Performance evaluation of nonlinear filters on impact point prediction of ballistic targets

Abstract

Several estimation algorithms have been developed in the literature to improve the radar tracking performance of ballistic targets. The most widely used one of these algorithms is the Extended Kalman Filter (EKF) where nonlinear system and measurement models and linearization techniques are used. In the first method presented in this paper, the kinematic state vector composed of the position and velocity of the target is augmented with a parameter called ballistic coefficient. In this way, acceleration of the target due to the aerodynamic forces is taken into consideration and parameter identification process is performed together with state estimation in the EKF. Impact point prediction is performed in different parts of the trajectory in order to evaluate filter and parameter estimation performance. However, significant errors can occur in estimating the impact point of the ballistic target because of the low observability of the ballistic coefficient. In the second method proposed, the ballistic coefficient related to the target speed is assumed to be known in advance. A Multiple Model Kalman filter (MMKF) is implemented with this a priori ballistic coefficient information. The impact point and model probabilities according to the radar measurements are calculated for each model. In addition to these two methods, Doppler measurements and a smoother implementation on the ballistic coefficient are utilized in the EKF. Accordingly, possible improvements in prediction performance are assessed in the presence of Doppler measurements and smoothing on the ballistic coefficient at subsonic speeds.