A fast robust LMS algorithm utilizing the dynamics of a damped pendulum

In this paper, a new fast LMS-based adaptive algorithm is proposed. It is derived by incorporating a damping force in the LMS update recursion similar to the force acting upon a damped planar pendulum. An expression for evolution and the steady-state behavior for the mean weight vector is developed. This expression provides a mathematical bound which constrains the parameter that controls the maximum contribution of the introduced damping force. Furthermore, an expression for the mean square error is developed to examine algorithm behavior in the mean square sense. Simulation results show an improved robust performance for the new algorithm as compared with the conventional LMS and Momentum LMS (MLMS) algorithms in smoothly tracking the optimal solution in stationary, correlated and nonstationary noisy environments. Moreover, simulation examples include system identification with varying power environments.