New State and Measurement Models for Endo-Atmospheric Tracking of Ballistic Targets using Seeker Measurements

Two state models and a measurement model for estimation of relative kinematics using measurements from RF seekers are proposed. The state vector for the first state model includes the acceleration of the target along with target-interceptor relative position and velocity in the state vector. In the other state model, the jerk of the target is also included among the state variables. Both models also include the ratio of the air density and the ballistic coefficient and its time derivatives as elements of the state vector to account for the aerodynamic drag in the endo-atmospheric phase. Such formulations obviate the need for assuming empirical models of air density and drag coefficient. In the proposed measurement model, the line of sight (LOS) angle is derived from the seeker measurements of LOS rate and gimbal angle and used for measurement update of the state estimator. This reduces the dimension of the measurement vector and obviates the need for modeling the dynamics of the seeker tracking and the stabilization loop. Performance results of the proposed methods have been compared with a well- known model from the literature under closed-loop guidance employing the augmented proportional navigation (APN) law for endo-atmospheric ballistic target tracking. It is clearly seen that the proposed methods yield more accurate estimates of target acceleration in terms of reduced mean error and a more favourable cumulative distribution of miss distances that effectively increase the probability of hit for a given warhead lethality radius.