Fixed-point generalized maximum correntropy: Convergence analysis and convex combination algorithms

Compared with the MSE criterion, the generalized maximum correntropy (GMC) criterion shows a better robustness against impulsive noise. Some gradient based GMC adaptive algorithms have been derived and available for practice. But, the fixed-point algorithm on GMC has not yet been well studied in the literature. In this paper, we study a fixed-point GMC (FP-GMC) algorithm for linear regression, and derive a sufficient condition to guarantee the convergence of the FP-GMC. Also, we apply sliding-window and recursive methods to the FP-GMC to derive online algorithms for practice, these two called sliding-window GMC (SW-GMC) and recursive GMC (RGMC) algorithms, respectively. Since the solution of RGMC is not analyzable, we derive some approximations that fundamentally result in the poor convergence rate of the RGMC in non-stationary situations. To overcome this issue, we propose a novel robust filtering algorithm (termed adaptive convex combination of RGMC algorithms (AC-RGMC)), which relies on the convex combination of two RGMC algorithms with different memories. Moreover, by an efficient weight control method, the tracking performance of the AC-RGMC is further improved, and this new one is called AC-RGMC-C algorithm. The good performance of proposed algorithms are tested in plant identification scenarios with abrupt change under impulsive noise environment.