A novel filter-based multi-stage parameter estimation for a class of hybrid nonlinear models

This paper presents a novel recursive parameter estimation method to identify the gradient radial basis function based varying-coefficient autoregressive (GRBF-AR) model with colored noises. Considering the global nonlinearity and local linearity of the model, the identification process is divided into several stages to identify the linear parameters and the nonlinear parameters separately. Then, several improved stochastic gradient sub-algorithms are derived for estimating the separated parameters correspondingly, incorporating the multi-innovation theory to improve the estimation accuracy. To mitigate the negative influence of colored noises, this paper designs a linear prefilter to whiten the colored noise for obtaining the unbiased parameters. The convergence analysis and the simulation results demonstrate the effectiveness of the presented method.