Optimizing the Deployment of Ground Tracking Stations for Low Earth Orbit Satellite Constellations Based on Evolutionary Algorithms  
[PERSON]  
1 SNARS Laboratory, School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China; [EMAIL_ADDRESS] (M.K. ); [EMAIL_ADDRESS] (A.T.); [EMAIL_ADDRESS] (A.O.) [PERSON]  
1 SNARS Laboratory, School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China; [EMAIL_ADDRESS] (M.K. ); [EMAIL_ADDRESS] (A.T.); [EMAIL_ADDRESS] (A.O.) [PERSON]  
1 SNARS Laboratory, School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China; [EMAIL_ADDRESS] (M.K. ); [EMAIL_ADDRESS] (A.T.); [EMAIL_ADDRESS] (A.O.) [PERSON]  
1 SNARS Laboratory, School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China; [EMAIL_ADDRESS] (M.K. ); [EMAIL_ADDRESS] (A.T.); [EMAIL_ADDRESS] (A.O.) [PERSON]  
3 Institute of Remote Sensing Satellite, China Academy of Space Technology, Beijing 100094, China; [EMAIL_ADDRESS] *Correspondence: [EMAIL_ADDRESS]; Tel. : +86-10-823139293  
The analyses in the above studies, including LEO-PNT and LEO-augmented GNSSs, are based on the supposition of precise orbit determination, which can only be assured through the thorough analysis of ground segments. Subsequently, the optimal distribution of ground stations (GSs) plays a vital role in utilizing LEO constellations as a reliable support for navigation. More than 71% of Earth's area is covered by oceans, making it difficult to determine the optimal configuration for distributing and deploying GSs for tracking LEO satellites. In their work, [PERSON] and [PERSON] [13] analyzed the quadruple coverage of the GLONASS constellation by ground stations (i.e., where at least four stations are visible to each satellite at any given time). The authors concluded that with the uniform distribution of 21 ground stations, the GLONASS constellation can achieve quadruple coverage, and a good distribution of GSs improves the accuracy of the orbit determination and the satellite clock estimation. In the study of [PERSON] et al. [14], 25 ground stations were used with a triangular irregular network (TIN) formation to achieve an enhancement in the clock accuracy of global positioning system (GPS) satellites. The authors concluded that augmenting the number of ground stations does not necessarily improve accuracy. Therefore, the optimal number together with optimal deployment must be ensured. [PERSON] et al. [15] used the grid control method, which is based on the globe's division into a grid, to obtain the optimal distribution of global stations. The authors discussed the impact of geometric distribution on precise orbit determination. However, obtaining an optimal distribution of ground stations for constellation monitoring remains difficult due to the non-uniformity in the geographic coordinate grid (latitude and longitude) divisions of the Earth. The geometric dilution of precision (GDOP) is one widely used metric that is applied in the optimization of ground station (GS) deployment. In their study, [PERSON] and [PERSON] [16] considered other factors in addition to the GDOP, namely signal availability level, number of visible satellites, scintillation fade depth, ionospheric delay and rainfall attenuation, to select ground station locations to develop a local satellite-based augmentation system (SBAS). Based on grid control probabilities, a method of configuring global station tracking networks was proposed by [PERSON] et al. [17] to achieve an optimal configuration with a minimum GDOP. The objectives of the optimal configuration were the rapid orbit of GNSSs and satellite clock estimation. [PERSON] et al. [18] studied how ground tracking station deployment structure impacted the accuracy of the orbit determination of the BeiDou Navigation Satellite System (BDS) constellation. Two scenarios of distribution were analyzed to study their effect on the accuracy of the real-time orbit determination of the BDS.