Robust constrained maximum total correntropy algorithm

•This paper proposes a novel constrained maximum total correntropy (CMTC) algorithm using the stochastic gradient.•The stability condition and mean square deviation (MSD) of CMTC are obtained for theoretical analysis in the paper.•This paper validates the correctness of the theoretical MSD and the superiorities of CMTC for noisy input and output by simulation results. Constrained adaptive filtering has been paid more attentions recently. As a robust constrained adaptive filtering algorithm, constrained maximum correntropy criterion (CMCC) has shown its superiority for the output data contaminated by heavy-tail impulsive noises. However, when both input and output are contaminated by noises, the performance of CMCC will deteriorate dramatically. To address this issue, based on an errors-in-variables (EIV) model for noisy input and output, this paper proposes a novel constrained maximum total correntropy (CMTC) algorithm using the stochastic gradient. Then, the stability condition and the mean square deviation (MSD) of CMTC are obtained for theoretical analysis. Finally, simulation results validate the correctness of the theoretical MSD and the superiorities of CMTC for noisy input and output.