雷达波束驻留模式下空间碎片数量的置信区间估计

Estimation of the Confidence Interval for Space Debris Population Using Radar in Beam-park Mode

碎片数量估计是空间碎片环境统计特征描述的重要内容之一,对于空间碎片环境模型验证、航天器碰撞风险分析以及碎片数量增长趋势预测有重要意义.针对波束指向正东、正南任意仰角的雷达波束驻留(Beam- park)模式(天顶指向是波束指向仰角为90°时的特例),给出了一种估计碎片数量置信区间的方法.对于给定轨道高度范围内一个具有穿越雷达波束可能性(即雷达散射截面足够大,且轨道倾角相对测站纬度足够大)的碎片,将其是否真正穿越波束这一随机事件用(0-1)分布来建模,根据所采集的轨道高度和倾角数据,计算出该轨道高度范围内碎片穿越波束的平均概率,进而采用中心极限定理来估计碎片数量的置信区间.仿真结果表明了方法的有效性.

Debris population estimation is an important task in statistical characterization of space debris environment, and is of great significance for validation of space debris environment models, assessment of impact risk to spacecrafts and prediction of the long-term growth potential of the number of debris. A method of estimating the confidence interval for debris population using radar in beam-park mode with the beam pointed due east and due south with any elevation is given. This method is also applied to the vertical staring radar, which is a special case when the beam elevation is 90°. In the beam-park mode, the antenna beam is parked at fixed azimuth and elevation angles for a long time, usually longer than 24 hours. Debris objects crossing the beam randomly would be detected, and measurements for detected target would be obtained. No attempt is made to track debris objects passing through the observation volume. In this operating mode, the random event that a debris object in a given altitude bin, which may cross the beam, i.e. has large enough radar cross section and inclination relative to the latitude of the radar site, is actually observed is modeled as a （0-1） distribution. Using debris altitude and inclination data collected, the average probability of crossing the beam for all debris objects in the given altitude bin is obtained. The confidence interval for space debris population is estimated by the Central Limitation Theorem. Simulation results show the effectiveness of the method.