Objective  More and more space debris has seriously threatened the safety and normal operation of spacecraft in orbit. The removal of space debris is imperative, and the primary task is to conduct high-precision orbit determination. So in recent years, space debris laser ranging has become a research hotspot. At present, the main problems of space debris laser ranging are poor orbit accuracy and few observation time. Therefore, a theoretical formula for the success probability of space debris laser ranging detection is established in this paper. Combining with the solar orientation information and target orbit prediction information, the relative difficulty of target detection can be judged in real time, providing a certain reference for observation. This method can improve the observation efficiency and orbital accuracy of space debris, and increase its total observation time.

  Methods  Based on the RADAR equation and the daytime noise estimation formula, a calculation method for the success probability of space debris laser ranging is derived. The influence of atmospheric transmission and sky background noise in this method is simulated. On this basis, the effects of sun altitude angle, target zenith angle, target orbital distance and target cross-sectional area on the success probability of target detection are simulated.

  Results and Discussions  The success probability of target detection decreases with the increase of the sun altitude angle, and the relationship is basically linear. That is, the higher the sun altitude angle is, the greater the system noise and the higher the false alarm rate is, resulting in a lower success probability of target detection (Fig.6). The success probability of target detection gradually decreases with the increase of target zenith angle. When the target zenith angle increases to 70°, the success probability of target detection begins to decrease rapidly. Therefore, in the actual measurement of laser ranging, it is difficult to detect the target when the elevation angle is lower than 20° (Fig.7). The success probability of target detection of the system decreases sharply with the increase of orbital distance (Fig.8). When the orbital distance of the target is fixed, the success probability of target detection increases with the increase of the cross-sectional area of the target, which is approximately linear (Fig.9).

  Conclusions  The success probability formula of target detection established above, combining with the sun orientation information and target orbit prediction information, can determine the relative difficulty of target detection in real time, and provide a certain reference for observation. This method can improve the observation efficiency and orbit accuracy of space debris, and increase its total observation time. At the same time, the method can be extended to other stations, especially in the new automatic space debris observation station, which has great application value. Recently, Europe has built a lot of low-cost, miniaturized and intelligent mobile stations, aiming to comprehensively improve the total observation time of space debris. For automatic unattended stations, this method will help to select observation targets, thus greatly improving the observation efficiency of the system.