Robust Partially Coupled Parameter Estimation Approach for the Nonlinear Exponential Autoregressive Model With Non‐Gaussian Noise Based on the Cauchy Kernel Correntropy

This paper focuses on the parameter estimation issue of the nonlinear exponential autoregressive model with non‐Gaussian noise. By exploiting the property that the Cauchy kernel correntropy is insensitive to non‐Gaussian noise and the kernel bandwidth, a Cauchy kernel correntropy‐based criterion function is presented to obtain robust estimation performance. Since the nonlinear exponential autoregressive model includes the coupling term of the linear and nonlinear parameters, the identification model is decomposed into two fictitious sub‐models with a common parameter vector. A Cauchy kernel correntropy‐based robust partially coupled recursive least squares stochastic gradient algorithm is proposed by coordinating the coupling term arising from the model decomposition. Compared with the existing recursive least squares and least mean squares algorithms, the proposed algorithm not only demonstrates robustness to non‐Gaussian noise but also achieves higher estimation accuracy. The simulation examples exhibit the effectiveness of the proposed algorithm.