Ballistic coefficient learning based impact point prediction of ballistic targets

Abstract

Several methods for improving the tracking performance of ballistic targets have been developed in the literature. Extended Kalman Filter (EKF), the most widely used one of these algorithms, gets use of nonlinear system and measurement models and linearization techniques. The kinematic state vector composed of the position and velocity of the target is augmented with a parameter called ballistic coefficient. Acceleration of the target due to the aerodynamic forces is considered and parameter identification process is performed together with state estimation in the EKF. Ballistic Coefficient is a parameter that changes with target speed and it substantially determines aerodynamic forces on the target. Furthermore, significant errors can occur in estimating the impact point of the ballistic target because of the low observability of the ballistic coefficient. Due to the parameter estimation errors and the speed dependent characteristics of the ballistic parameter, it is not possible to predict a ballistic trajectory perfectly. As a first proposed method in this study, the ballistic coefficient characteristics with respect to the target speed is assumed to be known in advance. In the study, using aerodynamic analysis techniques, a priori ballistic coefficient information is acquired for three types of ballistic targets. This a priori information is used in Multiple Model Kalman Filter to classify the target type and to better predict the impact point of the target. In the second proposed method, it is assumed for the ballistic coefficient to be linear with respect to target speed in three different speed regimes. A smoothing algorithm together with Robust Least Square Error method is used to learn the ballistic coefficient's slope for speed regions above mentioned.