The augmentation of the Global Navigation Satellite System (GNSS) by Low Earth Orbit (LEO) satellites is proposed as an effective method to improve the precision and shorten the convergence time of Precise Point Positioning (PPP). Serving as navigation satellites in the future, LEO satellites need to be provided with their high-accuracy orbits in real-time. This would potentially enable the high-accuracy real-time LEO satellite clock determination, and eventually facilitate the high-accuracy ground-based positioning. Studies have been performed to achieve such real-time orbits using a Kalman filter in both the kinematic and reduced-dynamic modes. Batch Least-Squares (BLS) adjustment delivers more stable orbits in near-real-time, as it performs better phase screening. However, it suffers from longer delays compared to the Kalman filter. With the LEO satellite orbit prediction strategies improved over time, this latency can be bridged by short-term orbit prediction. In this study, using real-time GNSS satellite products, the real-time LEO satellite orbits are obtained based on the batch least-squares adjustment and short-term prediction. LEO ephemeris parameters are generated within specific prediction time windows. Using real data from the 500 km GRACE C satellite and 810 km Sentinel-3B satellite, the near-real-time BLS Precise Orbit Determination (POD) results exhibit good accuracy with an Orbital User Range Error (OURE) of 2–4 cm using different real-time GNSS products. A range of delays of the BLS POD processes are assumed, based on tests performed on different processing machines, leading to various prediction windows, from 3–8 min to 12–17 min that correspond to the real-time usage. The orbital prediction errors are shown to be highly correlated with the orbital height and the prediction time. The computational efficiency thus becomes essential to reduce the prediction errors for a certain LEO satellite. For advanced processing units leading to a prediction window shorter or equal to 6–11 min, one can expect a total real-time orbital error budget of 3–5 cm, provided that an appropriate prediction strategy is applied and high-quality GNSS products are used. For a given fitting interval, the ephemeris fitting errors are generally related to the number of ephemeris parameters and the orbital height. Compared with the prediction errors, the ephemeris fitting errors do not play a significant role in the total error budget when using 22 ephemeris parameters.

The utilization of Low Earth Orbit (LEO) satellites is anticipated to augment various aspects of traditional GNSS-based Positioning, Navigation, and Timing (PNT) services. While the LEO satellite orbital products can nowadays be produced with rather high accuracy in real-time of a few centimeters, the precision of the LEO satellite clock products that can be achieved in real-time is less studied. The latter, however, plays an essential role in the LEO-augmented positioning and timing performances. In real-time, the users eventually use the predicted LEO satellite clocks, with their precision determined by both the near-real-time clock precision and the prediction time needed to match the time window for real-time applications, i.e., the precision loss during the prediction phase. In this study, a real-time LEO satellite clock determination method, consisting of near-real-time clock determination with ultra-short-term clock prediction is proposed and implemented. The principles and strategies of this method are discussed in detail. The proposed method utilized Kalman-filter-based processing, but supports restarts at pre-defined times, thus hampering continuous bias propagation and accumulation from ancient epochs. Based on the method, using Sentinel-3B GNSS observations and the real-time GNSS products from the National Center for Space Studies (CNES) in France, the near-real-time LEO satellite clocks can reach a precision of 0.2 to 0.3 ns, and the precision loss during the prediction phase is within 0.07 ns for a prediction time window from 30 to 90 s. This results in a total error budget in the real-time LEO satellite clocks of about 0.3 ns.

Augmentation of the Global Navigation Satellite System by low earth orbit (LEO) satellites is a promising approach benefiting from the advantages of LEO satellites. This, however, requires errors and biases in the satellite downlink navigation signals to be calibrated, modeled, or eliminated. This contribution introduces an approach for in-orbit calibration of the phase center offsets (PCOs) and code hardware delays of the LEO downlink navigation signal transmitter/antenna. Using the satellite geometries of Sentinel-3B and Sentinel-6A as examples, the study analyzed the formal precision and bias influences for potential downlink antenna PCOs and hardware delays of LEO satellites under different ground network distributions, and processing periods. It was found that increasing the number of tracking stations and processing periods can improve the formal precision of PCOs and hardware delay. Less than 3.5 mm and 3 cm, respectively, can be achieved with 10 stations and 6 processing days. The bias projections of the real-time LEO satellite orbital and clock errors can reach below 3 mm in such a case. For near-polar LEO satellites, stations in polar areas are essential for strengthening the observation model.

High-precision Low Earth Orbit (LEO) satellite clocks are essential for LEO-augmented Positioning, Navigation, and Timing (PNT) services. Nowadays, high-precision LEO satellite clocks can be determined in real-time using a Kalman filter either onboard or on the ground, as long as the GNSS observations collected onboard LEO satellites can be transmitted to the ground in real-time. While various real-time and high-precision GNSS products are available nowadays in the latter case, their continuity and latencies in engineering reality are not as perfect as expected and will lead to unignorable impacts on the precision of the real-time LEO satellite clocks. In this study, based on real observations of Sentinel-3B, the impacts of different latencies and continuity of the real-time GNSS products on LEO real-time clocks are determined and discussed for two scenarios, namely the “epoch estimation” and “arc estimation” scenarios. The former case refers to the traditional filter-based processing epoch-by-epoch, and the latter case connects LEO satellite clocks from different rounds of filter-based processing under a certain arc length. The two scenarios lead to the “end-loss” and “mid-gap” situations. Latencies of the real-time GNSS products are discussed for the cases of orbit-only latency, clock-only latency, and combined forms, and different handling methods for the missing GNSS satellite clocks are discussed and compared. Results show that the real-time LEO satellite clock precision is very sensitive to the precision of real-time GNSS satellite clocks, and prediction of the latter becomes essential in case of their latencies. For the “end-loss” situation, with a latency of 30 to 120 s for the GNSS real-time clocks, the LEO satellite clock precision is reduced from about 0.2 to 0.28–0.57 ns. Waiting for the GNSS products in case of their short latencies and predicting the LEO satellite clocks instead could be a better option. For “arc-estimation”, when the gap of GNSS real-time products increases from 5 to 60 min, the real-time LEO clock precision decreases from 0.26 to 0.32 ns.

Low earth orbit (LEO) satellites will enhance the Global Navigation Satellite Systems (GNSSs) in future positioning, navigation, and timing services. In addition to achieving high orbital accuracy of the LEO satellites, ensuring the reliability and safety of the near-real-time (NRT) LEO satellite precise orbit determination (POD) is equally essential for maintaining integrity in LEO-augmented positioning and timing, yet it is less studied. Compared to the favorable data conditions of scientific LEO satellites in post-processing mode, GNSS observations collected by navigation-oriented LEO satellites may encounter significant discontinuities due to not only tracking problems, but also transmission delays and interruptions within potential data downlinking for NRT ground-based POD, posing challenges to its integrity monitoring (IM). In particular, the protection level (PL) during observation gaps may encounter large increases and strongly harm the IM availability. This study investigates the algorithm calculating the NRT LEO satellite PLs under various observation gaps, followed by different lengths of observation tails based on the reduced-dynamic model. Experiments are conducted using seven consecutive days of Sentinel-6 A real GNSS data, assuming several hours of observation gaps per day. The strategy estimating (RD) and not estimating (CD) piecewise-constant stochastic accelerations in the POD process are both tested. While the former benefits the POD accuracy in complete data conditions, the latter exhibited its advantage in reducing the PLs within large data gaps. Results showed that during observation discontinuities, the RD strategy yields significantly degraded PLs in all three directions, which increase rapidly with gap duration. In the 9 h gap case, the along-track PL exceeds 20 m, while under nominal conditions, it remains around 0.51 m. In contrast, the CD strategy achieves more stable PLs, i.e. below 2 m even during a 9 h gap, although its convergence after observation recovery is slower. Furthermore, the study derives suitable thresholds of alert limits to bound 99% of the PLs under various gap conditions, providing a reference for LEO integrity assessment under such conditions.