Hierarchical Estimation Approach for RBF-AR Models With Regression Weights Based on the Increasing Data Length

In the radial basis function-based state-dependent autoregressive (RBF-AR) models with regression weights, the local linear models are included between the hidden layers and the output layers of the networks. The parameter estimation for the RBF-AR models with regression weights is studied in this brief. Considering the separable feature of the models, two criterion functions based on the increasing data length are defined to fit the observation data of the whole dynamical process. Two sub-algorithms are proposed by minimizing the criterion functions. Aiming to overcome the existence of the singular matrix during the Newton search and to make the algorithm more stable, a positive definite diagonal matrix is introduced to the algorithm. Based on the hierarchical principle, a hierarchical Newton recursive algorithm is proposed, which can realize the on-line parameter estimation. Simulation results verify the validity.