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Real-time, high-accuracy orbital products for low Earth orbit (LEO) satellites are essential for LEO-augmented real-time positioning, navigation and timing services. In particular, complete and continuous global navigation satellite system (GNSS) observations onboard tracked LEO satellites are necessary to guarantee precise orbit determination (POD) and generate short-term predicted orbits that can be fit with real-time ephemeris parameters. However, in practice, GNSS observations of LEO satellites often suffer from discontinuities due to tracking problems, data transmission problems, or downlinking strategies. Understanding the effect of these observation gaps on orbit accuracy is therefore essential for developing strategies to minimize accuracy degradation in real-time LEO satellite orbits. This study investigates trade-offs between two suites of strategies for addressing multi-hour observation data gaps followed by short segments of tail data during reduced-dynamic POD. The first strategy, EP, involves sacrificing the tail data and extending the prediction time. The second set of strategies retain the tail data but vary the POD strategies: the tested options include maintaining stochastic accelerations as estimable parameters (RP), not estimating stochastic accelerations (CP), or combining the RP-based orbits from the non-gap periods with the CP-based orbits during the gap (BP). Using real GNSS observations from the LEO satellite Sentinel-6A, we evaluated the accuracy and integrity of these strategies for 1-h orbital predictions with assumed gap lengths of 3, 5, 7, and 9 h and tail data lengths set to 15, 30, 45, and 60 min. Results show that the BP strategy achieves the highest prediction accuracy, with mean orbital user range errors (OUREs) of approximately 5.7 and 13.4 cm for a 3-h data gap followed by 60-min and 15-min tails, respectively. In contrast, the EP strategy demonstrates the highest integrity. For a 15-min tail, the 99.9% confidence level of the OURE for the EP strategy reaches approximately 3.1 and 8.7 dm for gap lengths of 3 h and 9 h, respectively. Overall, BP is the preferred strategy for maximizing prediction accuracy, while the EP strategy is preferable for short gaps and tails. The CP strategy provides a balanced approach, maintaining reasonably strong performance for both prediction accuracy and integrity.

Atmospheric drag is an important influencing factor in precise orbit determination and the prediction of low-orbit space debris. It has received widespread attention. Currently, calculating atmospheric drag mainly relies on different atmospheric density models. This experiment was designed to explore the impact of different atmospheric density models on the orbit prediction of space debris. In the experiment, satellite laser ranging data published by the ILRS (International Laser Ranging Service) were used as the basis for the precise orbit determination for space debris. The prediction error of space debris orbits at different orbital heights using different atmospheric density models was used as a criterion to evaluate the impact of atmospheric density models on the determination of space-target orbits. Eight atmospheric density models, DTM78, DTM94, DTM2000, J71, RJ71, JB2006, MSIS86, and NRLMSISE00, were compared in the experiment. The experimental results indicated that the DTM2000 atmospheric density model is best for determining and predicting the orbits of LEO (low-Earth-orbit) targets.

Precise Global Navigation Satellite System (GNSS) orbit prediction is critical for real-time positioning applications. Current orbit prediction accuracy for the BeiDou Navigation Satellite System-3 (BDS-3) exhibits a notable disparity compared to GPS and Galileo, with limited advancements from traditional dynamic modeling approaches. This study introduces a novel data-driven methodology, Sample Convolution and Interaction Network with Self-Attention (SCINet-SA), to augment dynamic methods and improve BDS-3 ultra-rapid orbit prediction. SCINet-SA leverages deep learning to model the temporal characteristics of orbit differences between BDS-3 ultra-rapid and final products. By training on historical orbit difference data, SCINet-SA predicts future discrepancies, facilitating the refinement of ultra-rapid orbit estimates. The incorporation of a self-attention mechanism within SCINet-SA enables the model to effectively capture long-range temporal dependencies, thereby enhancing long-term prediction capabilities and mitigating the latency associated with final product availability. Rigorous experimental evaluation demonstrates the superior performance of SCINet-SA in enhancing BDS-3 ultra-rapid orbit prediction accuracy relative to alternative deep learning models. Specifically, SCINet-SA achieved the highest average relative improvement (IMP) in 3D Root Mean Square (RMS) error across 1 d, 7 d, and 15 d prediction horizons, yielding improvements of 21.69%, 18.66%, and 15.42%, respectively. The observed IMP range spanned from 7.78% to 38.91% for 1 d, 4.34% to 35.96% for 7 d, and 1.68% to 31.13% for 15 d predictions, underscoring the efficacy of the proposed methodology in advancing BDS-3 orbit prediction accuracy.

AbstractIn January 2023, the International Laser Ranging Service (ILRS) approved the tracking of 20 additional BeiDou-3 Medium Earth Orbit (BDS-3 MEO) satellites, integrating them into the ILRS tracking network. Before that, only 4 BDS-3 MEO satellites had been tracked. BDS satellites employ highly advanced GNSS components and technological solutions; however, microwave-based orbits still contain systematic errors. Satellite Laser Ranging (SLR) tracking is thus crucial for better identification and understanding of orbit modeling issues. Orbit improvements are necessary to consider BDS in future realizations of terrestrial reference frames, supporting the determination of global geodetic parameters and utilizing them for the co-location of GNSS and SLR in space. In this study, we summarize the first 6 months of SLR tracking 24 BDS-3 MEO satellites. The study indicates that the ILRS network effectively executed the request to track the entire BDS-3 MEO constellation. The number of observations is approximately 1300 and 450 for high- and low-priority BDS-3 satellites, respectively, over the 6 months. More than half of the SLR observations to BDS-3 MEO satellites were provided by 5 out of the 24 laser stations, which actively measured GNSS targets. For 14 out of 24 BDS-3 MEO satellites, the standard deviation of SLR residuals is at the level of 19–20 mm, which is comparable with the quality of the state-of-the-art Galileo orbit solutions. However, the SLR validation of the individual satellites revealed that the BDS-3 MEO constellation consists of more ambiguous groups of satellites than originally reported in the official metadata files distributed by the BDS operators. For 8 BDS-3 satellites, the quality of the orbits is noticeably inferior with a standard deviation of SLR residuals above 100 mm. Therefore, improving orbit modeling for BDS-3 MEO satellites remains an urgent challenge for the GNSS community.

Low Earth Orbit (LEO) satellites have been widely used in scientific fields or commercial applications in recent decades. The demands of the real time scientific research or real time applications require real time precise LEO orbits. Usually, the predicted orbit is one of the solutions for real time users, so it is of great importance to investigate LEO orbit prediction for users who need real time LEO orbits. The centimeter level precision orbit is needed for high precision applications. Aiming at obtaining the predicted LEO orbit with centimeter precision, this article demonstrates the traditional method to conduct orbit prediction and put forward an idea of LEO orbit prediction by using onboard accelerometer data for real time applications. The procedure of LEO orbit prediction is proposed after comparing three different estimation strategies of retrieving initial conditions and dynamic parameters. Three strategies are estimating empirical coefficients every one cycle per revolution, which is the traditional method, estimating calibration parameters of one bias of accelerometer hourly for each direction by using accelerometer data, and estimating calibration parameters of one bias and one scale factor of the accelerometer for each direction with one arc by using accelerometer data. The results show that the predicted LEO orbit precision by using the traditional method can reach 10 cm when the predicted time is shorter than 20 min, while the predicted LEO orbit with better than 5 cm for each orbit direction can be achieved with accelerometer data even to predict one hour.

The technology of satellite orbit prediction (OP) is crucial in space engineering. However, it is difficult to precisely predict medium and long-term orbit for the low Earth-orbit (LEO) satellites because of time-varying space weather and inaccurate atmospheric density models. To address the problem, a novel intelligent OP method based on the variational mode decomposition-support vector machine (VMD-SVM) framework is presented. First, the concept of a pseudo-drag coefficient is defined, transforming the OP problem into a pseudo-drag coefficient prediction problem. Second, the relationship between space weather parameters and the pseudo-drag coefficient is analyzed using the VMD method, from which a strong correlation is shown. Furthermore, an SVM model combined with space weather characteristic parameters is employed to predict the pseudo-drag coefficient, significantly improving the precision of OP when further integrated into the orbital dynamics model. Experiments with data from engineering applications show that VMD-SVM medium and long-term OP technology is practical and effective.

The BeiDou Global Navigation Satellite System (BDS-3) provides real-time precise point positioning (PPP) service via B2b signals, offering real-time decimeter-level positioning for users in China and surrounding areas. However, common interruptions and outliers in PPP-B2b services arise due to factors such as the Geostationary Orbit (GEO) satellite “south wall effect”, Issue of Data (IOD) matching errors, and PPP-B2b signal broadcast priorities, posing challenges to continuous high-precision positioning. This study meticulously examines the completeness, continuity, and jumps in PPP-B2b orbit and clock correction using extensive observational data. Based on this analysis, a two-step method for detecting outliers in PPP-B2b orbit and clock corrections is devised, leveraging epoch differences and median absolute deviation. Subsequently, distinct prediction methods are developed for BDS-3 and GPS orbit and clock corrections. Results from simulated and real-time dynamic positioning experiments indicate that predicted corrections can maintain the same accuracy as normal correction values for up to 10 min and sustain decimeter-level positioning accuracy within 30 min. The adoption of predicted correction values significantly enhances the duration of sustaining real-time PPP during signal interruptions.

The increasing proliferation of space debris, intermittent space incidents, and the rapid emergence of massive LEO satellite constellations pose significant threats to satellites in orbit. Ground-based optical observations play a crucial role in space surveillance and space situational awareness (SSA). The Zhulong telescopic observation network stands as a pivotal resource in the realm of space object tracking and prediction. This publicly available network plays a critical role in furnishing essential data for accurately delineating and forecasting the orbit of space objects in Earth orbit. Comprising a sophisticated array of hardware components including precise telescopes, optical sensors, and image sensors, the Zhulong network synergistically collaborates to achieve unparalleled levels of precision in tracking and observing space objects. Central to the network’s efficacy is its ability to extract positional information, referred to as angular data, from consecutive images. These angular data serve as the cornerstone for precise orbit determination and prediction. In this study, the CPF (Consolidated Prediction Format) orbit serves as the reference standard against which the accuracy of the angular data is evaluated. The findings reveal that the angular data error of the Zhulong network remains consistently below 3 arcseconds, attesting to its remarkable precision. Moreover, through the accumulation of angular data over time, coupled with the utilization of numerical integration and least squares methods, the Zhulong network facilitates highly accurate orbit determination and prediction for space objects. These methodologies leverage the wealth of data collected by the network to extrapolate trajectories with unprecedented accuracy, offering invaluable insights into the behavior and movement of celestial bodies. The results presented herein underscore the immense potential of electric optic telescopes in the realm of space surveillance. By harnessing the capabilities of the Zhulong network, researchers and astronomers can gain deeper insights into the dynamics of space objects, thereby advancing our understanding of the cosmos. Ultimately, the Zhulong telescopic observation network emerges as a pioneering tool in the quest to unravel the mysteries of the universe.

Orbit prediction (OP) for global navigation satellite system (GNSS) satellites is crucial for current location-based Internet of Things (IoT) applications. However, the prediction accuracy is subject to the precision of solar radiation pressure (SRP) model. This paper proposes a novel, time-varying a-priori SRP model for the BeiDou-3 navigation satellite system (BDS-3) medium Earth orbit (MEO) satellite OP, designated A-ECOM. Utilizing the extended CODE (Center for Orbit Determination in Europe) orbit model (ECOM) as the background model, the time series of SRP parameters from 2019 to 2021 are obtained through fitting precise ephemerides; their primary frequencies are then characterized using the fast Fourier transform (FFT). Based on this analysis, A-ECOM is constructed for each satellite, represented by a combination of linear and periodical terms. The OP validation of A-ECOM is conducted with different fitting arc lengths throughout 2022. When predicting BDS-3 orbits with a fitting arc length shorter than 1 d, the utilization of A-ECOM with a relatively tight constraint significantly improves the orbit accuracy compared to the classical ECOM model. For instance, a long-term OP (14-d) with a 4-h fitting arc length reveals a dramatic reduction in the average signal-in-space ranging error (SISRE) from 250.36 m to 7.17 m for MEO satellites manufactured by China Academy of Space Technology (MEO-CAST) and from 273.84 m to 9.36 m for MEO satellites manufactured by Shanghai Engineering Center for Microsatellites (MEO-SECM). Furthermore, this model features an advantage for long-term OP as it captures the temporal variations in SRP parameters, thereby generating dynamic SRP parameters during orbit fitting and prediction. For the 14th-d OP with a long fitting arc length of 5 d, the average SISRE of MEO-CAST exhibits a significant reduction from 3.69 m to 1.90 m, while that of MEO-SECM is reduced from 2.51 m to 2.06 m, compared to the ECOM model.

As the deployment of large Low Earth Orbiters (LEO) communication constellations, navigation from the LEO satellites becomes an emerging opportunity to enhance the existing satellite navigation systems. The LEO navigation augmentation (LEO-NA) systems require a centimeter to decimeter accuracy broadcast ephemeris to support high accuracy positioning applications. Thus, how to design the broadcast ephemeris becomes the key issue for the LEO-NA systems. In this paper, the temporal variation characteristics of the LEO orbit elements were analyzed via a spectrum analysis. A non-singular element set for orbit fitting was introduced to overcome the potential singularity problem of the LEO orbits. Based on the orbit characteristics, a few new parameters were introduced into the classical 16 parameter ephemeris set to improve the LEO orbit fitting accuracy. In order to identify the optimal parameter set, different parameter sets were tested and compared and the 21 parameters data set was recommended to make an optimal balance between the orbit accuracy and the bandwidth requirements. Considering the real-time broadcast ephemeris generation procedure, the performance of the LEO ephemeris based on the predicted orbit is also investigated. The performance of the proposed ephemeris set was evaluated with four in-orbit LEO satellites and the results indicate the proposed 21 parameter schemes improve the fitting accuracy by 87.4% subject to the 16 parameters scheme. The accuracy for the predicted LEO ephemeris is strongly dependent on the orbit altitude. For these LEO satellites operating higher than 500 km, 10 cm signal-in-space ranging error (SISRE) is achievable for over 20 min prediction.