A conditional boost-phase trajectory estimation method based on ballistic missile （BM） information database and classification is developed to estimate and predict boos-phase BM trajectory. The main uncertain factor...A conditional boost-phase trajectory estimation method based on ballistic missile （BM） information database and classification is developed to estimate and predict boos-phase BM trajectory. The main uncertain factors to describe BM dynamics equation are reduced to the control law of trajectory pitch angle in boost-phase. After the BM mass at the beginning of estimation, the BM attack angle and the modification of engine thrust denoting BM acceleration are modeled reasonably, the boost-phase BM trajectory estimation with ground based radar is well realized. The validity of this estimation method is testified by computer simulation with a typical example.展开更多
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...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.展开更多
文摘A conditional boost-phase trajectory estimation method based on ballistic missile （BM） information database and classification is developed to estimate and predict boos-phase BM trajectory. The main uncertain factors to describe BM dynamics equation are reduced to the control law of trajectory pitch angle in boost-phase. After the BM mass at the beginning of estimation, the BM attack angle and the modification of engine thrust denoting BM acceleration are modeled reasonably, the boost-phase BM trajectory estimation with ground based radar is well realized. The validity of this estimation method is testified by computer simulation with a typical example.
基金support from National Natural Science Foundation of China(Nos.61873205,61771399)Aerospace Science Foundation of China(No.2019-HT-XGD)Natural Science Basic Research Plan in Shaanxi Province of China(No.2020JM-101).
文摘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.
