航天器碰撞概率简化计算方法的比较与应用

    Comparison and Application of Simplified Calculation Methods for Spacecraft Collision Probability

    • 针对空间飞行器碰撞概率问题, 基于碰撞概率的假设条件与计算原理, 对现有常见方法进行分析, 归纳每种方法在线性与非线性、空间目标是否规则等方面的适用性及特点, 通过数值计算验证了上述方法, 并从计算速度与计算精度两个维度对每种方法进行评估. 评估结果表明, 中心概率密度法的计算速度最快,曲线积分法的相对误差最小, 基于辛普森公式的二维积分方法具有较均衡的效果, 三维体积积分适用于非线性场景,蒙特卡洛法最为精准但是运算速度最慢. 综合考虑计算精度、计算速度、相对速度、相对位置关系等因素, 根据每种方法的特点提出了多种场景下较为适用的碰撞概率简化计算方法, 研究结果可以为在轨碰撞概率的计算与分析提供参考.

       

      Abstract: 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.

       

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