Passive ranging errors due to multipath distortion of deterministic transient signals with application to the localization of small arms fire.

A passive ranging technique based on wavefront curvature is used to estimate the ranges and bearings of impulsive sound sources represented by small arms fire. The discharge of a firearm results in the generation of a transient acoustic signal whose energy propagates radially outwards from the omnidirectional source. The radius of curvature of the spherical wavefront at any instant is equal to the instantaneous range from the source. The curvature of the acoustic wavefront is sensed with a three-microphone linear array by first estimating the differential time of arrival (or time delay) of the acoustic wavefront at each of the two adjacent sensor pairs and then processing the time-delay information to extract the range and bearing of the source. However, modeling the passive ranging performance of the wavefront curvature method for a deterministic transient signal source in a multipath environment shows that when the multipath and direct path arrivals are unresolvable, the time-delay estimates are biased which, in turn, biases the range estimates. The model explains the observed under-ranging of small arms firing positions during a field experiment.