Explore the vast range of titles available.

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.

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.

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 accuracy of the timing group delay (TGD) transmitted in the broadcast ephemeris is an important factor that affects the service performance of a GNSS system. In this contribution, an apparent bias is found by comparing the orbit and clock difference using half-year data of the BeiDou navigation satellite system (BDS) broadcast ephemeris and precise post-processed products. The bias differs at each satellite on each frequency and shows a general systematic difference between BDS-2 and BDS-3. We attribute this to the satellite-dependent TGD bias of the BDS broadcast ephemeris, which is subsequently calibrated. Moreover, to calibrate the bias independently, a network solution strategy is proposed based on 87 globally distributed multi-GNSS experiment (MGEX) stations spanning 25 weeks. The estimated bias shows good agreement with the values observed from the orbit and clock comparison. For the validation of the bias, we compared the signal-in-space range error (SISRE) performance with and without the TGD bias correction. The results show that the SISRE of the BDS improved from 0.71, 0.81, and 1.40 m to 0.64, 0.66, and 0.64 m in the B1I, B3I, and B1I/B3I frequencies. For BDS-3, the SISRE is well within 0.50 m after the bias correction. To further validate the bias, a week’s data were collected at 97 globally distributed MGEX stations. When the TGD bias is corrected, the root mean square (RMS) of single point positioning (SPP) can be improved by 5.6, 8.4, and 21.6% in the B1I, B3I, and B1I/B3I frequencies. Meanwhile, the SISRE and SPP assessment results also indicate that the TGD bias should be corrected by each satellite rather than only corrected between BDS-2 and BDS-3.

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.

Broadcast ephemeris data are essential for the precision and reliability of the BeiDou Navigation Satellite System (BDS) but are highly susceptible to anomalies caused by various interference factors, such as ionospheric and tropospheric effects, solar radiation pressure, and satellite clock biases. Traditional threshold-based methods and manual review processes are often insufficient for detecting these complex anomalies, especially considering the distinct characteristics of different satellite types. To address these limitations, this study proposes an automated anomaly detection method using the IF-TEA-LSTM model. By transforming broadcast ephemeris data into multivariate time series and integrating anomaly score sequences, the model enhances detection robustness through data integrity assessments and stationarity tests. Evaluation results show that the IF-TEA-LSTM model reduces the RMSE by up to 20.80% for orbital parameters and improves clock deviation prediction accuracy for MEO satellites by 68.37% in short-term forecasts, outperforming baseline models. This method significantly enhances anomaly detection accuracy across GEO, IGSO, and MEO satellite orbits, demonstrating its superiority in long-term data processing and its capacity to improve the reliability of satellite operations within the BDS.

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.

The Galileo satellite navigation system now provides initial services. With further satellite launches, the performance of Galileo will gradually improve, and new services will be introduced. This study aims to provide a comprehensive analysis of Galileo Single Point Positioning (SPP) using different broadcast ephemeris data sources. This study investigates the completeness of Galileo navigation message records from different institutions. The results show that IGS provides the best completeness across different data sources (ECR > 70%), while IGN exhibits the lowest completeness. Analyze the proportions of different data sources within the Galileo navigation message in the broadcast ephemeris files provided by IGS during the study period. The proportions of FNAV_258, INAV_513, INAV_516, and INAV_517 during the study period are 25.83%, 24.76%, 23.61%, and 25.80%, respectively, suggesting better data completeness for FNAV_258 and INAV_517 and poorer completeness for INAV_513 and INAV_516. Finally, this study explores SPP solutions for GPS and Galileo systems using different data sources. The results indicate that a higher ECR corresponds to better positioning performance. Although GPS exhibits smaller error fluctuations and smoother positioning results, Galileo’s SPP positioning accuracy surpasses that of GPS. The introduction of dual-frequency observations effectively reduces data dispersion and enhances vertical positioning accuracy.

This study investigates and verifies the feasibility of the precise point positioning (PPP)-B2b enhanced real-time (RT) precise orbit determination (POD) of low Earth orbit (LEO) satellites. The principles and characteristics of matching various PPP-B2b corrections are introduced and analyzed. The performance and accuracy of broadcast ephemeris and PPP-B2b signals are compared and evaluated by referring to the precise ephemeris. The root mean square (RMS) errors in the Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS)-3 broadcast ephemeris orbits in the along direction are larger than those in the other two (radial and cross) directions, and correspondingly, the along component PPP-B2b corrections are greatest. The continuity and smoothness of the GPS and BDS-3 broadcast ephemeris orbits and clock offsets are improved with the PPP-B2b corrections. The availability of PPP-B2b corrections is comprehensively analyzed for the TJU-01 satellite. Several comparative schemes are adopted for the RT POD of the TJU-01 satellite using the broadcast ephemeris and PPP-B2b corrections. The RT POD performance is improved considerably with the broadcast ephemeris corrected by the PPP-B2b signals. The RMS of the RT orbital errors in the radial, along, and cross directions is 0.10, 0.13, and 0.09 m, respectively, using BDS-3 and GPS PPP-B2b corrections, with reference to the solutions calculated with the precise ephemeris. The accuracy is improved by 5.1%, 43.9%, and 28.7% in the three directions, respectively, relative to that achieved with the broadcast ephemeris. It is concluded that a greater proportion of received PPP-B2b satellite signals corresponds to a greater improvement in the accuracy of the RT POD of the LEO satellite.