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Highlights • This paper provides the development of the robust censored adaptive algorithm for the impulsive noise. • This paper gives Consideration of non-Gaussian background noise as different from previous literature which only consider the Gaussian noise. • Theoretical insights into the mean and mean square performance of the CR-MCC algorithm are provided. • Simulation examples to demonstrate the performance of the proposed algorithm in impulsive noise scenarios are given. Abstract Censored observations and impulsive measurement noise are encountered in many practical applications of adaptive signal processing. Traditional adaptive filtering algorithms may fail to work in such cases. This paper proposes a robust adaptive filter algorithm predicated on maximum correntropy criteria (MCC) for censored regression. A detailed performance analysis in terms of mean and mean-square behaviour is provided. Simulations with Gaussian and non-Gaussian noise are presented to verify the theoretical results, and to demonstrate the superior performance of the proposed algorithm over existing algorithms. [ABSTRACT FROM AUTHOR]