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In August 2016, Milena (E14) and Doresa (E18) satellites started to broadcast ephemeris in navigation message for testing purposes. If these satellites could be used, an improvement in the position accuracy would be achieved. A small error in the ephemeris would impact the accuracy of positioning up to ±2.5 m, thus orbit error must be assessed. The ephemeris quality was evaluated by calculating the SISEorbit (in orbit Signal In Space Error) using six different ephemeris validity time thresholds (14,400 s, 10,800 s, 7200 s, 3600 s, 1800 s, and 900 s). Two different periods of 2018 were analyzed by using IGS products: DOYs 52–71 and DOYs 172–191. For the first period, two different types of ephemeris were used: those received in IGS YEL2 station and the BRDM ones. Milena (E14) and Doresa (E18) satellites show a higher SISEorbit than the others. If validity time is reduced, the SISEorbit RMS of Milena (E14) and Doresa (E18) greatly decreases differently from the other satellites, for which the improvement, although present, is small. Milena (E14) and Doresa (E18) reach a SISEorbit RMS of about 1 m (comparable to that of the other Galileo satellites reach with the nominal validity time) when validity time of 1800 s is used. Therefore, using this threshold, the two satellites could be used to improve single point positioning accuracy.

The integration of low Earth orbit (LEO) satellite constellations into the Global Navigation Satellite System (GNSS) has emerged as a prominent research focus, as LEO satellites can significantly enhance the precision of GNSS positioning, navigation, and timing (PNT) services. In the design of LEO navigation constellations, the development of an efficient broadcast ephemeris model is critical for delivering high-accuracy navigation solutions. This study extends the conventional 16-parameter Keplerian broadcast ephemeris model by proposing enhanced 18-, 20-, 22-, and 24-parameter models, ensuring compatibility with existing GNSS ephemeris standards. The performance of these models was evaluated using precise science orbit from five satellites at varying altitudes, ranging from 320 km to 1336 km. By analyzing fitting errors, Signal-in-Space Range Error (SISRE), and Message Size Bits (MSB) across different fitting arc durations and parameter counts, the optimal model configuration was identified. The results demonstrate that the 22-parameter model, which was constructed by augmenting the standard 16-parameter ephemeris with (a˙, n˙, Crs3, Crc3, Crs1, Crc1) delivers the best balance of accuracy and efficiency. With a fitting arc length of 20 min, the SISRE for the GRACE-A (320 km), GRACE-C (475 km), Sentinel-2A (786 km), HY-2A (966 km), and Sentinel-6A (1336 km) satellites were measured at 8.88 cm, 6.21 cm, 2.87 cm, 2.11 cm, and 0.75 cm, respectively. Meanwhile, the corresponding MSB remained compact at 501, 490, 491, 487, and 476 bits. These findings confirm that the proposed 22-parameter broadcast ephemeris model meets the stringent accuracy requirements for next-generation LEO-augmented GNSSs, paving the way for enhanced global navigation services.

The accuracy of GNSS positioning is largely determined by the type of ephemeris data applied. These include broadcast ephemeris, which is accessible in real time, and precise ephemeris, which is released after post-processing by institutions like the International GNSS Service (IGS). In this study, the performance of two receiver classes was assessed, namely the U-Blox F9P as a representative of cost-efficient GNSS technology and a Trimble model as a professional-grade geodetic receiver, under both broadcast and precise ephemeris conditions. The collected GNSS observations were analyzed in post-processing mode using RTKLib, with the respective ephemeris settings applied. Both instruments were able to continuously track 8 to 11 satellites during all sessions, showing very little difference between the two ephemeris types. For the U-Blox F9P, the mean Root Mean Square Error (RMSE) obtained with broadcast ephemeris reached 0.259 m along the North component, 0.351 m on the East component, and 0.157 m in the Height. With precise ephemeris, the average RMSE results were 0.261 m (North), 0.344 m (East), and 0.157 m (Height). For the Trimble geodetic receiver, the corresponding RMSE values were 0.212 m (North), 0.346 m (East), and 0.139 m (Height) using broadcast data, and 0.261 m (North), 0.343 m (East), and 0.151 m (Height) using precise data. These outcomes indicate that switching between ephemeris types offers only minor, almost negligible, benefits in positioning accuracy for both categories of receivers in static post-processing. The results also highlight that the U-Blox F9P demonstrates performance comparable to the Trimble receiver, especially in terms of horizontal accuracy. This shows that affordable GNSS devices have strong potential for spatial data applications where cost efficiency is critical and sub-meter accuracy is sufficient.

Low earth orbit (LEO) satellite constellations have the potential to augment global navigation satellite system services. Among the ongoing tasks of LEO-based navigation, providing broadcast ephemerides that satisfy the accuracy requirement for positioning, navigation, and timing is one of the most critical prerequisites. Singularities can occur when fitting broadcast ephemeris parameters in the case of a small eccentricity or small or large inclination. We choose an improved nonsingular element set for the LEO broadcast ephemeris design. We establish suitable broadcast ephemeris models, considering the fit accuracy, number of parameters, orbital altitude, and inclination. The fit accuracy using different orbital altitudes, orbital inclinations, and eccentricities suggests that the optimal parameters are n˙, n¨, Crc3, Crs3, Cλc3, and Cλs3, together with the basic broadcast ephemeris model. After adding these six parameters, a fit accuracy of better than 10 cm can be achieved with a 20 min arc length and 500–1400 km orbital altitudes. The effects of the number of parameters, orbital altitude, inclination, and eccentricity on the fit accuracy are discussed in detail. Finally, the performance is validated with real LEO satellites to confirm the effectiveness of the proposed method.

Due to errors of earth rotation parameters (ERPs) adopted when generating the broadcast ephemeris, GNSS broadcast ephemeris suffers orientation deficiencies called constellation rotation errors. Moreover, significant rotation inconsistencies are indicated among different GNSS ephemerides as they utilize different sets of ERPs. Based on the ERP datasets from broadcast navigation messages, we investigate the correlation between broadcast ERPs and ephemeris rotation errors for GPS and BDS-3, and then explore orbital rotation correction using broadcast ERPs. Evaluation of the broadcast ERPs indicates the average root mean square errors (RMSEs) of GPS xp, yp, and UT1-UTC are 1.00, 0.67 mas, and 0.17 ms, respectively, while those of BDS-3 are 2.52, 1.51 mas, and 0.44 ms. BDS-3 performs about 2–3 times worse due to its longer update latency. Comparing to the rotation parameters derived from Helmert transformation between broadcast and precise ephemerides, we demonstrate that the GPS and BDS-3 broadcast ERPs exhibit a prominent correlation with orbital orientation. The correlation coefficients between polar motion errors and X/Y-axis rotation parameters exceed 0.88 for GPS and 0.77 for BDS, whereas no significant correlation is found between the UT1-UTC error and the Z-axis rotation. We propose to correct the orbital orientation inconsistencies between BDS-3 and GPS by aligning their broadcast ERPs, explicitly the polar motion. The GPS ERPs are utilized as a reference due to higher precision and real-time availability. The BDS-3 broadcast orbit after correction reveals precision improvement of approximately 3.0 and 1.0 cm in the along-track and cross-track components, respectively. Static precise point positioning test with GPS and BDS-3 ephemerides also indicates a remarkable positioning improvement in north direction of 21.9% when BDS-3 ephemeris is corrected by the ERP alignment approach.

Since BeiDou Navigation Satellite System (BDS) and Japan’s Quasi-Zenith Satellite System (QZSS) have more visible satellites in the Asia-Pacific region, and navigation satellites of Global Positioning System (GPS), Galileo satellite navigation system (Galileo), and GLONASS satellite navigation system (GLONASS) are uniformly distributed globally, the service level of multi-mode Global Navigation Satellite System (GNSS) in the Asia-Pacific region should represent the best service capability. Based on the observation data of 10 Multi-GNSS Experiment (MGEX) stations, broadcast ephemeris and precision ephemeris from 13 to 19 October 2021, this paper comprehensively evaluated the service capability of multi-GNSS in the Asia-Pacific region from three aspects of observation data quality, broadcast ephemeris performance, and precision positioning level. The results show that: (1) the carrier-to-noise-density ratio (C/N0) quality of the GPS and Galileo is the best, followed by BDS and GLONASS, and QZSS is the worst. GPS, BDS-2, GLONASS, and QZSS pseudorange multipath values range from 0 to 0.6 m, while Galileo system and BDS-3 pseudorange multipath values range from 0 to 0.8 m. (2) In terms of broadcast ephemeris accuracy, BDS-3 broadcast ephemeris has the best orbit, and the three-dimensional (3D) Root Mean Square (RMS) is 0.21 m; BDS-2 was the worst, with a 3D RMS of 1.99 m. The broadcast ephemeris orbits of GPS, Galileo, QZSS, and GLONASS have 3D RMS of 0.60 m, 0.62 m, 0.83 m, and 1.27 m, respectively. For broadcast ephemeris clock offset: Galileo has the best performance, 0.61 ns, GLONASS is the worst, standard deviation (STD) is 3.10 ns, GPS, QZSS, BDS-3 and BDS-2 are 0.65 ns, 0.75 ns, and 1.72 ns, respectively. For signal-in-space ranging errors (SISRE), the SISRE results of GPS and Galileo systems are the best, fluctuating in the range of 0 m–2 m, followed by QZSS, BDS-3, Galileo, and BDS-2. (3) GPS, BDS, GLONASS, Galileo, GPS/QZSS, and BDS/QZSS were used for positioning experiments. In static PPP, the convergence time and positioning accuracy of GPS show the best performance. The positioning accuracy of GPS/QZSS and BDS/QZSS is improved compared with that of GPS and BDS. In terms of kinematic PPP, the convergence time and positioning accuracy of GPS/QZSS and BDS/QZSS are improved compared with that of GPS and BDS. In addition to GLONASS and Galileo systems, the other combinations outperformed 3 cm, 3 cm, and 5 cm in the east, north, and up directions.

Most global navigation satellite systems (GNSSs) ephemeris representations require straightforward, albeit specialized algorithms to compute the transmitter position at a time of interest. As potential positioning, navigation, and timing (PNT) signal sources expand beyond medium Earth orbit, these representations must be modified to capture the dynamics of the host platforms. This work introduces the use of B-splines as a flexible framework to represent transmitter ephemerides that are applicable to any orbital or airborne regime and host platform. With this approach, the user equipment implements a simple, generic algorithm to compute transmitter positions from the B-spline representation that require no orbit or platform specific models. Here we propose a B-spline ephemeris approach in which we compare the required navigation message length and fit accuracy to the legacy Global Positioning System (GPS) broadcast for use with medium Earth orbit transmission. We also demonstrate the applicability of this approach for a PNT satellite in low Earth orbit.

This article deals with the prediction of the upcoming solar activity cycle, Solar Cycle 25. We propose that astronomical ephemeris, specifically taken from the catalogs of aphelia of the four Jovian planets, could be drivers of variations in solar activity, represented by the series of sunspot numbers (SSN) from 1749 to 2020. We use singular spectrum analysis (SSA) to associate components with similar periods in the ephemeris and SSN. We determine the transfer function between the two data sets. We improve the match in successive steps: first with Jupiter only, then with the four Jovian planets and finally including commensurable periods of pairs and pairs of pairs of the Jovian planets (following Mörth and Schlamminger in Planetary Motion, Sunspots and Climate, Solar-Terrestrial Influences on Weather and Climate , 193, 1979 ). The transfer function can be applied to the ephemeris to predict future cycles. We test this with success using the “hindcast prediction” of Solar Cycles 21 to 24, using only data preceding these cycles, and by analyzing separately two 130 and 140 year-long halves of the original series. We conclude with a prediction of Solar Cycle 25 that can be compared to a dozen predictions by other authors: the maximum would occur in 2026.2 (± 1 yr) and reach an amplitude of 97.6 (± 7.8), similar to that of Solar Cycle 24, therefore sketching a new “Modern minimum”, following the Dalton and Gleissberg minima.

Previous studies indicate that the accuracy of the BDS-3 broadcast orbit is comparable to that of the real-time precise products provided by International GNSS Service (IGS). However, the precision of both the broadcast orbit and clock remains limited by the hourly update. This characteristic enables Precise Point Positioning (PPP) implementation with broadcast ephemeris, yet introduces critical challenges, namely, hourly discontinuities and the associated ephemeris uncertainties. To address these limitations, a PPP estimation strategy incorporating covariance-adaptive Kalman filter is proposed in this paper. The strategy aims to mitigate the impact of broadcast ephemeris discontinuities and to adjust the covariance matrix to accommodate the actual uncertainties caused by these discontinuities. Specifically, the proposed approach employs a parameter-augmented state model capable of simultaneously estimating position parameters and compensating for the errors resulting from the discontinuities. Furthermore, an adaptive factor is proposed to adjust the covariance matrix according to the uncertainties induced by the periodically updated ephemeris. The proposed algorithm was rigorously evaluated with comprehensive static and kinematic tests. In the static assessments, the observations spanning one week at seven globally distributed IGS stations were utilized. The outcomes demonstrated a mean horizontal Root-Mean-Square (RMS) value of 18.04 cm and a Three-Dimensional (3D) RMS value of 24.64 cm were achieved, representing a 30.82% improvement compared with conventional broadcast ephemeris PPP algorithm. Dynamic validation was conducted using 10 h maritime experiment data in the south China sea. The results show that the horizontal, vertical, and 3D accuracies are improved by 7.32%, 45.32%, and 39.07%, respectively, confirming the effectiveness of the algorithm in both static and dynamic applications.

The BDS-3 preliminary system was declared functional on December 27, 2018. It enables positioning service on a global scale. This study conducts a comprehensive investigation of the BDS-3 global service from the perspective of positioning, including satellite ephemeris, benefits of the new BDS-3 satellites, and the new signal effect on three positioning modes: single-point positioning (SPP), precise-point positioning (PPP) and real-time kinematic (RTK). First, the broadcast and precise ephemeris availabilities of 18 BDS-3 Medium Earth orbit (MEO) satellites from January to June 2019 are investigated. Due to the shorter operational timespans of BDS-3 satellites, their broadcast and precise ephemeris files retrieved from Multi-GNSS Experiment (MGEX) have 1.2–19.4% and 10.9–13.77% discontinuities, respectively, while the discontinuities of BDS-2 satellite broadcast and precise ephemeris are only 0.1 and 2.1%. Second, the BDS-3 satellite orbit accuracies and clock precisions are significantly improved, i.e., below 0.5 m and 1.82 ns compared to 2 m and 2.91 ns for BDS-2 because of the inter-satellite links of BDS-3 satellites. Third, an average of 4.4–5.7 BDS satellites can be observed at stations located in North/South America, and 8.9 for the European station FFMJ located in Germany after the BDS-3 global system announcement. As a result, continuous positioning is feasible in these regions. As to four Asia–Pacific stations, their SPP accuracies are improved by 12.1–60.2% compared to those of the BDS-2-only solution. Meanwhile, the PPP and RTK convergence times of Asia–Pacific stations are also shortened. Last but not least, the new B1C signal does not bring convincing improvement to PPP and RTK positioning accuracies in this study, due to the limited number of available B1C new signals at this time.