Linking auto- and cross-correlation functions with correlation equations: Application to estimating the relative travel times and amplitudes of multipath

A location problem is considered where the sound which propagates along multipath are impractical to model because the environment is poorly known. The acoustic bandwidth is assumed to be large enough so that the cross-correlation functions between pairs of receivers contain multiple peaks from multipath. The highest peak may not correspond to the difference in path lengths between the source and the receivers. Using similarities in the patterns of peaks in auto-and cross-correlation functions, an algorithm is developed to identify which cross-correlation peak corresponds to the difference in first arrivals, which can be used for locating the source if these arrivals are straight. The similarities are expressed with new "correlation equations." The number of lag-type correlation equations is O((RN2)-N-2), where N is the typical number of multipath at each of R receivers. The correlation equations may be impractical to solve exactly. Accurate solutions are found in simulations for the numbers, relative travel times, and amplitudes of all the multipath with the aid of a new "augmented-template correlation function" which is a cross-correlation of nonnegative lags of an auto-correlation function with lags from a cross-correlation function. The technique relies on time series which are filtered to yield one dominant source. (C) 1998 Acoustical Society of America.