Statistical convergence of the adaptive least mean fourth algorithm

This paper presents a statistical convergence analysis of the adaptive least mean fourth (LMF) algorithm that minimizes the estimation error in the mean fourth sense. A set of nonlinear evolution equations for the mean and mean-squared behavior of the algorithm is derived. A condition for the mean convergence is also found, and it turns out that the convergence of the LMF algorithm strongly depends on the choice of initial conditions. Through the extensive computer simulations, we have observed that there are many cases in which the LMF algorithm outperforms the LMS algorithm from the viewpoints of the convergence speed as well as the precision of adaptations.