Due to an increasing number of sniper attacks in different crises and security threats around the world, there is a need for new technologies and applications to take place in helping to prepare against such offensives. Estimation of sound wave direction of arrival (DOA) based on time differences between separate microphones is typically applied for sound source localization, and the existing research achievements of the field are utilized in the presented study. In this paper, a new method for estimating the state of a supersonic bullet is proposed. State is defined here to consist of bullet's trajectory, caliber, and speed. The method is based on a mathematical modeling of the bullet shock wave, and the parameter estimation procedure is built over the Bayesian inference. Both simulations and real shooting data are used to test and verify the performance of the proposed method. Bringing shock wave modeling and Bayesian inference together is the main focus of the study.