Partial Update Algorithms and Echo Delay Estimation

Abstract

In this paper, we introduce methods for extracting an echo delay between speech signals using adaptive filtering algorithms. Time delay estimation is an initial step for many speech processing applications. Conventional techniques that estimate a time difference of arrival between two signals are based on the peak determination of the generalized cross-correlation between the signals. To achieve a good precision and stability in estimation, the input sequences have to be multiplied by an appropriate weighting function. Regularly, the weighting functions are dependent on the signals power spectra. The spectra are generally unknown and have to be estimated in advance. An implementation of the time delay estimation via the adaptive least mean squares is analogous to estimating the Roth generalized cross-correlation weighting function. The estimated parameters using the adaptive filter have a smaller variance, because it avoids the need for the spectrum estimation. In the following, we discuss proportionate and partial-update adaptive techniques and consider their performance in term of delay estimation.