Optimum leakage factor for the MOV-LMS algorithm in nonlinear modeling and control systems

This work studies the Minimum Output Variance Least Mean Square Estimator (MOV-LMS) when the output of the adaptive filter is constrained by a saturation-type nonlinearity. This situation is typical in several adaptive modeling and control systems where the associated hardware and transducers have a finite power handling capability. Analytical expressions are obtained for the behaviors of the mean weight vector and for mean square error for Gaussian inputs and slow learning. The optimum leakage factor is determined, which provides an unbiased solution to the associated nonlinear mean square estimation. problem. Monte Carlo simulations show excellent agreement between model and simulations for transient and steady-state conditions. The results in this paper demonstrate that the MOV-LMS algorithm with the optimized leakage factor has a superior steady-state performance than the LMS algorithm in the studied nonlinear environment.