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Abstract This paper discusses the identification problem of the nonlinear exponential autoregressive model in the non‐Gaussian noise environment. To suppress the negative influence caused by the non‐Gaussian noise on the accuracy of the identification, this paper employs a Cauchy kernel correntropy‐based criterion function to present a robust gradient algorithm for calculating the parameter estimates of the model. To solve the difficulty of selecting the step‐size in the gradient algorithm, this paper derives an optimal step‐size related to the bandwidth of the Cauchy kernel. Moreover, in order to improve the accuracy of the parameter estimations, a Cauchy kernel correntropy‐based robust multi‐innovation identification method is developed by utilizing the multi‐innovation identification theory. Two simulation examples exhibit that the proposed algorithms can effectively reduce the negative influence of the non‐Gaussian noise on parameter estimation in contrast with the conventional least mean squares algorithm.
Zhao et al. (Sun,) studied this question.