A generalized maximum correntropy based constraint adaptive filtering: Constraint-forcing and performance analyses

The quadratic cost functions, exemplified by mean-square-error, often exhibit limited robustness and flexibility when confronted with impulsive noise contamination. In contrast, the generalized maximum correntropy (GMC) criterion, serving as a robust nonlinear similarity measure, offers superior performance in such scenarios. In this paper, we develop a recursive constrained adaptive filtering algorithm named recursive generalized maximum correntropy with a forgetting factor (FF-RCGMC). This algorithm integrates the exponential weighted GMC criterion with a linear constraint framework based on least-squares. However, the lack of constraint information during the learning process may lead to divergence or malfunctioning of FF-RCGMC after a certain number of iterations because of round-off errors. To rectify this deficiency, we introduce a constraint-forcing strategy into FF-RCGMC, resulting in a more stable variant termed robust type constraint-forcing FF-RCGMC (CFFF-RCGMC). In the context of CFFF-RCGMC, we embark on a thorough examination of its computational burden, encompassing both mean and mean-square stability analyses, along with an in-depth exploration of its transient and steady-state filtering characteristics under a set of plausible assumptions. Our simulation-based evaluations, specifically tailored for system identification tasks within non-Gaussian noisy environments, unequivocally underscore the excellent performance of CFFF-RCGMC when against its relevant algorithmic counterparts.