On Cross Correlation Based Discrete Time Delay Estimation

The cross correlation function (CCF) is a powerful tool in time delay estimation and parabola functions are widely used as parametric models of it. However, no study has been done on the accuracy of the parabola approximation of CCF. In this paper, we analyze the CCF of multi-sensors and derive the analytic forms of CCF for the stationary processes of the exponential auto-correlation function with respect to two important types of sensor kernels. We demonstrate that the Gaussian function is a better and more robust approximation of CCF than the parabola in these cases. This new approach leads to higher precision in time delay estimation using the CCF peak locating strategy.