Learning-based multi-level impact point prediction method for long-range vehicles under the influence of a disturbing gravity field

The influence of a disturbing gravity field on the impact points of long-range vehicles (LRVs) has become increasingly prominent, which is an important factor affecting the accuracy of impact point prediction (IPP). To achieve high-accuracy and fast IPP for LRVs under the influence of a disturbing gravity field, a data-driven multi-level IPP method is proposed to balance the prediction accuracy and real-time performance. At the first level, the impact point of the current flight state is predicted based on elliptical trajectory theory, and the impact deviation of the elliptical trajectory (ID-ET) is calculated. At the second and third levels, a neural network (NN) model is established to learn the ID-ET caused by the J₂ term and re-entry aerodynamic drag as well as that caused by the disturbing gravity field. To improve the NN prediction performance, an auxiliary circle is applied to decouple the ID-ET. To reduce the difficulty of NN learning, a training strategy is designed based on the idea of curriculum learning, which improves training accuracy. At the same time, a hybrid sample generation strategy is proposed to improve the NN generalization ability. A detailed simulation experiment is designed to analyze the advantages and computational complexity of the proposed method. The simulation results showed that the proposed model has a high prediction accuracy, strong generalization ability, and good real-time performance under the influence of the disturbing gravity field and re-entry aerodynamic drag. Among the 317,360 samples contained in the training and test sets, the 3σ prediction error was 6.21 m. On an STM32F407 single-chip microcomputer, the IPP required 3.415 ms. The proposed method can provide support for the design of guidance algorithms and is applicable to engineering practice.