With the completion of Chinese BeiDou Navigation Satellite System (BDS), the world has begun to enjoy the Positioning, Navigation, and Timing (PNT) services of four Global Navigation Satellite Systems (GNSS). In order to improve the GNSS performance and expand its applications, Low Earth Orbit (LEO) Enhanced Global Navigation Satellite System (LeGNSS) is being vigorously advocated. Combined with high-, medium-, and low- earth orbit satellites, it can improve GNSS performance in terms of orbit determination, Precise Point Positioning (PPP) convergence time, etc. This paper comprehensively reviews the current status of LeGNSS, focusing on analyzing its advantages and challenges for precise orbit and clock determination, PPP convergence, earth rotation parameter estimation, and global ionosphere modeling. Thanks to the fast geometric change brought by LEO satellites, LeGNSS is expected to fundamentally solve the problem of the long convergence time of PPP without any augmentation. The convergence time can be shortened within 1 minute if appropriate LEO constellations are deployed. However, there are still some issues to overcome, such as the optimization of LEO constellation as well as the real time LEO precise orbit and clock determination.

With the fast development of Low Earth Orbit enhanced Global Navigation Satellite System (LeGNSS), there is huge demand in LEO real-time Precise Orbit Determination (POD). Real-time Service (RTS) from International GNSS Service (IGS) provides the real-time precise GNSS orbit and clock products, which gives an opportunity to make use of kinematic precise point positioning (PPP) method for LEO POD. However, real-time precise GNSS products and onboard GNSS observations interrupt inevitably or even frequently (especially for real-time clock products), resulting in PPP reconvergence as well as large orbit errors in LEO orbit solutions. A new method is put forward to reduce such influence of two types of data interruptions. For interruption of clock products, the Chebyshev extrapolation is used to maintain the continuity of real-time GNSS clock products. For the onboard observation interruption, the predicted dynamic orbits are employed as constraints to overcome the PPP reconvergence. Results show that zero-reconvergence PPP can be realized with our new method, which means there is almost no reconvergence time after data interruption. Moreover, clock prediction can reduce the root mean square errors (RMSE) for real-time LEO orbit from 5.40, 4.70, and 7.33 cm to 5.18, 4.55, and 5.99 cm in along-track, cross-track, and radial directions, respectively, while the predicted dynamic orbit constraints reduce the orbit RMSE by 20-30% in cross-track component and 60-80% in other two components.

This article is dedicated to addressing the localization challenge in 5G environments, specifically utilizing time-of-arrival (TOA) measurements. The focus is on scenarios where the user equipment (UE) and base transceiver stations (BTSs) or first-generation NodeBs (gNBs) face challenges related to synchronization or inaccurate BTS or gNB positions. First, we present the range-weighted majorization minimization (RW-MM) algorithm, harnessing majorization minimization (MM) techniques for UE localization. We rigorously establish the algorithm’s monotonicity and demonstrate its convergence to a stationary point, providing a theoretical foundation for the RW-MM method. In addition, we present a novel UE localization method called robust range-weighted semidefinite relaxation (RRW-SDR). This method is specifically designed for situations involving bounded gNB position errors. The RRW-SDR algorithm optimizes the worst-case weighted least square function while uniquely addressing the individual error constraints associated with each gNB. Furthermore, we derive the Cramér-Rao lower bound (CRLB) for TOA-based UE localization. We additionally establish a more stringent lower bound on the determinant of the target estimation error covariance. This is particularly significant when dealing with scenarios that include independent measurement noise with varying variances. Moreover, we identify an optimal user-gNB geometrical configuration capable of achieving this lower bound. To validate the effectiveness and practical applicability of our contributions, we conduct a series of meticulous numerical simulations. These experiments affirm the robustness and utility of the developed methods.

The Korean government has a plan to build a new regional satellite navigation system called the Korean Positioning System (KPS). The initial KPS constellation is designed to consist of seven satellites, which include three geostationary Earth orbit (GEO) satellites and four inclined geosynchronous orbit (IGSO) satellites. KPS will provide an independent positioning, navigation, and timing (PNT) service in the Asia-Oceania region and can also be compatible with GPS. In the simulation for KPS, we employ 24 GPS as designed initially and 7 KPS satellites. Compared to the true orbit that we simulated, the averaged root mean square (RMS) values of orbit-only signal-in-space ranging errors (SISRE) are approximately 4.3 and 3.9 cm for KPS GEO and IGSO. Two different positioning solutions are analyzed to demonstrate the KPS performance. KPS standard point positioning (SPP) errors in the service area are about 4.7, 3.9, and 7.1 m for east (E), north (N), and up (U) components, respectively. The combined KPS+GPS SPP accuracy can be improved by 25.0%, 31.8%, and 35.0% compared to GPS in E, N, and U components. The averaged position errors for KPS kinematic precise point positioning (KPPP) are less than 10 cm. In the fringe of the KPS service area, however, the position RMS errors can reach about 40 cm. Unlike KPS, GPS solutions show high positioning accuracy in the KPS service area. The combined KPS+GPS can be improved by 28.7%, 27.1%, and 30.5% compared to GPS in E, N, and U components, respectively. It is noted that KPS can provide better performance with GPS in the Asia-Oceania region.