A method for calculating the discovery time of ballistic missiles detected by an infrared early warning satellite

To determine the high dynamic change characteristics of the relative space position between a ballistic missile and an early warning satellite during detection, a centric motion model of the ballistic missile and the early warning satellite are established first. Then, the space geometric relationship is presented. Based on the gray body radiation characteristics, the calculation model of the infrared radiation characteristics of the ballistic missile in the boost phase is established. Then, a method of early warning satellite detection and discrimination considering geometric visibility and infrared visibility is proposed. Finally, the simulation and key factor comparison analysis are carried out with a typical early warning satellite, infrared detector, and ballistic missile data. Validation results show that this method can quickly and accurately calculate the discovery time and flight height of ballistic missiles detected by early warning satellites. The validation results reveal that the missile trajectory and detection bands have a significant effect on the discovery time, and the discovery time in the 2.7 µm band is earlier than that in the 4.3 µm band for the same missile trajectory. It is also found that the change in SNRth between 4.24 and 7.58 has limited influence (less than 2 s) on the discovery time. The research conclusions have important significance for improving the detection strategy of ballistic missile defense. It can also provide support for optimizing missile trajectories.