A least-squares algorithm for multipath time-delay estimation

We consider the problem of estimating the arrival times of overlapping ocean-acoustic signals from a noisy received waveform that consists of attenuated and delayed replicas of a known transient signal. We assume that the transmitted signal and the number of paths in the multipath environment are known and develop an algorithm that gives least-squares (LS) estimates of the amplitude and time delay of each path. Direct computation of the LS estimates would involve minimization of a highly oscillatory error function. By allowing the amplitudes to be complex valued, a much smoother error function that is easier to minimize using gradient-based techniques is obtained. Using this property and the knowledge (derived from the data) of the spacing between adjacent minima in the actual LS error function, an efficient algorithm is devised. The algorithm is a function of a data-dependent parameter, and we give rules for choosing this parameter. The algorithm is demonstrated on a broad-band signal, using simulated data. The proposed method is shown to achieve the Cramer-Rao lower bound over a wide range of SNR´s. Comparisons are made with alternating projection (AP) and estimate maximize (EM) algorithms