Digital algorithm for maximisation of symmetric ambiguity functions and application to signal time-delay estimation

Ambiguity functions are usually symmetric around their maximum. In such a case, a consistent estimator of their median value can also detect their maximum. A digital algorithm searches for the zero-crossing point of the Hilbert transform of the estimated function samples. The performance of such a method is analysed by a reduced Taylor expansion, depending on the second-order statistics of the estimated ambiguity samples. The accuracy is explicitly provided in the case of time-delay estimation between random Gaussian signals, corrupted by Gaussian noises. The optimal length of an FIR implementation of the Hilbert filter is also discussed with reference to the generalised cross-correlation method