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Present techniques that estimate the difference in arrival time between two signals corrupted by noise, received at two separate sensors, are based on the determination of the peak of the generalized cross correlation between the signals. To achieve good resolution and stability in the estimates, the input sequences are first weighted. Invariably, the weights are dependent on input spectra which are generally unknown and hence have to be estimated. By approximating the time shift as a finite impulse response filter, estimation of time delay becomes one of determination of the filter coefficients. With this formulation, a host of techniques in the well-developed area of parameter estimation is available to the time-delay estimation problem-with the possibilities of reduced computation time as compared with present methods. In particular, it is shown that the least squares estimation of the filter coefficients is equivalent to estimating the Roth processor. However, the parameter estimation approach is expected to have a smaller variance since it avoids the need for spectra estimation. Indeed, experimental results from two examples show that the Roth processor, found by least squares parameter estimation, has a smaller variance than the approximate maximum likelihood estimator of Hannan-Thomson where spectral estimation is required. A detector that uses the sum of the estimated parameters as a test statistic is also given, together with its receiver operating characteristics.