Optimum estimation of time delay by a generalized correlator

Optimum filters are designed to enhance the estimation of time delay between signals received at two spatially separate sensors. The resulting filters are placed in the predetection stage of a basic cross correlator. The transfer functions of the optimum filters are derived to operate according to two stated performance criteria. One selected criterion maximizes the expected peak at the time delay relative to the total background noise, and the other minimizes the difference between the incoming signal at the time delay and its estimated value. The flexibility and simplicity of the derivations lend themselves to the generalization of results and clarity of interpretation. The derived filters are contrasted with those found in the literature. One of the present filters is identical to that obtained by other authors when using the criterion of maximum likelihood. The reason for the difference between the present and maximum likelihood filters from the Eckart filter is pinpointed. Finally, the relationships among the various optimum and ad hoc filters are clarified.