of a special class of nonlinear systems, Quadratic AutoRegressive Moving Average systems, QARMA. In the first part, we discuss the relationship between this model and the Volterra models and also the property of stability of these systems. The second part is devoted to the derivation of the two equation sets needed for a possibly time-variant QARMA identification. The equation sets use higher-order moments and the first set is derived under the assumption of finite length correlation of the input data. The coefficients of this first system depend on a mixed set of third- and fourth-order moments. The second set of equations assumes only unskewed input data and the equation coefficients are a linear combination of moments from the third up to the sixth order with the system coefficients at previous lags. In order to validate the identification methods and to numerically verify the accuracy of the estimated coefficients for both equation sets, the QARMA methods were applied to the deconvolution of L-PAM symbols, the rate of good estimation of these symbols allowing a numerical comparison between the respective performances of both equation sets. Another application presented in this paper is a Second-Order Volterra Model (SOVM) identification although the QARMA model cannot be strictly equal to a SOVM.