Finding the right cross-correlation peak for locating sounds in multipath environments with a fourth-moment function

To locate calling animals in reverberant environments from recordings on widely separated receivers, a fourth-moment "Augmented-Template Correlation Function" (ATCF) helps identify which of many peaks in each cross-correlation function is that corresponding to the difference in travel times for the first arrivals (reference-lag). This peak may not be the largest. The ATCF, by providing an approximate correlation between auto- and cross-correlation functions, can be orders of magnitude more efficient in selecting the reference-lag than the alternative of randomly selecting peaks. The ATCF's efficacy increases with the number of paths and their signal-to-noise ratios.