Recursive methods for estimating the radial basis function-based state-dependent autoregressive model

Identifying a nonlinear radial basis function-based state-dependent autoregressive (RBF-AR) time series model is the basis for solving the corresponding prediction and control problems. This paper studies some recursive parameter estimation algorithms for the RBF-AR model. Considering the difficulty of the nonlinear optimal problem arising in estimating the RBF-AR model, an overall forgetting gradient algorithm is deduced based on the negative gradient search. A numerical method with a forgetting factor is provided to solve the problem of determining the optimal convergence factor. In order to improve the parameter estimation accuracy, the multi-innovation identification theory is applied to develop an overall multi-innovation forgetting gradient (O-MIFG) algorithm. The simulation results indicate that the estimation model based on the O-MIFG algorithm can capture the dynamics of the RBF-AR model very well.