【作者】 吴波；

【导师】 赵拥军；

【作者基本信息】 解放军信息工程大学 ， 军事情报学， 2011， 硕士

【摘要】 碰撞概率计算是实现轨道预警,确保航天器飞行安全的一种重要方法。现有短时碰撞概率算法求解二维概率密度函数时计算复杂,在交会平面进行积分区域转化时引入误差较大,空间目标等效模型只采用了简单的球体模型。针对上述问题,本文以现有碰撞模型为基础,给出了计算二维概率密度函数的简化方法和高精度的碰撞概率快速算法,从概率分布和空间目标形状等效两个方面给出改进模型及相应的碰撞概率算法,并对长时交会的碰撞情况进行了分析。本文主要工作如下:1.研究了短时交会模型。通过轨道预测数据分析验证了交会区域空间目标的运动为线性运动。给出了一种能同时计算相对位置误差二维概率密度函数均值和方差的方法,该方法利用正交投影和特征分解,在将三维问题转化到交会平面的过程中,无需联立方程组就能求得二维概率密度函数参数。2.给出了一种基于圆域的碰撞概率快速计算方法。该方法采用近似积分法则,将二维问题转化为多项式求解,避免了积分区域转化对计算精度的影响,实验表明其计算精度与二维积分直接计算相当,近似值与精确值之比达到了0.99。3.结合碰撞预警需求,从概率分布和空间目标形状等效两个方面改进了原有模型。位置误差服从均匀分布时的碰撞概率算法在计算效率上得到较大提高,可以用作先期筛选。空间目标椭球体等效模型的碰撞概率方法,对空间目标的描述更符合实际,并为进一步建立符合空间目标实际形状的高精度碰撞模型提供了参考。4.给出了长时交会情况下的碰撞概率算法,该算法利用相对运动方程和蒙特卡罗积分,以及碰撞概率模型中目标函数与重要性函数的一致性,得到了方差最小的碰撞概率,并与短时交会碰撞概率算法进行了分析比较。更多还原

【Abstract】 The calculation of collision probability is an important method to trajectory early warning and the safety of spacecraft. Currently, there are some problems with the algorithm of calculating collision probability, the computing efficiency is not ideal to acquire planar probability density function; the incoming error cannot be ignored when changing the integral area on the encounter plane; and the description to the equivalent model only gives one simple spherical model. Based on the short-term encounter model, a method that can compute the value of mean and variance simultaneity is proposed and a precise algorithm of collision probability at encounter plane is also put forward; the improvement of the old model is presented in detail from the attribution of density and equivalent model of space objects with corresponding algorithm. At last, the collision in the case of long-term encounter is analyzed particularly.The primary work of the paper is as follows:Firstly, the short-term encounter model is studied and the linear movement of space objects is validated in the encounter area with orbit forecast data. Experiments show that it is feasible to approximate curve with beeline in short arc. A method is put forward to obtain mean and variance of the planar probability density function simultaneously. Based on orthogonal projection and eigenvalue decomposition, it can be obtained without simultaneous equations in the process of changing the three-dimension problem to encounter plane.Secondly, one fast algorithm of collision probability is proposed based on round area. It adopts approximate integral theorem, turns the two-dimension problem to multinomial, and avoids the infection of the change of integral area to the compute precision. Experiments show that the precision of the method is close to the result of direct integral and the ratio between approximation and exact value arrives at 0.99.Thirdly, the original model is improved on probability distribution and equivalent model of space objects. A collision model is developed with corresponding algorithm when the position error submits to uniformity. Experiments show that the method can get the collision probability more efficiency and can be used as early filtration. The ellipsoid equivalent model of space objects and corresponding algorithm is developed. The experiment shows that the description of space object is more accurate to its characteristic and the model can provide an important reference to establish the actual shape model of space objects.Finally, algorithm for computing the collision probability of long-term encounter is proposed with Clohessey-Whiltshire equation and Monte Carlo integral, and the minimal variance is acquired because of the coherence of objective function and important function. At last the method of long-term encounter is compared with the algorithm of short-term encounter.更多还原