A robust variable projection algorithm for RBF-AR model

The radial basis function network-based autoregressive (RBF-AR) model is a powerful statistical model which can be expressed as a linear combination of nonlinear functions and frequently appears in a wide range of application fields. Variable projection algorithm is designed for solving smooth separable optimization problems with least squares form and has been used as an efficient tool for the identification of RBF-AR model. However, in real applications, the observations are usually disturbed by non-Gaussian noise or contain outliers. This often leads to nonlinear regression problems. Since there are both linear and nonlinear parameters in such problems, how to optimize such models is still challenging. In this paper, we design a robust variable projection algorithm for the identification of RBF-AR model. The proposed method takes into account the coupling of the linear and nonlinear parameters of RBF-AR model, which eliminates the linear parameters by solving a linear programming and optimizes the reduced function that only contains nonlinear parameters. Numerical results on RBF-AR model to synthetic data and real-world data confirm the effectiveness of the proposed algorithm.