Modified leaky delayed LMS algorithm for imperfect estimate system delay

This paper proposes a modified leaky delayed least-mean-square (MLDLMS) algorithm, aiming to circumvent algorithm instability problems under imperfect system delay estimates. In addition, a model for the first and second moments of the algorithm is proposed. Such a model is obtained without invoking the independence theory and considering a slow adaptation condition. Numerical simulations corroborate the very good agreement between the results obtained with the Monte Carlo method and those from the proposed model for colored Gaussian inputs.