Optimal step size of least mean absolute third algorithm

This paper proposes an optimized least mean absolute third (OPLMAT) algorithm to improve the capability of the adaptive filtering algorithm against Gaussian and non-Gaussian noises when the unknown system is a time-varying parameter system under low signal–noise rate. The optimal step size of the OPLMAT is obtained based on minimizing the mean-square deviation at the current time. In addition, the mean convergence and steady-state error of the OPLMAT algorithm are derived theoretically, and the computational complexity of OPLMAT is analyzed. Furthermore, the simulation experimental results of system identification presented illustrate the principle and efficiency of the OPLMAT algorithm. Simulation results demonstrate that the proposed algorithm performs much better than the LMAT and NLMAT algorithms.