A Robust Least Mean M-estimate Adaptive Filtering Algorithm Based on Geometric Algebra for System Identification

In this paper, a novel robust algorithm called geometric algebra least mean M-estimate (GA-LMM) is proposed, which is the extension of the conventional LMM algorithm in GA space. To further improve the convergence performance, variable step-size GA-LMM (VSS-GA-LMM) algorithm is also proposed, which effectively balances the trade-off between convergence rate and steady-state misalignment. Finally, a multidimensional system identification problem is considered to verify the performance of the proposed GA-LMM and VSS-GA-LMM algorithms. Simulation results show that the proposed algorithms are superior to other GA-based algorithms in terns of convergence rate and steady-state misalignment in impulsive noise environments.