Adaptive time delay estimation in noisy environments

A model to improve the performance of an adaptive tracker for delay estimation in noisy environments is proposed. The system consists of an adaptive filter and a time varying gain control. While the adaptive filter inserts an appropriate time shift to the incoming signal, the gain control will provide a proper scaling to the filter output respective to the additive noise. Both the filter coefficients and the variable gain are adjusted simultaneously by minimizing the output mean-square error according to Widrow´s least mean square (LMS) algorithm. This arrangement can decouple the adaptation of time shift and noise statistics, which in turn will give rise to a better convergence characteristics of the delay. Simulation results are included to demonstrate its capability in tracking time shift accurately under noisy environments