Robust Constrained Generalized Correntropy and Maximum Versoria Criterion Adaptive Filters

The constrained least mean square algorithm is extensively used for adaptive filtering applications which need to satisfy a set of linear constraints. However, it is not robust when non-Gaussian or impulsive noise is present at the error sensor. To effectively overcome this issue, in this brief, we propose the constrained generalized maximum correntropy criterion (CGMCC) algorithm. To further improve steady state convergence behavior of the adaptive filter in such scenarios, we also propose the constrained maximum Versoria criterion (CMVC) algorithm. The expressions of the optimal weight vector for both the proposed algorithms are derived. Bound on learning rates are also derived to ensure the stability of the proposed adaptive systems in the mean square sense. The computational expense of the proposed algorithms is also studied. Simulation studies carried out demonstrate the improvement in steady state convergence performance and robustness achieved by the proposed algorithms.