A parameter estimation approach to time delay estimation

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. In addition, the parameter estimation approach is expected to have a smaller variance since it avoids the need for spectral estimation. Indeed, experimental results from two examples show that the time delay estimate, found by least squares parameter estimation, has a smaller variance than the approximate maximum likelihood estimator of Hannan-Thomson where spectral estimation is required.