Identification of nonlinear stochastic systems described by PARAFAC-Volterra

In this paper we extend the Alternating RGLS (Recursive Generalized Least Square) algorithm proposed for the identification of the reduced complexity Volterra model describing stochastic nonlinear systems corrupted by AR (AutoRegressive) noise to case of systems corrupted by ARMA (AutoRegressive Moving Average) noise. The reduced Volterra model used is the 3rd order PARAFC-Volterra model provided using the PARAFAC (PARAllel FACtor) tensor decomposition of the Volterra kernels of order higher than two of the classical Volterra model. The recursive stochastic algorithm ARGLS (Alternating RGLS) consists of the execution in an alternating way of the classical RGLS algorithm developed to identify the linear stochastic input-output models. The efficiency of the proposed identification approach is proved using Monte Carlo simulation on a nonlinear satellite channel.