Adaptive estimation of time delays in sampled data systems

An adaptive technique is developed which iteratively determines the time delay between two sampled signals that are highly correlated. Although the procedure does not require a priori information on the input signals, it does require that the signals have a unimodal or periodically unimodal cross-correlation function. The adaptive delay algorithm uses a gradient technique to find the value of the adaptive delay that minimizes the mean-squared (MS) error function. This iterative algorithm is similar to the adaptive filter coefficient algorithm developed by Widrow. However, the MS error function for the adaptive delay is not quadratic, as it is in the adaptive filter. A statistical analysis determines the value of the convergence parameter which effects rapid convergence of the adaptive delay. This convergence parameter is a function of the power of the input signal. Computer simulations are presented which verify that the adaptive delay correctly estimates the time delay difference between two sinusoids, including those in noisy environments. The adaptive delay is also shown to perform correctly in a time delay tracking application.