A quantitative study of optimum and sub-optimum filters in the generalized correlator

Various optimum and sub-optimum filters have been added to the basic cross-correlator in order to enhance its time delay estimation capability in the presence of noise. These pre-detection filters include the Hannan-Thomson, the Eckart, the Smoothed Coherence Transform, some least-squares, and two optimum filters recently derived by the authors. Here, a quantitative comparison of all six filters has been conducted by extensive simulation for various input signal and noise ratio and signal and noise bandwidths. The results define the actual enhancement in time delay detection when using the optimum filters and the amount of performance degradation from the optimum for the other filters. The rank ordering of the filters is carried out. Histograms of the time delay estimates, their mean and variance are presented. Confirmation of analytical predictions is noted.