A Family of Data-Reuse-Based Recursive Generalized Maximum Correntropy Algorithm

Adaptive filtering algorithms (AFAs) have seen significant advancements, particularly in handling non-Gaussian signals with impulsive characteristics. Traditional AFAs, relying on Gaussian models, often struggle with such signals, leading to performance deterioration. This article addresses this challenge by employing the -norm as a cost function, deriving robust AFAs like the recursive generalized maximum correntropy (RGMC) algorithm. The RGMC algorithm, while accurate in steady-state environments, faces convergence issues with varying forgetting factors. To mitigate this, the article introduces the data-reuse (DR) strategy, enhancing the RGMC algorithm's convergence speed and steady-state performance. Furthermore, the article extends the DR-RGMC algorithm to sparse system identifications, presenting the DR proportional RGMC (DR-PRGMC) algorithms, DR-PRGMC-I and DR-PRGMC-II. These variants are designed to exploit sparse characteristics, improving filtering performance in sparse environments. The article also provides a detailed performance analysis, including mean convergence and steady-state excess mean-square-error (EMSE) analyses, supported by simulation results. The innovative approaches and comprehensive analyses make this article a crucial read for those interested in advancing adaptive filtering techniques.