| dc.description.abstract | The supersonic flight of a bullet generates a ballistic shock wave (SW). As the bullet is subjected to both drag and gravity, its speed decreases with the distance travelled and its trajectory is more or less curvilinear. Given the drag coefficient exponent and the ballistic constant of the bullet, its curvilinear trajectory is specified by five parameters. In this paper, these five parameters are estimated using a SW-based method, which utilizes differential time of arrival (DTOA) of SW measurements from an acoustic sensor array and assumes a linear trajectory, a drag coefficient exponent of 0.5, and a known ballistic constant for the bullet. The point of fire is then located by tracing the estimated curvilinear trajectory of the bullet backwards until it intercepts some obstruction on a digital map. The performance of the SW-based method is evaluated using simulated DTOA data for 36 different types of real bullets, which are generated using Doppler radar measured speeds of the bullets with the gravity taken into account. The standard deviation in the estimates of each parameter is compared with the Cramer-Rao lower bound. The effect of using an erroneous ballistic constant on the performance of the SW-based method is studied. | en_US |
