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Identification of an ARX-type Nonlinear Rational Model Based on the Renyi Error Entropy and the Epanechnikov Kernel

Shaoxue Jing*, Tianhong Pan, and Quanmin Zhu
International Journal of Control, Automation, and Systems, vol. 20, no. 10, pp.3233-3240, 2022

Abstract : "In this paper, a novel stochastic gradient algorithm based on the minimum Renyi entropy is proposed to identify a nonlinear rational model contaminated by the impulse noise. Firstly, the minimum error entropy using the Epanechnikov kernel is taken to suppress the impulse noise. Secondly, the stochastic gradient of the Renyi entropy rather than the Shannon entropy is adopted to decrease the computational cost. Finally, an adaptive step size considering the energy of the errors is used to accelerate the algorithm. The proposed algorithm is validated by numerical examples and case study. Results show that the algorithm can give accurate estimates with a fast convergence rate for the nonlinear rational model with the impulse noise. "

Keyword : "Adaptive step size, Epanechnikov kernel, impulse noise, nonlinear rational model, parameter estimation, Renyi entropy, stochastic information gradient. "

 
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