Measures of tracking performance for the LMS algorithm

Two measures of tracking performance for the LMS (least mean square) algorithm are compared and contrasted. These are the conventional time-average or temporal mean of the nonstationary mean-squared error (MSE) in excess of the minimum attainable MSE, and the novel temporal root-mean-squared value of the excess MSE, which takes into account the temporal variance as well as the temporal mean of the nonstationary MSE. These measures are evaluated for the LMS algorithm applied to two time-variant system identification problems, one involving a random Markov system and the other a periodic system. Optimal step-size parameters and minimum misadjustments are evaluated. It is shown that the conventional time-average performance measure is adequate only when the degree of nonstationarity is sufficiently low. For higher degrees of nonstationarity, the time-average performance measure can be misleading in studies of the tracking behavior of the LMS algorithm