L₁/L₂-Mode Switching Adaptive Filter Algorithm Based on Novel Mean Square Deviation Analysis

This paper proposes an L
₁
/L
₂
-mode switching adaptive filter algorithm by comparing the performances in L
₁
and L
₂
modes. In the L
₁
or L
₂
mode, the proposed algorithm adopts, as the update equation, that of the normalized sign (NS) algorithm or that of the normalized least mean square (NLMS) algorithm, respectively. By analyzing the mean square deviations (MSDs) of the NS algorithm as well as of the NLMS algorithm, the algorithm selects the better mode in the sense that the next MSD of the algorithm in the selected mode becomes smaller than that in the other mode. The algorithm mainly operates in the L
₁
mode when the impulsive noises occur but in the L
₂
mode otherwise, which leads to robustness against the impulsive noises like the NS algorithm and also leads to a low steady-state misalignment like the NLMS algorithm. Furthermore, the proposed algorithm is faster than the NS and the NLMS algorithms in terms of the convergence rate. A modified reset algorithm is also applied to maintain performance when the unknown system is abruptly changed. Simulations conducted in various system identification scenarios show that the proposed algorithm outperforms the conventional algorithms in terms of the convergence rate and the steady-state misalignment, whenever impulsive noises exist or not.