Modeling Nonlinear Processes Using the Radial Basis Function-Based State-Dependent Autoregressive Models

Radial basis function-based state-dependent autoregressive (RBF-AR) models are a class of nonlinear combined models. This letter focuses on the parameter estimation for the RBF-AR models. To overcome the estimation difficulty due to the highly nonlinear relations between the parameters and the model output, the separated idea is used to transform the original optimization problem into a quadratic and a nonlinear optimization problems. Applying the hierarchical identification principle and the multi-innovation theory, two interactive algorithms are proposed for the RBF-AR models. In addition, an approach based on data weighting is proposed to overcome the data saturation in the algorithms. The simulation results verify the effectiveness of the proposed algorithms from the aspects of parameter estimation accuracy and prediction performance.