空间目标碰撞概率的等效矩形域快速算法

针对线性相对运动假设下的碰撞概率计算问题，提出了等效矩形域方法。利用该方法将概率积分计算进行近似处理，推导出概率密度积分的解析表达式。针对空间目标误差椭球形状固定的情况，给出了最大碰撞概率的计算方法。对目标在交会时刻相距较远和接近碰撞的情况进行了碰撞概率以及最大碰撞概率计算。通过将计算结果与空间压缩无穷级数法的对比，验证了等效矩形域方法近似计算碰撞概率积分的可靠性，同时对于不同的碰撞概率计算情况，等效矩形域方法显示出更高精确度和更好的估计偏差稳定性。

Rapid Algorithm of Space Objects Collision Probability with Equivalent Rectangular Area

The equivalent rectangular area algorithm is provided for the calculation of the collision probability, assuming that the relative motion of the objects is linear motion at the encounter time. The probability density approximates to analytical expression via the method. Besides, based on the approximation, the maximum collision probability is calculated in certain error ellipsoid shape case. For the application examples of the far and the close encounter with collision objects, the collision probability and the maximum collision probability are obtained by the method. The results from our method are compared with the algorithm based on space compression and infinite series. The comparisons show that the equivalent rectangular area algorithm is reliable, and the results from the different cases calculated by the equivalent rectangular area algorithm reveal a better accuracy and a more stable offset error.