编队卫星技术是一种将多颗卫星组成编队，利用相互协作完成特定任务的技术，该技术已经被广泛应用于地球观测、通信、导航等领域。其中，自主定轨技术是编队卫星技术中的重要内容，它可以使编队卫星实现精确定位和控制，从而更好地完成任务。本文针对地球轨道多星编队，研究了基于量子测距和天文测角的编队卫星自主定轨方法，主要工作如下：

首先，研究了基于量子测距和天文测角的观测方法。观测方法是编队卫星自主定轨的重要组成部分，其中星间测距和测角是关键观测手段。量子测距采用发出纠缠双光子进而获得相关函数计算出测距值的方法；星间测角利用星敏感器对星座内卫星和恒星的拍照观测方法，在拍照之前模拟出星图图像以提高测量精度和准确性，同时加入星敏感器测量得到的轨道高度。通过研究量子测距、天文测角和轨道测高的组合导航方法，并将它们应用于编队卫星自主定轨中，为实现高精度、高可靠性的卫星定轨提供重要支持。

之后，研究了双星和三星编队自主定轨方法。通过建立状态模型、量测模型和估计模型，在此基础上设计了基于无迹卡尔曼滤波的双星自主定轨方法。对于三星编队，由于卫星数量增加后，角度测量实施较为困难，提出在三星编队中存在两颗主星和一颗副星的假设，主星采用量子测距、天文测角和轨道测高的组合测量方法，由三边定位法给出副星采用量子测距和轨道测高的观测量进行自主定轨，省略了其角度测量。使用仿真验证了所提出的双星和三星自主定轨方法的有效性，仿真结果表明双星的定位精度达到1m以内，三星定轨方法的定位精度达到1.5m以内。

最后，研究了多卫星编队自主定轨方法。该方法中主星采用量子测距、天文测角和轨道测高的组合测量方法，副星由三边定位法仅采用量子测距方法，通过融合算法层和测量层对多颗卫星进行定轨。由于各卫星间的测量距离值到达副卫星不是同时刻，利用插值法来估计副星和其他各颗卫星间的相对距离。在仿真中，通过对七颗编队卫星进行模拟，结果表明在空间圆形编队半径约为1km的情况下，该方案实现了40cm以内的多卫星相对导航精度。当主卫星数量减少时会大大降低多卫星角度测量的实施难度，此时精度仅会轻微减小。因此，该方法既满足了高精度，又满足了扩展性的要求。

Formation satellite technology is a technique that forms a team of multiple satellites to accomplish specific tasks through mutual cooperation, which has been widely applied in fields such as Earth observation, communication, and navigation. Autonomous orbit determination technology is an important part of formation satellite technology, which enables precise positioning and control of formation satellites, thus better accomplishing tasks. This paper focuses on the study of formation satellite autonomous orbit determination methods based on quantum ranging and astronomical observation for multiple satellites in Earth orbit. The main work is as follows:

Firstly, the observation methods based on quantum ranging and astronomical observation are studied. Ranging and angle measurement between stars are critical observation means for formation satellite autonomous orbit determination. The quantum ranging uses the method of emitting entangled two photons and obtaining the correlation function to calculate the ranging value. Inter-satellite Angle measurement uses the star sensor to take pictures of satellites and stars in the constellation. Before taking pictures, star map images are simulated to improve the measurement accuracy and accuracy. At the same time, orbital altitude measured by the star sensor is added. By studying the combined navigation method of quantum ranging, astronomical observation, and orbit height measurement, and applying them to formation satellite autonomous orbit determination, important support is provided to achieve high-precision and high-reliability satellite orbit determination.

Next, autonomous orbit determination methods for dual-star and triple-star formations are studied. By establishing state models, measurement models, and estimation models, an autonomous orbit determination method based on the unscented Kalman filter for dual-star formation is designed. For a triple-star formation, due to the difficulty in angle measurement with an increasing number of satellites, the hypothesis of two main stars and one auxiliary star is proposed. The main stars adopted a combined measurement method of quantum ranging, astronomical observation, and orbit height measurement. The auxiliary star used only quantum ranging and orbit height measurement for autonomous orbit determination by three-point localization. The angle measurement is omitted. The effectiveness of the proposed autonomous orbit determination methods for dual-star and triple-star formations is verified by simulation, and the results showed that the positioning accuracy of the dual-star formation is within 1m, and the positioning accuracy of three-star orbit determination method is less than 1.5m.

Finally, a method for autonomous orbit determination of multi-satellite formations is studied. In this method, the main star adopted a combined measurement method of quantum ranging, astronomical observation, and orbit height measurement, and the auxiliary stars used only quantum ranging for autonomous orbit determination by fusion algorithms and measurement layers. Since the measurement distance values between each satellite and the auxiliary satellite did not arrive simultaneously, interpolation is used to estimate the relative distance between the auxiliary satellite and other satellites. In the simulation, by simulating seven formation satellites, the results showed that this method achieved a relative navigation accuracy of less than 40cm in a circular formation with a radius of about 1km. When the number of main satellites is reduced, the difficulty of angle measurement for multiple satellites would be greatly reduced, and the accuracy would only decrease slightly. Therefore, this method not only meets the requirements of high precision but also satisfies the requirements of scalability.

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