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Most of the cost functions of adaptive filtering algorithms include the square error, which depends on the current error signal. When the additive noise is impulsive, we can expect that the square error will be very large. By contrast, the cross error, which is the correlation of the error signal and its delay, may be very small. Based on this fact, we propose a new cost function called the mean square cross error for adaptive filters, and provide the mean value and mean square performancedoi:10.1186/s13634-021-00733-7 doaj:806ad4932ca24b3aa8a2e638e20efc1a fatcat:vwauaapo6zg4xk7zo3aznvws4u