Recursive Constrained Maximum Correntropy Criterion Algorithm for Adaptive Filtering

Recently, the gradient based constrained maximum correntropy criterion (GCMCC) algorithm has received considerable attention since it provides superior performance to the traditional methods and is robust to the non-Gaussian noise. However, the convergence of GCMCC algorithm depends on the learning rate. With a large learning rate, GCMCC converges fast but achieves a high steady state mean square deviation (MSD), and vice versa. To balance the convergence rate and the MSD, we propose a novel recursive CMCC (RCMCC) algorithm in this brief by utilizing the matrix inversion lemma. Furthermore, we provide a computationally efficient version of RCMCC (ERCMCC) algorithm by using some approximations. More importantly, we provide the convergence analysis of the RCMCC algorithm, and derive the stability condition and theoretical MSD. The theoretical analysis and superiorities of RCMCC and ERCMCC are validated by simulations.