Parameter identification of a nonlinear radial basis function-based state-dependent autoregressive network with autoregressive noise via the filtering technique and the multiinnovation theory

This article studies the parameter estimation problems of radial basis function-based state-dependent autoregressive models with autoregressive noises (RBF-ARAR models). To reduce the effect of the colored noise to parameter estimation, the data filtering technique is applied and a filtering based generalized stochastic gradient algorithm is derived for the RBF-ARAR models. In order to achieve more accurate parameter estimates, a filtering based multiinnovation generalized stochastic gradient (F-MI-GSG) algorithm is proposed by utilizing the current and past innovations. Introducing two forgetting factors, a filtering based multiinnovation generalized forgetting gradient algorithm is developed to improve the transient performance of the F-MI-GSG algorithm. The effectiveness of the proposed algorithms is verified through the simulation examples.