Combined-Step-Size Geometric-Algebra Affine Projection Versoria algorithm against impulsive noise

In this brief, a new geometric-algebra affine projection Versoria (GA-APV) algorithm is proposed. Compared with the geometric-algebra LMS/NLMS algorithms, the GAAPV algorithm derived by shows faster convergence for highly correlated inputs and robustness to non-Gaussian impulsive signals due to the reuse of input signals and the geometricalgebra Versoria cost function. As well, a variant of GA-APV known as combined-step-size GA-APV (CSS-GA-APV) algorithm is designed to reconcile the convergence speed and steady-state error. Finally, numerical experiments have been performed to testify the tracking and steady-state performances of the GAAPV and CSS-GA-APV algorithms.