Comparative study of five LMS-based adaptive time delay estimators

A number of adaptive algorithms have been proposed to model the delay betwe en signals received at two spatially separated sensors using an FIR filter. Among them, there an the LMSTDE. CTDE, ETDE, SETDE and ETDGE, which are co mputationally efficient because of the LMS implementation. These five metho ds are compared in terms of estimation accuracy and computational complexit y. It is proved that the LMSTDE and ETDGE attain identical performance for sufficiently long filter lengths, although the ETDE and SETDE perform simil arly to the ETDGE at high signal-to-noise ratio (SNR) and low SNR, respecti vely. The CTDE involves minimum computational load but it is the worst esti mator in the presence of noise. In addition, optimum realisations of the LM STDE as well as the ETDE and its Variants are derived and their delay varia nces are compared with the Cramer-Rao lower bound. Simulation results show that ETDGE outperforms the other four methods for a wide range of filter le ngths at different SNRs.