Robust hyperbolic tangent Geman-McClure adaptive filter based on NKP decomposition and its performance analysis

For the identification of long impulse response systems in impulsive noise environments, existing algorithms have disadvantages such as slow convergence speed, large steady-state error, and poor tracking performance. In this brief, we propose the nearest Kronecker product decomposition based robust hyperbolic tangent Geman-McClure adaptive filter (NKP-HTGM) and analyze its performance. This algorithm uses the Geman-McClure function under hyperbolic tangent framework to remove the characteristic of the abnormal amplitude in the dataset, significantly improving the robustness against impulsive noise. Moreover, a novel variable step-size method (VSS) is introduced to further enhance the performance of NKP-HTGM (VSS-NKP-HTGM). Finally, the simulation results validate the effectiveness of the NKP-HTGM algorithm in system identification and the correctness of the theoretical analysis.