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

Abstract

Summary 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.

Kernel‐based regularization least squares algorithm for nonlinear time‐delayed systems using self‐organizing maps

“…For example, in Reference 28, Li et al constructed a kernel function‐based nonlinear system, which had a good performance in fitting nonlinear systems. In Reference 29, Zhou et al studied some recursive parameter estimation algorithms for a nonlinear radial basis function‐based state‐dependent autoregressive (RBF‐AR) time series model. In Reference 30, Brenner et al proposed a regularization method for solving the ill‐posed problem.…”

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

“…In terms of the identification of RBF-AR models, several variable projection (VP) algorithms were proposed based on the orthogonal projection [17,18,19]. Because the VP algorithms are off-line methods, in order to realize the on-line identification of this kind of models, a multi-innovation recursive algorithm was developed by employing the innovation modification [20]. However, the parameter estimation performance of the multi-innovation recursive algorithm has a lot to do with the selection of the innovation length, and it often takes many tests to get an appropriate innovation length.…”

Parameter identification of a nonlinear radial basis function‐based state‐dependent autoregressive network with autoregressive noise via the filtering technique and the multiinnovation theory

“…[20][21][22] In order to continue to update the parameter estimates of the RBF-AR models when new sample data come, some on-line gradient-based methods have also been developed by applying the recursive technique. 23 In engineering, the input and output signals always involve the noise interferences from the process environments. 24,25 There are two forms of external noises, the white noise and the colored noise.…”

“…Regarding for the identification of the RBF‐AR models, some off‐line methods, including the structured nonlinear parameter optimization methods and the variable projection methods, have been proposed 20‐22 . In order to continue to update the parameter estimates of the RBF‐AR models when new sample data come, some on‐line gradient‐based methods have also been developed by applying the recursive technique 23 …”