Prediction in LMS-type adaptive algorithms for smoothly time varying environments

The aim of this correspondence is to improve the performance of the least mean square (LMS) and normalized-LMS (NLMS) adaptive algorithms in tracking of time-varying models. A new procedure for estimation of weight increments for including in the LMS-type adaptive algorithms is proposed. This procedure applies a simple smoothing on the increment of the estimated weights to estimate the speed of weights. The estimated speeds are then used to predict the weights for the next iteration. The efficiency of the algorithm is confirmed by simulation results. The algorithm has a very low order of arithmetic complexity. Moreover, this procedure could be combined with a wide class of adaptive filters (e.g., RLS, gradient lattice algorithm, etc.) to improve their behaviors. The proposed algorithm is obtained by simplifying a Kalman filter. To this end, a Markov model of second order is considered for the weight vector. This model shows that the estimation of parameter increments inferred from the predicted parameters improves the tracking performance.