A trajectory prediction method for boost phase BM based on adaptive tracking and GPR

Trajectory prediction (TP) of ballistic missile (BM) is a critical task in the field of military and defense security. However, influenced by various external factors, including target maneuverability, interference, and atmospheric conditions, BMs encounter complex forces during the boost flight phase, making their trajectories complex and variable. Furthermore, the conventional numerical integration and polynomial fitting TP methods are highly dependent on fixed motion models and precise initial observations, so they tend to engender error accumulation and inaccurate predictions. Thus, in terms of this issue, this paper proposed a TP method based on adaptive tracking and Gaussian Process Regression (GPR) to achieve stability in short-term TP for boost phase BM. Specifically, a database of trajectories for boost phase BM is created and used for training GPR predictive models, in which the unknown noise's covariance matrix is dynamically adjusted according to the statistical characteristics of observations to provide more precise trajectory data for model training. At the same time, incremental learning is adopted to add tracking results from real-time tests to improve further and update the predictive model. Additionally, the output uncertainty of GPR is also beneficial for decision-making systems usually making decisions in accordance with the uncertainty. Simulation results based on the GEO dual-satellite positioning system show that the absolute average TP RMSE of the boost phase BM of our proposed method can be less than 0.35 km, 0.51 km, and 0.62 km in future 20 s, 40 s, and 60 s, which outperforms those of the numerical integration method of 2.1 km, 3.7 km, and 6.9 km and the function approximation method of 0.89 km, 3.1 km, and 6.1 km. This paper provides a significant reference for the positioning, tracking, and prediction of BM in boost phase.