Time delay estimation using the LMS adaptive filter--Static behavior

A new application of the LMS adaptive filter, that of determining the time delay in a signal between two split-array outputs, is described. In a split array sonar, this time delay can be converted to the bearing of the target radiating the signal. The performance of such a tracker is analyzed for stationary broad-band targets. It is shown that a continuous adaptive tracker performs within 0.5 dB of the Cramér-Rao lower bound. Further, performance predictions are developed for a discrete adaptive tracker which demonstrates excellent agreement with simulations. It is shown that the adaptive tracker can have significantly less sensitivity to changing input spectra than a conventional tracker using a fixed input filter.