Time-delay estimation via optimizing highly oscillatory cost functions

In sonar and many other applications, time-delay estimation is an important problem. When bandpass probe signals are used, the correlation function between the received and the known transmitted signals oscillates near the carrier frequency of the transmitted signal. In this case, many existing time-delay estimation algorithms perform poorly due to converging to local optimum points. In this paper, two efficient algorithms, Hybrid-WRELAX and EXIP-WRELAX, are proposed to deal with the above problem. They are relaxation-based global minimizers of a highly oscillatory nonlinear least-squares cost function. Both algorithms are shown to achieve the Cramer-Rao bound and require only a sequence of weighted Fourier transforms.