Hybrid Geometric Algebra Correntropy: Definition and Application to Robust Adaptive Filtering

In order to address the performance degradation of the geometric algebra LMS algorithms (GA-LMS) in the face of non-Gaussian disturbances, this brief proposes a robust adaptive filtering algorithm based on hybrid maximum geometric algebra correntropy (HMGACC) perspective. Specially, we define the hybrid geometric algebra correntropy (HGAC) cost function, which can increase the flexibility of the correntropy. Secondly, we introduce a proportionality parameter to make the HGAC algorithm more general, which can be changed into a traditional single kernel GAC algorithm by changing the proportionality parameter. Furthermore, the addition of the proportionality parameter also allows for a non-fixed form of step-size, i.e., the step-size of the proposed algorithm in this brief is a hybrid step-size, which will be more useful for us to improve the performance of the algorithm. Finally, in the experimental simulations, the proposed algorithm can achieve better convergence and steady-state performance in comparison with other competing algorithms under different non-Gaussian disturbances, which confirms the feasibility of the proposed method.