Locating far-field impulsive sound sources in air by triangulation

The firing of a gun generates an acoustic impulse that propagates radially outwards from the source. Acoustic gun-ranging systems estimate the source position by measuring the relative time of arrival of the impulse at a number of spatially distributed acoustic sensors. The sound-ranging problem is revisited here using improved time-delay estimation methods to refine the source position estimates. The time difference for the acoustic wavefront to arrive at two spatially separated sensors is estimated by cross correlating the digitized outputs of the sensors. The time-delay estimate is used to calculate the source bearing, and the source position is cross fixed by triangulation using the bearings from two widely separated receiving nodes. The variability in the bearing and position estimates is quantified by processing acoustic sensor data recorded during field experiments for a variety of impulsive sound sources: artillery guns, mortars, and grenades. Imperfect knowledge of the effective speed of sound travel results in bias errors in the source bearing estimates, which are found to depend on the orientation of the sensor pair axis with respect to the source direction. Combining the time-delay estimates from two orthogonal pairs of sensors reduces these bias errors.