Time delay estimation using phase data

The estimation of time delays between two received signals using phase measurements is discussed and the accuracy of such estimates is detailed. For the ideal case of statistically independent noise and no scattering at the receiver locations, it is shown that phase data regression lines yield time delay estimates with the same accuracy as other optimal time delay estimation procedures. For less ideal situations, the potential advantages of time delay estimation using phase data are discussed and illustrated. It is shown that regression analysis of phase estimates at properly selected frequencies can sometimes be employed to reduce bias errors in time delay estimates due to correlated receiver noise. It is also shown that the estimation errors due to scattering at the receiver location can often be assessed in nonparametric terms to provide time delay estimates with a realistic error bound.