Comparative study of five LMS-based adaptive time delay estimators

A number of adaptive algorithms have been proposed to model the delay between signals received at two spatially separated sensors using an FIR filter. Among them, there are the LMSTDE, CTDE, ETDE, SETDE and ETDGE, which are computationally efficient because of the LMS implementation. These five methods are compared in terms of estimation accuracy and computational complexity. It is proved that the LMSTDE and ETDGE attain performance for sufficiently long filter lengths, although the ETDE and SETDE perform similarly to the ETDGE at high signal-to-noise ratio (SNR) and low SNR, respectively. The CTDE involves minimum computational load but it is the worst estimator in the presence of noise. In addition, optimum realisations of the LMSTDE as well as the ETDE and its variants are derived and their delay variances are compared with the Cramer-Rao lower bound. Simulation results show that ETDGE outperforms the other four methods for a wide range of filter lengths at different SNRs