Outdoor Acoustics: Range Estimation Of Gunfire Over An Acoustically Soft Impedance Ground In A Homogeneous Atmosphere

Abstract

Predicting outdoor sound propagation in uncertain conditions remains a challenge. This increases the complexity of the inverse problem, e.g. parameter recovery in the presence of a particular sound source such as like gunfire. This paper investigates the use of maximum likelihood methods, both frequentist and Bayesian, in inverting true parameters from measured and simulated data. A simple source-receiver acoustic model is used which assumes; a homogeneous atmosphere, soft impedance ground and some medium range sound propagation to predict the deviation in sound pressure at the receiver. A blank firing pistol, Bruni Mod 92, is used to record a realistic sound source spectrum in an anechoic chamber. Gaussian noise is added to model predictions for this type of source to mimic uncertainty of real-life observations. Error analysis is performed by repeatedly generating observations and then evaluating the errors between the true range and recovered range estimate. This analysis is performed in broadband and octave frequency bands. It was found that the frequentist method greatly underestimates the range while the Bayesian method, even with a particularly flat prior, greatly reduces both over-and underestimations, significantly improving the range estimate to within ±5 of the true value in the majority of cases. The inclusion of octave band filters in the infrasonic frequency showed these bands were mostly responsible for the accurate range estimates. This paper paves the way for applications of this class of statistical models to real-life acoustic data for source parameter recovery.

Likelihood maximisation techniques for ranging gunfire over grassland

“…A large portion of energy output of a firearm exists in the infrasonic frequency range. As highlighted in recent works [6], there is strong evidence to suggest that combining octave windows between in the low and infrasonic, frequency range will greatly improve parameter inference for firearms. Usual techniques try to use information from the supersonic projectile (bullet) which is good for 3D problems (location via miss angle), but may not actually be the best method.…”

“…More recent work by J. A. Parry et al used a simple excess attenuation model, with and without a priori knowledge to infer the source range and simulated data for sound propagation from a blank firing pistol [6]. The ground in this instance was assumed to be vegetative, creating an acoustically softer ground.…”