Laser inter-satellite links (LISLs) are crucial for enabling rapid information exchange within low earth orbit (LEO) constellations. Previous research on laser link establishment often relied on the idealized probability density function (PDF) of the pointing uncertainty regions (PURs) when designing scan-and-capture methods, neglecting the impact of various practical uncertainties. To address the above issues, there is an urgent need to analyze the practical uncertainties to enhance the stability and reliability of LISL. This paper first provides a comprehensive introduction to the alignment process in LISL and mathematically formulates typical sources of uncertainty errors. Subsequently, a generalized system model (GSM) for laser link establishment was established at three stages: Orbit, Attitude, and Laser terminal. Finally, we integrate uncertainty models into the GSM and propose a PUR generating method to obtain precise PDFs. The research method proposed in this study can consider the influence of multiple uncertainties and generate the PDF for the PURs. Compared with traditional research, the PDF obtained by fitting the oscillation range considering dynamics is more detailed. By analyzing the PDF generated by typical uncertainty errors, it is observed that the orbit initial uncertainty may be the predominant factor influencing the PUR.

中文翻译：

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多种不确定性下星间激光对准系统的指向不确定性区域分析

激光卫星间链路 (LISL) 对于实现低地球轨道 (LEO) 星座内的快速信息交换至关重要。以往的激光链路建立研究在设计扫描捕获方法时往往依赖于指向不确定性区域（PUR）的理想化概率密度函数（PDF），忽略了各种实际不确定性的影响。针对上述问题，迫切需要分析实际的不确定性，以增强LISL的稳定性和可靠性。本文首先全面介绍了 LISL 中的对准过程，并从数学上公式化了不确定性误差的典型来源。随后，分轨道、姿态、激光终端三个阶段建立了激光链路建立的通用系统模型（GSM）。最后，我们将不确定性模型集成到 GSM 中，并提出了一种 PUR 生成方法来获得精确的 PDF。本研究提出的研究方法可以考虑多种不确定性的影响并生成 PUR 的 PDF。与传统研究相比，考虑动力学的振荡范围拟合得到的PDF更加详细。通过分析典型不确定性误差产生的PDF，观察到轨道初始不确定性可能是影响PUR的主要因素。