Variable Step Filtered-X Least Mean Square Algorithm Based on Piecewise Logarithmic Function

In order to improve the problem that the filtered-x least mean square (FxLMS) algorithm cannot take into account the convergence speed, steady-state error during active noise control.A piecewise variable step size FxLMS algorithm based on logarithmic function(PLFxLMS) is proposed, and the genetic algorithm are introduced to optimize the parameters of logarithmic variable step size FxLMS(LFxLMS), improved logarithmic variable step size Films(IFxLMS), and PLFxLMS algorithms. Bandlimited white noise is used as the input signal, FxLMS, LFxLMS, ILFxLMS, and PLFxLMS algorithms are used to conduct active noise control simulation, and the convergence speed and steady-state characteristic of four algorithms are comparatively analyzed.Compared with the other three algorithms, the PLFxLMS algorithm proposed in this paper has the fastest convergence speed, and small steady-state error. The PLFxLMS algorithm can effectively improve the convergence speed and steady-state error of the FxLMS algorithm that cannot be controlled at the same time,and achieve the optimal effect.