On the application of cross correlation function to subsample discrete time delay estimation

Cross correlation function (CCF) of signals is an important tool of multi-sensors signal processing. Parabola functions are commonly used as parametric models of the CCF in time delay estimation. The parameters are determined by fitting samples near the maximum of the CCF to a parabola function. In this paper we analyze the CCF for the stationary processes of exponential auto-correlation function, with respect to two important types of sensor sampling kernels. Our analysis explains why the parabola is an acceptable model of CCF in estimating the time delay. More importantly, we demonstrate that the Gaussian function is a better and more robust approximation of CCF than the parabola. This new approximation approach leads to higher precision in time delay estimation using the CCF peak locating strategy. Simulations are also carried out to evaluate the performance of the proposed estimation method for different sample window sizes and signal to noise ratios. The new method offers significant improvement over the current parabola based method.