Meifang Wu

Low Earth orbit (LEO)-augmented positioning, navigation, and timing (PNT) has been a research hotspot in recent years, and high-precision LEO real-time (RT) clocks are one of the essential pre-conditions to enable single-receiver-based high-precision RT PNT services. The precision of the RT LEO satellite clocks typically needs to be considered from two aspects: (i) near-real-time (NRT) clock determination based on onboard Global Navigation Satellite System (GNSS) observation data; (ii) short-term clock prediction to compensate for delays caused by computation and transmission. While the latter part typically causes only slight precision loss due to the short prediction time, the former part majorly influences the RT LEO satellite clock prediction. In this study, various factors that influence NRT clock determination are analyzed using onboard GNSS observations from the LEO satellite Gravity Recovery and Climate Experiment Follow-On. Tests are performed with two processing strategies, namely with a Kalman filter (KF) kinematic precision orbit determination (POD) model and a reduced-dynamic (RD) POD model with batch-least-squares (BLS) adjustment. The KF-based processing is started at pre-defined times each round to hamper bias influences of historical epochs. It is found that shortening the observation arc length incurs minimal precision loss, yet notably enhances computational efficiency. Shortening the sampling interval improves clock precision while increasing processing time. With an observation arc length of 6 h and a sampling interval of 30 s, the RT clock precision is about 0.15 ns. Compared to the KF-based model, the BLS-based RD model is typically more time-consuming but more precise. Shortening the observation arc length can cause significant border effects in the NRT BLS clock results.

High precision of real-time (RT) low Earth orbit (LEO) satellite clocks is crucial for enabling future LEO-enhanced positioning, navigation, and timing services. For filter-based RT processing, multi-GNSS observations from onboard LEO satellites can strengthen the observation model and improve the LEO precise orbit determination, but have limited improvement effect on the clock estimation. The time references for RT GNSS clocks of different constellations (even from the same analysis center) are different and vary with time. This requires estimating constellation-wise LEO satellite clocks or time-varying inter-system biases (ISBs). This contribution investigates multi-GNSS LEO satellite clock and the corresponding signal-in-space ranging errors (SISRE) using GPS/Galileo observations collected onboard Sentinel-6A satellite, and GNSS products from various analysis centers with different latencies, including the Centre National d’Etudes Spatiales real-time (RT), the GeoForschungsZentrum Multi-GNSS Experimental (MGEX) rapid, the European Space Agency MGEX final, and the Wuhan University MGEX final products. Three ISB stochastic models were implemented, i.e. the constant, the random walk, and the white noise models. Results show that the ISB estimates exhibit systematic effects of orbital periods (ca. 1.85 h) when applying the random walk or white noise models using the post-processing products. The white noise model shows the best performance when applying the RT GNSS products with large time-varying differences in the constellation-wise time references, with improvements of about 40.8% and 12.5% for clock precision, and about 38.1% and 7.9% for SISRE, respectively, compared to the constant and random walk models. When using the post-processing products with very similar time references for different constellations, the three ISB stochastic models do not deliver significant differences in clock precision and SISRE. This contribution provides a reference for ISB estimation strategy when using multi-constellation GNSS measurements to estimate RT LEO satellite clocks.

To realize the various benefits brought by Low Earth Orbit (LEO) satellites in single-receiver high-precision GNSS-based Positioning Navigation and Timing (PNT) services, LEO satellite orbits and clocks need to be processed and delivered to users in real-time with precision of a few centimeters. While post-processing of cm-level LEO satellite orbits and clocks can be widely achieved, real-time processing faces various Challenges. When the number of LEO satellites increases, the observation data downlinked to the processing center may experience large and complicated discontinuities and incompleteness depending on the downlinking strategies. Even with the observations downlinked in real-time, the LEO satellite clock precision tends to be very sensitive to the continuity and quality of the GNSS real-time products. This study first introduces the procedure for ground-based cm-level real-time LEO satellite Precise Orbit Determination (POD), including near-real-time POD, short-term prediction, and ephemeris fitting/broadcasting. Next, the short-term predicted orbits and long-term predicted clocks of LEO satellites are introduced and properly constrained in filter-based real-time LEO satellite clock determination to achieve a precision of about 0.2 ns. Strategies to deal with sub-optimal observation data and GNSS products are explained. With the proposed methods, a Signal-In-Space Ranging Error at sub-dm to 1 dm can be achieved in practice.

A uniformly distributed global ground network is essential for the accurate determination of GNSS orbit and clock parameters. However, achieving an ideal ground network is often difficult. When limited to a sparse or regional network of ground stations, the integration of LEO satellites can substantially enhance the accuracy of GNSS Precise Orbit Determination (POD). In practical processing, discontinuities with complicated gaps can occur in LEO attitude quaternions, particularly when working with a restricted observation network. This hampers the accuracy of determining GNSS/LEO integrated orbits. To address this, an investigation was conducted using data from seven LEO satellites, including those from Sentinel-3, GRACE-FO, and Swarm, to evaluate integrated POD performance under sparse or regional station conditions. Particular focus was placed on addressing attitude discontinuities. Four scenarios were analyzed, encompassing both continuous data availability and one-, two-, and three-hour interruptions after one hour of continuous data availability. The results showed that the proposed quaternion rotation matrix interpolation method is reliable for the integrated POD of GNSSs and LEOs with strict attitude control.

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.

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.