Ballistic Object Trajectory Separation Point Estimation Using Fourth Order Runge-Kutta Method and Extended Kalman Filter

Ballistic missiles enter the free-flight phase upon the cessation of their booster engines, traversing the outer atmosphere for approximately 20 minutes. During this period, separation release events occur, deploying multiple warheads and decoys, presenting the optimal window for tracking, identification, and interception. However, due to the curvature of the Earth, it is challenging to ascertain the precise timing of these separation release events until the ballistic target reaches a certain altitude detectable by ground-based radar. This paper proposes a method for estimating the separation point of ballistic objects. Initially, the trajectory information of the warheads and decoys detected by radar is enhanced through Extended Kalman filtering and smoothing to improve trajectory accuracy. Subsequently, employing the fourth-order Runge-Kutta method, trajectory backtracking is initiated from the initial points of the trajectories. The Mahalanobis distance between the trajectories of the decoys and warheads is computed to determine the separation release relationship and estimate the timing of decoy separation release. Simulation results validate the effectiveness of the proposed method.