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The state of charge (SOC) plays a crucial role in battery management system, which directly reflects the usage of the battery. Recently the extreme learning machine (ELM) model as a data-driven method has been utilized to estimate SOC due to its simple single hidden layer structure and fast learning performance. The battery management system, however, may usually work in complex working conditions, which means that the non-Gaussian complex noise (or outliers) interference problem may exist in some measurement data for model training. So the performance of the classical ELM with mean square error (MSE) criterion may be degraded under this case. This work considers Non-Gaussian noise interference issue, the MSE in ELM is substituted by mixture generalized maximum correntropy criterion (MGMCC), and a novel robust ELM model is developed to improve the SOC estimation capability which mainly relies on the stable and robust nonlinear similarity characteristics of the MGMCC. A data set from a Panasonic 18,650 battery cell is used to verify the robustness of the proposed model, the experiment results demonstrate that it can achieve better estimation performance in terms of different evaluation metrics compared with the traditional methods. • A mixture GMCC is defined which can be as a learning criterion for NN model. • A robust ELM with MGMCC is developed to improve robust performance of the traditional ELM. • The MMGCCELM based SOC estimation approach is proposed to improve estimation accuracy under non-Gaussian noise interferences. [ABSTRACT FROM AUTHOR]