Two-stage extended recursive gradient algorithm for locally linear RBF-based autoregressive models with colored noises

A novel parameter identification method for locally linear radial basis function-based autoregressive models in presence of colored noises is proposed in this paper. Taking advantage of the global nonlinear and local linear structural characteristics of the models, two dynamical criterion functions are constructed based on the separated parameters to realize the dynamical acquisition and utilization of the entire process data. Two recursive gradient sub-algorithms are derived for estimating the separated parameters by using the nonlinear gradient optimization. To coordinate the associated variables existing in the sub-algorithms and to estimate the unmeasurable noise terms, we combine the sub-algorithms and propose a two-stage extended recursive gradient (2S-ERG) algorithm. In addition, an extended recursive gradient algorithm is given as a comparison. The feasibility of the 2S-ERG algorithm is validated by numerical simulations.