Robust nonlinear autoregressive moving average model parameter estimation using stochastic recurrent artificial neural networks.

Abstract

In this study, we introduce a new approach for estimating linear and nonlinear stochastic autoregressive moving average (ARMA) model parameters, given a corrupt signal, using artificial recurrent neural networks. This new approach is a two-step approach in which the parameters of the deterministic part of the stochastic ARMA model are first estimated via a three-layer artificial neural network (deterministic estimation step) and then reestimated using the prediction error as one of the inputs to the artificial neural networks in an iterative algorithm (stochastic estimation step). The prediction error is obtained by subtracting the corrupt signal of the estimated ARMA model obtained via the deterministic estimation step from the system output response. We present computer simulation examples to show the efficacy of the proposed stochastic recurrent neural network approach in obtaining accurate model predictions. Furthermore, we compare the performance of the new approach to that of the deterministic recurrent neural network approach. Using this simple two-step procedure, we obtain more robust model predictions than with the deterministic recurrent neural network approach despite the presence of significant amounts of either dynamic or measurement noise in the output signal. The comparison between the deterministic and stochastic recurrent neural network approaches is furthered by applying both approaches to experimentally obtained renal blood pressure and flow signals.