Identification of an ARX model with impulse noise using a variable step size information gradient algorithm based on the kurtosis and minimum Renyi error entropy

ARX model is an autoregressive model with exogenous terms. Because of its simplicity and easy parameterization, the ARX model has been widely used in various applications. However, most reports on ARX identification are about Gaussian noise or white noise environment. In many practical industrial applications, impulse noise widely exists. For systems contaminated by this noise, the performance of the mean square error algorithm will deteriorate. To get more accurate results, a variable step size stochastic information gradient algorithm is proposed. The algorithm is based on the Renyi square error entropy and introduces a fourth‐order statistic of the error–kurtosis–into the variable step size, which not only effectively suppresses the impulse noise, but also accelerates the convergence speed. At the same time, a simple method of determining the maximum step size is given. The computational cost and the convergence are also analyzed. Numerical experiments and case study show that for the ARX model disturbed by impulse noise, the proposed algorithm can obtain high‐precision parameter estimates with fast convergence speed.