Orbital design of LEO navigation constellations and assessment of their augmentation to BDS
Introduction
With the development of the space industry, especially commercial spaceflight, the application of augmenting navigation systems using LEO satellites has attracted increasing attentions from academic and industry scientists (Reid et al., 2016, Ge et al., 2018, Su et al., 2019, Li et al., 2020b). Many organizations, such as Iridium, have focused on the potential applications of LEO satellites for navigation in satellite constellation construction (Joerger et al., 2010). Generally, LEO satellites can improve the navigation performance in two ways: information augmentation and signal augmentation. Information augmentation is a way of broadcasting GNSS navigation and error correction messages by LEO satellites to improve the positioning accuracy and integrity (Li et al., 2016, Wang et al., 2018b). For example, Iridium is used to broadcast differential GPS corrections for improving the positioning accuracy of GPS. Signal augmentation is a way of broadcasting independent navigation signals by LEO satellites, and observation from this new signal can be combined with GNSS to improve the positioning accuracy or achieve positioning independently when the number of LEO satellites in view is at least four. Compared with GNSS, LEO satellite navigation signals have some advantages, including a smaller signal transmission loss, a higher landing power, stronger anti-jamming and anti-occlusion abilities. Signal augmentation is currently an important issue in the field of navigation augmentation. Some in-orbit verification of signal augmentation has been carried out in previous research (Wang et al., 2018a).
Signal augmentation of LEO satellites can be combined with GNSS or provide positioning service independently (REID et al., 2018). These approaches are referred to as the combined work mode and independent work mode respectively. In the independent work mode, LEO constellation signals are received and used for positioning alone. In context of this, a suitable LEO constellation should be designed first to guarantee that the number of visible satellites is always at least four in the service areas (Yarlagadda et al., 2000). In the combined work mode, the signals of both GNSS and the LEO constellation are required to be received and applied for positioning, and thus, better position accuracy can generally be achieved compared with only using GNSS. Ge et al. (2018) analysed the visibility of the Iridium constellation at different stations, the geometric improvement for GNSS observations, and the acceleration of PPP convergence by adding the simulated observation from Iridium constellation. Focusing on providing real-time PPP services by the proposed LEO constellation enhanced GNSS (LeGNSS) system, Li et al. (2019) analysed precise orbit determination (POD) and precise clock estimation (PCE) of different schemes using simulated observation data of GNSS and Iridium, and also demonstrated LeGNSS have the precise positioning capacity by assessing the GDOP and signal-in-space ranging error (SISRE).
Combining LEO constellations with the BDS is the focus in this paper. The BDS is a satellite navigation system independently developed by China according to the strategy of “three steps”. BDS-1 is a verification system that includes two GEO satellites and has been in service since 2003. BDS-2 is a regional satellite navigation system and has been operational since 2012. The space segment of BDS-2 consists of five GEO, five IGSO and four MEO satellites. The service coverage of BDS-2 is 55°N ~ 55°S and 55°E ~ 180°E. BDS-3 is a global satellite navigation system and is expected to be completed and provide service since 2020. The space segment of BDS-3 consists of three GEO, three IGSO and twenty-four MEO satellites distributed equally in three orbital planes (Yang et al., 2018, Li et al., 2020a).
The DOP and user ranging error (URE) are essential factors that affect positioning accuracy, and the DOP is currently the only factor we focus on in this paper (Wang et al., 2019). MASSATT and RUDNICK (1990) derived geometric formulations for DOP computing. For the DOP calculation of GNSS, Fang (1987) found that the minimum of GDOP is 2.5 when four GPS satellites are used. Sairo et al. (2003) demonstrated that the minimum of GDOP was in theory, where represents the number of visible navigation satellites. Han et al. (2014) researched the minimum PDOP when the elevation mask angle of GNSS satellites was between 0 and . In the case of applying multi-GNSS constellations, the influence of adding satellites to the GDOP value has been researched theoretically (Teng and Wang, 2014), and the mathematical minimum GDOP values using different numbers of satellites among different constellations have been derived (Teng et al., 2015, Liu et al., 2017). The aforementioned studies focused on satellite selection for positioning among existing constellations. In satellite constellation design, Dufour et al. (1995) presented a DOP-based criterion to optimize the satellite constellation geometry and performed some constellation experiments. Considering satisfactory coverage and satellite failures, Lansard et al. (1998) designed satellite constellations based on walker patterns and new design patterns using a multi-criterion. In the application of LEO constellations, the DOP value is related to the number of LEO satellites in coverage and their geometric distribution with users on Earth, which is dependent on the LEO constellation design and is also generally used for assessing the performance of LEO constellations.
Iridium, which is a system used for global mobile communication, is generally used as an example to analyse its global coverage performance. The Iridium space segment consists of 66 LEO satellites evenly distributed on 6 orbital planes, with an orbital altitude of 780 km and an orbital inclination of 86.4° (Jia and Peng, 2010). Fan et al. (2012) analysed the visibility and GDOP values of Iridium, GPS and Galileo in different regions and proved that it is impossible to provide global navigation only using the Iridium constellation. This is because Iridium is designed as a communication constellation, and the design constraint is only satisfied with at least one overlay of earth. Therefore, it is necessary and meaningful to study the orbital design of LEO navigation constellations, which is the premise of the independent positioning of LEO navigation.
Therefore, the aim of this study is to design LEO navigation constellations following the principle of providing the ability of global navigation service independently, and we analyse the performance of the designed LEO constellations in the independent and combined work modes. The remaining parts of this paper are organized as follows. The methodology of the LEO constellation model and the calculation of the DOP values in different augmentation modes in this paper are given in Section 2. In Section 3, the LEO constellation simulations are analysed, and suitable constellations with different altitudes are derived. Two scenarios of LEO navigation augmentation in the combined work mode are analysed in Section 4. Some typical conclusions are presented at the end of this paper.
Section snippets
Methodology
In this section, the LEO constellation model is described first. Then, DOP calculations are derived for the two proposed LEO constellation work modes.
Numerical simulations and performance validation
In this section, some numerical simulations of the LEO constellation are designed first. Then, to derive the suitable constellations, we focus on the coverage performance of different LEO constellation simulations by performing visible satellite number analysis and GDOP value analysis in the independent work mode. Finally, the average DOP values of the suitable constellations with different altitudes are derived. Fig. 2 illustrates our basic idea for the design of numerical simulations.
Augmentation of LEO constellations in the combined work mode
In this section, we focus on LEO constellations working in the combined mode and analyse the coverage performance of LEO constellations combined with the BDS. On June 23, 2020, China launched the last BDS satellite and completed the construction of BDS constellation. In the combined work mode, two scenarios are designed; one entails time synchronization between the LEO constellation and the BDS, and the other does not.
Conclusion
Aiming at performing orbital design of LEO navigation augmentation constellations based on the principle of providing global navigation services, this paper performs a performance assessment of the LEO constellations in the independent work mode and combined with the BDS.
Following the introduction of the LEO satellite constellation model, the DOP values calculated in the independent positioning mode and the combined mode of LEO constellations are derived from a theoretical point of view. Based
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was partially supported by the National Key Research Program of China (No. 2017YFE0131400), the National Natural Science Foundation of China (No.41674043, 41704038, 41730109), the Young Top-Notch Talents Team Program of Beijing Excellent Talents Funding (2017000021223ZK13), the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA17010304, XDA17010200), and the CAS Pioneer Hundred Talents Program. Additionally, thanks to www.space-track.org for providing the
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