Tracking Reentry Ballistic Targets using Acceleration and Jerk Models

In this paper an acceleration model and a jerk model are proposed for estimation of the kinematic state of reentry ballistic targets (RBTs) using extended Kalman filters (EKF). The models proposed here use the equations of target kinematics only and do not assume any model parameterization for variation of the ballistic coefficient and air density a priori, as found in the literature. The novelty lies in estimation of the ratio (γ) of air density and ballistic coefficient and its time derivatives using a separate Kalman filter (KF) (γ-filter) which utilizes pseudo measurements of γ computed from the velocity and acceleration estimated by the EKF at each time step. The parameter γ and its derivatives estimated by the γ-filter are, in turn, used for the estimation of position, velocity, acceleration, and jerk in the EKF. The use of the pseudo measurements of γ makes the algorithms inherently adaptive to variations of the ballistic coefficient and air density during reentry. A comparative assessment of several dynamic models for reentry of ballistic targets reported in the literature and those proposed here demonstrates that the estimation errors in velocity and acceleration are significantly less for the proposed models compared with the existing ones.