The performances of least mean square (LMS) time delay estimator (TDE) are analyzed using biased and unbiased estimation methods.Then a modified LMS method based on Treichler’s

γ

-LMS algorithm is developed for unbiased estimation in the presence of white input and output noises

in which the input noise variance is simply obtained by the Euclidean geometric interpretation of the best approximation in adaptive filters without any a priori knowledge of the interference.With this estimated variance

the proposed bias-free LMS-TDE can iteratively eliminate the input noise effects and actually enhance the true peak

thus it can reduce the probability of anomalous peak in noisy environments at lower signal-to-noise ratio (SNR) levels.It gets rid of the assumptions that the input and output noise powers are the same or their ratio is known

or the

signals are all white processes.Simulations and real data application are both provided to validate its effectiveness.