Least-squares time-delay estimation for transient signals in a multipath environment

The problem of estimating the arrival times of overlapping ocean-acoustic signals from a noisy received waveform that consists of scaled and delayed replicas of a deterministic transient signal is considered. It is assumed that the transmitted signal and the number of paths in the multipath environment are known, and an algorithm is developed that gives least-squares estimates of the amplitude and time delay of each path. A method is given to ensure that the global minimum of the error surface is found in spite of the existence of numerous local minima. The algorithm is then extended to the case in which the transmitted signal is not known precisely, but is assumed to belong to a parametric class of signals. The extended algorithm additionally obtains the parameters that characterize the transmitted signal. The algorithm is demonstrated on the class of signals consisting of gated sinusoids, using both simulated and experimental data.