Supersonic projectile models for asynchronous shooter localization

In this work we consider the localization of a gunshot using a distributed sensor network measuring time differences of arrival between a firearm's muzzle blast and the shockwave induced by a supersonic bullet. This so-called MB-SW approach is desirable because time synchronization is not required between the sensors, however it suffers from increased computational complexity and requires knowledge of the bullet's velocity at all points along its trajectory. While the actual velocity profile of a particular gunshot is unknown, one may use a parameterized model for the velocity profile and simultaneously fit the model and localize the shooter. In this paper we study efficient solutions for the localization problem and identify deceleration models that trade off localization accuracy and computational complexity. We also develop a statistical analysis that includes bias due to mismatch between the true and actual deceleration models and covariance due to additive noise.