Effects of attenuation factor on adaptive time delay estimation

The effects of a nonunity attenuation factor on the performance of an adaptive time delay estimation algorithm are studied using both deterministic and stochastic averaging. Analysis shows that failing to estimate such an attenuation factor may degrade the performance of the algorithm. When the adaptive delay estimator is augmented with an attenuation factor estimator, larger adaptive gain is desired to estimate the time variant delay. When there is noise in the signal, first order stochastic averaging analysis reveals that, if the attenuation factor is estimated, the estimator is biased. It is nevertheless true that the time delay estimator is unbiased