A new method for unbiased time‐delay estimation in noisy environments

When input data are contaminated with noise, the least mean square time-delay estimation (LMSTDE) actually gives a biased estimate. In this paper, we propose and analyse a new adaptive filter structure for time-delay estimation (TDE), which can eliminate this bias. A new adaptive criterion is then constructed. We determine the corresponding analytical solution, and develop the stochastic gradient algorithm to calculate the optimum solution. Convergence of the stochastic gradient algorithm is established, and upper bounds on the step sizes are deduced for guaranteed convergence. Simulation results are included to illustrate the superiority of the new model and corroborate the theoretical developments. Copyright © 2007 John Wiley & Sons, Ltd.