A New Relativistic Autonomous Celestial Navigation Method for Near Earth Spacecraft

doi:10.3969/j.issn.1009-086x.2024.06.001

Abstract

Abstract:

Relativistic navigation is a new high-precision autonomous celestial navigation method. This method obtains spacecraft’s position and velocity information by establishing two types of relativistic effects models， namely starlight gravitational deflection and stellar aberration. Therefore， the accuracy of models directly affects the accuracy of relativistic navigation. However， when establishing the current relation model between starlight gravitational deflection and spacecraft position， only the nearest celestial body is considered. The actual starlight gravitational deflection is not only related to the distance between the spacecraft and the celestial body， but also to factors such as the gravitational coefficient of the celestial body， and the angle between star and celestial body. Therefore， this article takes near Earth spacecraft as the object and considers the starlight gravitational deflection caused by multiple celestial bodies. Thereby， the relation model between starlight gravitational deflection and spacecraft’s position and the relation model between stellar aberration and spacecraft’s velocity are established. Using high-precision stellar angular distance information measured by optical interferometers， combined with orbit dynamics model and optimal estimation algorithm， the high-precision position and velocity of the spacecraft can be obtained. Finally， simulation shows that for geostationary orbit satellites， when the stellar angular distance measurement accuracy is 1 mas， the position and velocity errors of the proposed method are within 100 m and 0.01 m/s， respectively.

Key words: celestial navigation, relativistic effects, starlight gravitational deflection, stellar aberration, autonomous navigation, optical interferometer

摘要：

相对论导航是近年来提出的一种新型高精度自主天文导航方法，该方法通过建立星光引力偏折和恒星光行差这两类相对论效应与航天器位置、速度之间的关系模型，获得航天器的位置、速度信息。可见，关系模型的精确性直接影响相对论导航的精度。然而，目前在建立星光引力偏折与航天器位置的关系模型时，仅考虑离航天器最近天体引力的影响，而星光引力偏折不仅与航天器到天体的距离有关，还与天体引力系数、恒星-天体间的夹角等因素有关。为此，以近地空间航天器为对象，综合考虑多个天体引起的星光引力偏折，建立了星光引力偏折与航天器位置的关系模型，以及恒星光行差与航天器速度的关系模型，并利用光学干涉仪测得高精度恒星角距信息，结合轨道动力学模型和最优估计算法，得到航天器高精度位置和速度信息。最后，仿真验证表明，对于地球同步轨道卫星，恒星角距测量精度为1 mas时，所提方法的位置和速度误差小于100 m和0.01 m/s。

关键词: 天文导航, 相对论效应, 星光引力偏折, 恒星光行差, 自主导航, 光学干涉仪

CLC Number:

V448.2

Xianjun ZHAN, Xinlong WANG, Xiucong SUN. A New Relativistic Autonomous Celestial Navigation Method for Near Earth Spacecraft[J]. Modern Defense Technology, 2024, 52(6): 1-8.

詹先军, 王新龙, 孙秀聪. 一种近地空间航天器相对论自主天文导航新方法[J]. 现代防御技术, 2024, 52(6): 1-8.

Figures/Tables 15

Fig. 1 Illustration of starlight gravitational deflection

Fig. 2 Magnitude of gravitational deflection of starlight caused by the gravitational fields of various celestial bodies

Table 1 Exclusion angles required to neglect each celestial body

天体	星光偏折角小于0.01 mas时恒星方向与天体方向之间夹角应满足的取值范围/（°）
太阳	179.7~180
地球	154.0~180
木星	11.2~180
土星	1.55~180
月球	0.75~180
火星、水星等其他天体	0.04~180

Fig. 3 Illustration of stellar aberration

Fig. 4 Working principle diagram of an optical interferometer

Fig. 5 Diagram of relativistic navigation scheme

Table 2 Initial orbital elements of spacecraft

半长轴/km

偏心率

轨道

倾角/（°）

升交点

赤经/（°）

近地点

幅角/（°）

平近

点角/（°）

42 166

0.003

120

Fig. 6 Illustration of relativistic navigation observation scheme

Table 3 Star sensor parameter configuration

极限星等/

恒星角距测量精度/

mas

数据更新率/

视场角

0.1

1°×1°

Fig. 7 Number of stars observed by star sensors

Fig. 8 Curve of position estimation error （traditional method）

Fig. 9 Curve of velocity estimation error （traditional method）

Fig. 10 Curve of position estimation error （proposed method）

Fig. 11 Curve of velocity estimation error （proposed method）

Table 4 Position and velocity errors for two methods

导航方案	位置误差/m			速度误差/（m·s^-1）
导航方案	x方向	y方向	z方向	x方向	y方向	z方向
传统方案	1 249.5	609.8	826.9	0.057	0.072	0.043
所提方案	58.8	65.2	38.9	0.006	0.005	0.003

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