Trajectory prediction of ballistic missiles using Gaussian process error model

Abstract

Ballistic Missile Trajectory Prediction (BMTP) is critical to air defense systems. Most Trajectory Prediction (TP) methods focus on the coast and reentry phases, in which the Ballistic Missile (BM) trajectories are modeled as ellipses or the state components are propagated by the dynamic integral equations on time scales. In contrast, the boost-phase TP is more challenging because there are many unknown forces acting on the BM in this phase. To tackle this difficult problem, a novel BMTP method by using Gaussian Processes (GPs) is proposed in this paper. In particular, the GP is employed to train the prediction error model of the boost-phase trajectory database, in which the error refers to the difference between the true BM state at the prediction moment and the integral extrapolation of the BM state. And the final BMTP is a combination of the dynamic equation based numerical integration and the GP-based prediction error. Since the trained GP aims to capture the relationship between the numerical integration and the unknown error, the modified BM state prediction is closer to the true one compared with the original TP. Furthermore, the GP is able to output the uncertainty information of the TP, which is of great significance for determining the warning range centered on the predicted BM state. Simulation results show that the proposed method effectively improves the BMTP accuracy during the boost phase and provides reliable uncertainty estimation boundaries.