Geometric Algebra Correntropy: Definition and Application to Robust Adaptive Filtering

Correntropy is an efficient tool for analyzing higher order statistical moments in non-Gaussian noise environments. Correntropy has been used with real, complex, and quaternion data. However, there is no literature studying the correntropy with geometric algebra data. The geometric algebra has been widely used in the engineering applications including the signal processing and image processing. From the probabilistic view, this brief presents a novel geometric algebra correntropy (GAC) which represents the similarity measure between two random geometric algebra (multivector valued) variables. Then, we develop the adaptive filter based on the maximum GAC criteria (MGACC), which is robust against the non-Gaussian noise. Simulation is conducted to verify the advantages of the proposed adaptive algorithm under the non-Gaussian environment.