A family of constrained maximum mixture total correntropy algorithms for adaptive filtering

As a robust adaptive filtering algorithm, the constrained maximum total correntropy (CMTC) algorithm exhibits good filtering performance compared to existing methods, especially when the system has noisy input and output signals. However, CMTC experiences some performance degradation when using a fixed kernel bandwidth. Therefore, we propose the constrained maximum mixture total correntropy (CMMTC) algorithm, which leverages mixture correntropy to enhance flexibility by adjusting the proportion of different kernel bandwidths. In general, increasing kernel bandwidth typically leads to a reduction in the convergence speed of CMTC. Hence, based on a combined strategy, we innovatively introduce two adaptive versions of the CMMTC algorithm by considering a variable mixture coefficient. For the proposed CMMTC algorithm, under some reasonable assumptions, we have derived the mean convergence condition and the theoretical mean-square-deviation expression, which are also verified by simulation results. In comparison with other related algorithms, several experimental results demonstrate that the proposed algorithms can realize superior filtering performance.