Time delay estimation by combining efficient algorithms and generalized cross-correlation methods
This paper analyzes the performance of the two efficient algorithms (presented by Stein and Cabot) for time delay of arrival estimation (TDE) between two signals. It is shown that these estimators are unbiased, and explicit expressions for the TDE mean-square error (MSE) are presented. It is also shown how to improve the performance of these algorithms by combining them with generalized cross-correlation (GCC) methods. In the analysis, we only assume stationary signals which are not necessarily Gaussian. The first algorithm (Stein) is indirect and uses the symmetry of the cross-correlation function between the two signals. It is shown here that the TDE-MSE depends on the unknown delay. The performance of this algorithm can be improved by combining it with the GCC method, and the pertinent TDE-MSE expressions are presented. The second algorithm (Cabot) is based on finding the zero of the cross-correlation function between one signal and the Hilbert transform of the other signal. Here, too, the pertinent TDE-MSE expressions are presented. This algorithm is also combined with the GCC method, and the optimal weight function for which the TDE-MSE expression coincides with the Cramer-Rao lower bound is found.