Abstract
A ballistic model-based method is proposed for ranging small arms fire using a single acoustic sensor node, without a priori knowledge of the two ballistic model parameters: the muzzle speed and ballistic constant of the bullet, except that their actual values lie within a known two-dimensional (2D) parameter subspace. The method assumes that the line of fire misses the sensor node by a small angle, referred to as the miss angle, typically within a few degrees. A closed-form range estimator is derived, which computes the mean value of the feasible range estimates over the 2D parameter subspace for a presumed miss angle, using the measurements of the differential time of arrival and differential angle of arrival of the muzzle blast and ballistic shock wave at the sensor node. The output of the range estimator for a small presumed miss angle provides the range estimate of the point of fire. The performance of the proposed method is evaluated using simulated data for 36 different types of bullets and using real data for two different types of bullets.
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