Page 25 - Acoustics Today Summer 2011

to estimate the wavefront’s radius of curvature, which corre-
sponds to the range of the firing point. Knowing the speed of
sound travel in the atmosphere (c) and the intersensor sepa-
ration distance (d), and measuring the differences in the
arrival times (τ12 and τ23) of the muzzle blast wavefront at
adjacent sensor pairs, enables the calculation of the source
range R (from the middle sensor) and source bearing β (with 24
respect to the array axis). The results of applying this method to the passive ranging of real gunshot data from five different firing positions are shown in Fig. 9; typically 260 rounds were fired from each position. The variance of the source range estimates increases with range, while the bear- ing estimates for the serial conducted at the longest range (475 m) have a bias error which could be attributed to atmos- pheric refraction of the sound or uncertainty in the ground truth data of the firing position. The variances of both the range and bearing estimates can be reduced by increasing the effective sensor separation distance (d sin β).24
A second method, which uses both muzzle blast and shock wave information, is referred to as the ballistic model-
25 Measuring the differences in the arrival times (∆τn=r/c-t(xn)-
based method for passive ranging of direct fire weapons.
Fig. 9. Variation with range of (a) relative range error and (b) bearing error for localizing the point of fire at five ranges using passive ranging by wavefront curva- ture of the muzzle blast wave only.
Fig. 7. Acoustic transient signals–the muzzle blast is generated at the point of fire and the ballistic shock wave originates from the detach point along the bullet’s trajectory.
travels away from its point of emission at the speed of sound. But, unlike the muzzle blast wavefront, it expands as a conical surface with the trajectory and nose of the bullet defining the axis and apex of the cone respectively. The angle θn (see Fig. 7) at the apex of the cone is referred to as the Mach angle, whose sine is equal to the reciprocal of the Mach number, which is defined as the ratio of the bullet’s
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direction of the muzzle blast that arrives later—see Fig 7.
By sensing these signals at spatially-separated sensors
and applying various acoustical signal processing methods
for sound source localization, it is possible to estimate the
position of the firing point. One method, which relies only on
speed v to the speed of sound c.
A casual listener will hear the shock wave before the muzzle blast and instinctively look in the direction of its origin (the detach point) and confuse it with the actual direction of the firer, which coincides with the
the muzzle blast, is referred to as passive ranging by wavefront 24
curvature. The simplest sensor configuration for this method consists of three equally-spaced microphones posi- tioned along a straight line—see Fig. 8. The basic principle is
Fig. 8. Source-sensor geometry for passive ranging by wavefront curvature.
Physical and Engineering Acoustics 21