基于回波光子数方程估计空间碎片激光测距系统作用距离时, 最小可接受回波光子数很难确定。本文提出了通过改变空间碎片实测数据回波稀疏性获得精度变化曲线的退化模型, 以"精度不变"作为衡量条件, 确定保精度情况下系统最小可识别有效回波概率, 从而估算系统作用距离的方法。首先, 根据单光子雪崩探测器"关门"特性, 得到了有效回波概率与测量距离关系。然后, 建立实测数据的稀疏性退化模型得到测量精度与有效回波概率的跃变曲线, 根据精度曲线中"保精度平台"的"跳变点"获得最小可识别有效回波概率。最后, 根据最小可识别回波概率获得系统对不同大小典型空间碎片的作用距离。分别处理了有效截面积为3.884 0, 6.391 2和9.855 5 m2的3种典型空间碎片的实验数据, 结果表明: 系统在满足m级测距精度的前提下, 可识别的最小有效回波概率为0.02~0.044, 对上述不同特性典型空间碎片相应的最大作用距离分别为820, 1 520和2 250 km。提出的模型在精度不变情况下解决了系统最小可识别有效回波概率难以确定的问题, 大大减少了实验成本。

Echo photon number equation is usually used to estimate the detection distance of a space debris laser ranging system. However, it can not exactly determine the minimum recognizable echo number threshold. In this article, a degradation model was proposed by degrading the echo sparsity of measured data to obtain a precision curve and to effectively evaluate the minimum recognizable echo probability with the precision guaranteed, and then to estimate the detection distance of the ranging system. Firstly, the relationship of efficient echo probability and ranging distance was obtained based on the “shutting down” effect of Single Photon Avalanche Diodes (SPADs). After that, the jumping curves of ranging precision and efficient echo probability were drawn based on experimental data. From the “jumping threshold” on “precision plateau” in jumping curves, the minimum recognizable echo probability was calculated and the detection distance for typical space debris with different sizes was obtained. The experiments for three typical space debris with Radar Cross Sections(RCSs) of 3.884 0 m2, 6.391 2 m2 and 9.855 5 m2 were performed. The results show that the minimum recognizable efficient echo probability is 0.02-0.04 with the meter-level precision guaranteed and the maximum detection range for these typical space debris are 820 km, 1 520 km and 2 250 km correspondingly. This proposed degradation model effectively solves the problem for determining minimum recognizable echo probability, and reduces experimental costs.