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.

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This paper discusses a new adaptive tec:hrci qua for system i cienti -f i cation of a model ci. tic a sparse impulse rasponce. The standard tc:hn i qua + or adaptive identification uses a -filter with adaptive coefficients that range fr-os a coefficient far the zero delay ta p through a coefficient for the largest delay tap that is assumed to be in the system.When the system to be model led has a sparse impulse response many of these coefficients will converge to zero, or very small values. Since each coefficient is updated in eac:h iteration, a good deal of the adaptation is spent updating these unnecessary weights.The technique presented in this paper represents a new technique that serially adapts each delay tap value as wall as the coefficient value. Thus, using this new technique, the number of delay taps can be greatly reduced if the system has a sparse impulse response.