Threshold effects in time delay estimation using narrowband signals

The results of a numerical study of time delay estimation via cross-correlation using narrowband signals are described and compared with theoretical performance predictions. Of particular interest is the correlator performance in the ambiguity dominated region of signal to noise ratio (SNR) where there is difficulty in distinguishing between the various correlation peaks. An approximate theoretical result for the probability of an anomalous estimate (i.e., deciding on the wrong peak) is derived and shown to agree well with the experimental results, except for very high SNR. The variance of the estimate, in the ambiguity dominated region of SNR, is compared with the Barankin bound of Chow and Schultheiss. The Barankin bound is shown to be a more realistic performance bound than the Cramer-Rao bound at moderate SNR; however, the threshold SNR above which the Barankin bound is predicted to fall rapidly below the Cramer-Rao bound is 10-20 dB lower than that observed using the correlator.