Comparison and Application of Simplified Calculation Methods for Spacecraft Collision Probability

With the rapid increase in the number of debris and spacecraft in space, spacecraft need to assess collision risks in real time. However, due to the limited on-board software and hardware resources, there is an urgent need for a collision probability calculation method with appropriate computational load and high assessment accuracy. Aiming at the problem of spacecraft collision probability, this paper firstly explains the assumptions and calculation principles of collision probability, then summarizes and analyzes the existing common methods, summarizes the applicability and characteristics of each method in terms of linearity and nonlinearity, whether the space target is regular, etc., and finally verifies the adaptability of the above methods through numerical calculation, and evaluates each method from the two dimensions of calculation speed and calculation accuracy. The evaluation results show that the central probability density method has the fastest calculation speed. The relative error of the curve integration method is the smallest, the two-dimensional integration method based on Simpson’s formula has a relatively balanced effect. 3D volume integration is suitable for nonlinear scenes, the Monte Carlo method is the most accurate, but the slowest. Considering the factors such as calculation accuracy, calculation speed, relative velocity, and relative position relationship, this paper proposes a simplified calculation method for collision probability in various scenarios according to the characteristics of each method, and the research results can provide a reference for the calculation and analysis of on-orbit collision probability.