Ultra-rapid Orbit Research Articles

Improved LS+MAR hybrid method to UT1-UTC ultra-short-term prediction by using first-order-difference UT1-UTC

Accurate ultra-short-term prediction of the Earth rotation parameters (ERP) holds paramount importance for real-time applications, particularly in reference frame conversion. Among them, diurnal rotation (UT1-UTC) which cannot be directly estimated through Global Navigation Satellite System (GNSS) techniques, significantly affects the rapid and ultra-rapid orbit determination of GNSS satellites. Presently, the traditional LS (least squares) + AR (autoregressive) and LS + MAR (multivariate autoregressive) hybrid methods stand as primary approaches for UT1-UTC ultra-short-term predictions (1–10 days). The LS + MAR hybrid method relies on the UT1-UTC and LOD (length of day) series. However, the correlation between LOD and first-order-difference UT1-UTC is stronger than that between LOD and UT1-UTC. In light of this, and with the aid of the first-order-difference UT1-UTC, we propose an enhanced LS + MAR hybrid method to UT1-UTC ultra-short-term prediction. By using the UT1-UTC and LOD data series of the IERS (International Earth Rotation and Reference Systems Service) EOP 14 C04 product, we conducted a thorough analysis and evaluation of the improved method's prediction performance compared to the traditional LS + AR and LS + MAR hybrid methods. According to the numerical results over more than 210 days, they demonstrate that, when considering the correlation information between the LOD and the first-order-difference UT1-UTC, the mean absolute errors (MAEs) of the improved LS + MAR hybrid method range from 21 to 934 μs in 1–10 days predictions. In comparison to the traditional LS + AR hybrid method, the MAEs show a reduction of 7–53 μs in 1–10 days predictions, with corresponding improvement percentages ranging from 1 to 28%. Similarly, when compared to the traditional LS + MAR hybrid method, the MAEs have a reduction of 5–42 μs in 1–10 days predictions, with corresponding improvement percentages ranging from 4–20%. Additionally, when aided by GNSS-derived LOD data series, the MAEs of improved LS + MAR hybrid method experience further reduction.

Modeling the Differences between Ultra-Rapid and Final Orbit Products of GPS Satellites Using Machine-Learning Approaches

The International GNSS Service analysis centers provide orbit products of GPS satellites with weekly, daily, and sub-daily latency. The most frequent ultra-rapid products, which include 24 h of orbits derived from observations and 24 h of orbit predictions, are vital for real-time applications. However, the predicted part of the ultra-rapid orbits is less accurate than the estimated part and has deviations of several decimeters with respect to the final products. In this study, we investigate the potential of applying machine-learning (ML) and deep-learning (DL) algorithms to further enhance physics-based orbit predictions. We employed multiple ML/DL algorithms and comprehensively compared the performances of different models. Since the prediction errors of the physics-based propagators accumulate with time and have sequential characteristics, specific sequential modeling algorithms, such as Long Short-Term Memory (LSTM), show superiority. Our approach shows promising results with average improvements of 47% in 3D RMS within the 24-hour prediction interval of the ultra-rapid products. In the end, we applied the orbit predictions improved by LSTM to kinematic precise point positioning and demonstrated the benefits of LSTM-improved orbit predictions for positioning applications. The accuracy of the station coordinates estimated based on these products is improved by 16% on average compared to those using ultra-rapid orbit predictions.

An improved approach for rapid filter convergence of GNSS satellite real-time orbit determination

Introduction: The real-time precise satellite orbit of Global Navigation Satellite System (GNSS) usually takes a long time to converge to a stable state using the filter method. The ultra-rapid orbit products are helpful to improve convergence speed by introducing them as external constraints. Reasonably determination of stochastic model of the constraint equation from the ultra-rapid products is the key for a better performance of convergence whereas it has not been well solved.Methods: We propose to establish the stochastic model of the orbit constraint equation by analyzing the differences between the predicted part of the ultra-rapid orbit and the filter orbit after convergence. To improve the orbit accuracy during the convergence, the constant stochastic model of the constraint equation is first determined for each system by averaging the root mean square (RMS) time-series of the differences between predicted orbit from the ultra-rapid products and the SRIF orbit after convergence in different time ranges. Besides, a time-dependent stochastic model of the constraint equation is then determined by analyzing the variation of the RMS time-series. To validate the proposed method, a month of multi-constellation data collected from 80 globally distributed stations is processed using the Square Root Information Filter (SRIF) algorithm.Results: Orbit results without introducing external orbit constraints show that the convergence time in the radial direction is 13.75, 15.25 and 17.75 h for GPS, Galileo and BDS-3 satellite, respectively. For the scheme of constant stochastic model using the average RMS over 6 h, results show that there is no significant convergence phenomenon for each system in all directions. The one-dimensional (1D) RMS during the constraint period is improved by 86.5%, 84.8%, 96.8% for GPS, Galileo and BDS-3 satellites when compared to the results without introducing external orbit constraints. As for the scheme of time-dependent stochastic model, results show that the quadratic function is suitable for modeling the RMS time-series for each system, and the accuracy of results during the constraint period has a further improvement of 1.3%, 3.7% in 1D direction for GPS, BDS-3 satellites when compared to the constant stochastic model using the average RMS over 6 h. In addition, the orbit accuracy with external orbit constraint is slightly better than those without external orbit constraint after the constraint period.Discussion: The above results show that when introducing the ultra-rapid product as the external constraint, there is basically no convergence phenomenon for GNSS satellite, while the orbit accuracy for time-dependent stochastic model has further improvement than constant stochastic model. These results indicate that the proposed method can significantly improve the convergence performance without damaging the orbit accuracy after convergence, and time-dependent stochastic model is better than constant stochastic model.

Studies and Analysis of Combining BDS-3/GNSS Ultra-Rapid Orbit Products from Different IGS Analysis Centers

The third generation of China’s BeiDou Navigation Satellite System (BDS-3) began to provide global service at the end of 2018, and the completion of BDS was announced in July 2020, which includes GEO (Geostationary Earth Orbit), IGSO (Inclined Geosynchronous orbit), and MEO (Medium Earth Orbit) satellites. The resulting BDS orbits vary due to the inconsistent alignment strategies used by different analysis centers. Therefore, it is necessary to study the method of determining the BDS-3 orbit products combined from different analysis centers. In this research, the accuracy of the combined orbits for BDS-3 and other GNSS systems is evaluated and analyzed. To verify the reliability of the orbit combination method proposed in this paper, the GPS orbit is first selected for verification. Compared to the analysis centers, the mean Signal in Space User Ranging Error (SISURE) for GPS combined orbits is significantly reduced, and the mean SISURE of combined orbits for Block IIF, Block IIR, and Block III is 4.15 mm, 5.43 mm, and 5.63 mm, respectively. This demonstrates the effectiveness of the orbit combination method in this research. Besides, the accuracy of the combined orbits is improved by the ERP correction, and the mean RMS of the without Earth rotation Parameters (ERP) correction orbits and with ERP correction orbits is 4.78 mm and 4.53 mm, respectively. This demonstrates that orbit consistency corrections should be considered when performing orbit combinations. Compared to the GFZ orbits, the accuracy of the combined orbits has improved for GPS, GLONASS, GALILEO, and BDS is 8.2%, 9.9%, 9.9%, and 5.5%, respectively. It shows that the orbit combination method improves the orbital accuracy compared to the individual analysis center orbits. The mean RMS of the combined orbits for GPS, GLONASS, GALILEO, BDS MEO, and BDS IGSO is 1.7 cm, 2.61 cm, 2.52 cm, 2.59 cm, and 4.90 cm, respectively. The results demonstrate that the accuracy of the combined orbit for the BDS-3 MEO satellite is already similar to other systems; an orbit combination also available for the BDS-3 satellite.

A Kalman filter-based online fractional cycle bias determination method for real-time ambiguity-fixing GPS satellite clock estimation

Integer ambiguity resolution (IAR) is one of the most powerful methods to improve the precision and the convergence of estimating real-time satellite clocks, which is an indispensable prerequisite to support the real-time precise point position (PPP) service. In this study, a Kalman filter-based online fractional cycle bias (FCB) determination method is proposed to facilitate the real-time IAR for satellite clock estimation. A real-time recursive algorithm for smoothing the average float wide-lane (WL) ambiguity is developed to mitigate the impact of pseudorange noise. Quality control procedures are established throughout the entire FCB filter process to remove low-quality observations and mitigate the impact of incorrect integer ambiguities. This method is designed as an embedded module in the clock estimation procedure to fix both integer WL and narrow-lane (NL) ambiguities in an epoch-by-epoch way for recovering the integer property of the undifferenced ionosphere-free (IF) ambiguities in real-time. The performance of the FCB filter and the ambiguity-fixing clock estimation is validated with a GPS network from the international GNSS service (IGS). Experiments show that the WL and NL FCB estimation accuracy reaches 0.004 cycles and 0.080 cycles for GPS satellites. The WL and NL residuals fit the normal distribution well after several minutes and 1.5 h, respectively, making the ambiguity-fixing clocks converge rapidly in about two hours. The online FCB filter method improves real-time ambiguity-fixing clock estimation accuracy significantly. Compared to the ambiguity-float solution, the STD of the ambiguity-fixing real-time satellite clocks is averagely improved by 31.0 % to 0.040 ns with the ultra-rapid orbits. The ambiguity-fixing satellite clocks can be applied in the real-time kinematic PPP ambiguity resolution, and the positioning accuracy is improved by 24.1 % to 51.7 % compared to that of using the ambiguity-float clock products.

Real-Time Multi-GNSS Precise Orbit Determination Based on the Hourly Updated Ultra-Rapid Orbit Prediction Method

Offering real-time precise point positioning (PPP) services for global and large areas based on global navigation satellite systems (GNSS) has drawn more and more attention from institutions and companies. A precise and reliable satellite orbit is a core premise for multi-GNSS real-time services, especially for the GPS and GLONASS, which are undergoing modernization, whereas the Galileo, BDS and QZSS have just fulfilled the construction stage. In this contribution, a real-time precise orbit determination (POD) strategy for the five operational constellations based on the hourly updated ultrarapid orbit prediction method is presented. After combination of 72 h arc through three adjacent 24 h arc normal equations, the predicted orbits are finally generated (hourly updated). The POD results indicate that the mean one-dimensional (1-D) root mean square (RMS) values compared with the Deutsches GeoForschungsZentrum (GFZ) final multi-GNSS orbits are approximately 3.7 cm, 10.2 cm, 5.8 cm, 5.7 cm, 4.1 cm and 25.1 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The mean 1-D RMS values of the hourly updated ultrarapid orbit boundary overlapping comparison are approximately 1.6 cm, 6.9 cm, 3.2 cm, 2.7 cm, 1.8 cm and 22.2 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The satellite laser ranging (SLR) validation illuminates that the mean RMS values are approximately 4.53 cm and 4.73 cm for the four MEOs of BDS-3 and four BDS-2 satellites, respectively.

Evaluation of strategies for the ultra-rapid orbit prediction of BDS GEO satellites

ABSTRACT The quality of BeiDou Navigation Satellite System (BDS) Geostationary Earth Orbit (GEO) ultra-rapid products is unsatisfactory because GEO satellites are nearly stationary relative to ground stations. To optimize the quality of these ultra-rapid orbit products, we investigated the effects of the fitting arc length, an a priori Solar-Radiation Pressure (SRP) model, and the along-track empirical acceleration on the prediction of BDS GEO satellite orbits. The predicted orbit arcs of 24-h were evaluated through comparisons with the corresponding observed orbit arc and Satellite Laser Ranging (SLR) observations. In both eclipse and non-eclipse seasons, accuracy of the orbit predictions obtained using a 48-h fitting arc length were better than those obtained using 24-h and 72-h fitting arc lengths. Although the overlapping precision of predicted orbits exhibited no obvious improvement when an a priori SRP model was employed, the systematic bias in the SLR residuals was significantly reduced. Specifically, the mean value of SLR residuals decreased from −0.248 m to −0.024 m during non-eclipse seasons and from −0.333 m to −0.041 m during eclipse seasons, respectively. In addition, when an empirical acceleration in the along-track direction was introduced, the three-Dimensional Root-Mean-Square (3D RMS) of overlapping orbits during eclipse seasons decreased from 2.964 to 1.080 m, which is comparable to that during non-eclipse seasons. Furthermore, the Standard Deviation (STD) of SLR residuals decreased from 0.419 to 0.221 m during eclipse seasons. The analysis of SRP estimates shows that the stability of SRP parameters was significantly enhanced after the introduction of along-track empirical acceleration in eclipse seasons. The optimal BDS GEO ultra-rapid orbit prediction products were yielded by using a 48-h fitting arc length, an a priori SRP model and an along-track empirical acceleration.

Water vapor monitoring with IGS RTS and GPT3/VMF3 functions over Turkey

Precise Point Positioning (PPP) has been proven as a cost-effective and efficient technique for monitoring the precipitable water vapor (PWV), which plays a critical role in weather forecasting. The recent developments of the International Global Navigation Satellite Systems Service (IGS) Real-Time Pilot Project (RTPP) ease the difficulties of real-time determination of PWV. In this study, the quality of the real-time PPP-derived PWVs and their correlation with precipitation estimates from different global products are investigated. The accuracies of the orbits and clocks derived from the IGS02 streams are evaluated and their performance outperforms the predicted part of IGS Ultra-rapid (IGU) orbits and clocks. A year of GNSS observations from 9 stations located in Turkey are processed to estimate the PWV in the real-time. Since there are no stations to collect meteorological data near GNSS stations, the real-time solutions employ empirical Global Pressure and Temperature 3 (GPT3) and its fully consistent discrete Vienna Mapping Function 3 (VMF3) to model the troposphere. The performance of the PWV estimates is assessed by comparing with Radiosonde-derived PWV values and post-processed PPP-derived PWV estimates employing the Center for Orbit Determination in Europe (CODE) final orbits and clocks. At most sites, the root-mean-square (RMS) differences of the estimated PWVs in comparison with the radiosonde-derived PWVs are less than 2.4 mm with correlation coefficients greater than 0.90. The RMS differences between RT and post-processed PPP PWV estimates are found to be less than 1.2 mm. The estimated RT zenith total delays (ZTDs) at two IGS sites agree well with the ZTDs provided by the IGS final products. A method of precipitation monitoring is proposed based on the daily standard deviation (SD) of the PWV estimates. Experimental analyses of the proposal are undertaken by comparing the daily SDs of the PWV estimates and the daily accumulated precipitation estimates from the global precipitation grids produced from rain gauges, satellite images, and reanalyses product sets. The results show that the daily variation of the PWVs and the high precipitation estimates present a good agreement for some days but not always. The PWVs overestimate and underestimate a significant number of events. Spatial refinement of GPT3 grids and gridded precipitation products with higher sampling over Turkey may offer better results.

A Parallel Approach for Multi-GNSS Ultra-Rapid Orbit Determination

Global Navigation Satellite System (GNSS) ultra-rapid orbit is critical for geoscience and real-time engineering applications. To improve the computational efficiency and the accuracy of predicted orbit, a parallel approach for multi-GNSS ultra-rapid orbit determination is proposed based on Message Passing Interface (MPI)/Open Multi Processing (OpenMP). This approach, compared with earlier efficient methods, can improve the efficiency of multi-GNSS ultra-rapid orbit solution without changing the original observation data and retaining the continuity and consistency of the original parameters to be estimated. To obtain high efficiency, three steps are involved in the approach. First and foremost, the normal equation construction is optimized in parallel based on MPI. Second, equivalent reduction of the estimated parameters is optimized using OpenMP parallel method. Third, multithreading is used for parallel orbit extrapolation. Thus, GNSS ultra-rapid orbit determination is comprehensively optimized in parallel, and the computation efficiency is greatly improved. Based on the data from MGEX and IGS stations, experiments are carried out to analyze the performance of the proposed approach in computational efficiency, accuracy and stability. The results show that the approach greatly improves the efficiency of satellite orbit determination. It can realize 1-h update frequency for the multi-GNSS ultra-rapid orbit determination using 88 stations with four-system observations. The accuracy of the GPS, GLONASS, Galileo and BDS ultra-rapid orbit with 1-h update frequency using the parallel approach is approximately 33.4%,31.4%,40.1% and 32.8% higher than that of the original orbit, respectively. The root mean squares (RMS) of GPS, GLONASS, Galileo and BDS predicted orbit are about 3.2 cm, 5.1 cm, 5.6 cm and 11.8 cm. Moreover, the orbit provided by the proposed method has a better stability. The precision loss of all parallel optimization can be negligible and the original correlation between the parameters is fully preserved.

Accuracy Analysis of GNSS Hourly Ultra-Rapid Orbit and Clock Products from SHAO AC of iGMAS

With the development of the global navigation satellite system(GNSS), the hourly ultra-rapid products of GNSS are attracting more attention due to their low latency and high accuracy. A new strategy and method was applied by the Shanghai Astronomical Observatory (SHAO) Analysis Center (AC) of the international GNSS Monitoring and Assessment Service (iGMAS) for generating 6-hourly and 1-hourly GNSS products, which mainly include the American Global Positioning System (GPS), the Russian Global’naya Navigatsionnaya Sputnikova Sistema (GLONASS), the European Union’s Galileo, and the Chinese BeiDou navigation satellite system (BDS). The 6-hourly and 1-hourly GNSS orbit and clock ultra-rapid products included a 24-h observation session which is determined by 24-h observation data from global tracking stations, and a 24-h prediction session which is predicted from the observation session. The accuracy of the 1-hourly orbit product improved about 1%, 31%, 13%, 11%, 23%, and 9% for the observation session and 18%, 43%, 45%, 34%, 53%, and 15% for the prediction session of GPS, GLONASS, Galileo, BDS Medium Earth Orbit (MEO), Inclined Geosynchronous Orbit (IGSO), and GEO orbit, when compared with reference products with high accuracy from the International GNSS service (IGS).The precision of the 1-hourly clock products can also be seen better than the 6-hourly clock products. The accuracy and precision of the 6-hourly and 1-hourly orbit and clock verify the availability and reliability of the hourly ultra-rapid products, which can be used for real-time or near-real-time applications, and show encouraging prospects.

Prediction of BeiDou Satellite Orbit Maneuvers to Improve the Reliability of Real-Time Navigation Products

The positioning, navigation, and timing (PNT) service of the Global Navigation Satellite System (GNSS) is developing in the direction of real time and high precision. However, there are some problems that restrict the development of real-time and high-precision PNT technology. Satellite orbit maneuvering is one of the factors that reduce the reliability of real-time navigation products, especially the high-frequency orbit maneuvering of geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. The BeiDou Navigation Satellite System (BDS) constellation is designed to contain GEO, IGSO, and medium earth orbit (MEO). These orbit maneuvers bring certain difficulties for data processing, especially for BeiDou satellites, such as decreased real-time service performance, which results in real-time navigation products including unusable maneuvered satellites. Additionally, the performance of real-time navigation products will decrease because the orbit maneuvers could not be known in advance, which diminishes the real-time PNT service performance of BDS for users. Common users cannot obtain maneuvering times and strategies owing to confidentiality, which can lead to a decline in the BDS real-time service performance. Thus, we propose a method to predict orbit maneuvers. BDS data from the broadcast ephemeris were analyzed to verify the availability of the proposed method. In addition, the results of real-time positioning were analyzed by using ultra-rapid orbit products, demonstrating that their reliability is improved by removing maneuvered satellites in advance. This is vital to improve the reliability of real-time navigation products and BDS service performance.

One-step correction strategy for BDS-2/BDS-3 satellite observation code bias and multipath delay

Global navigation satellite systems and positioning, navigation, and timing services, such as the newly developed BeiDou satellite system (BDS), require high-accuracy satellite observations. Satellite-induced code bias is present in BDS-2 satellite observations while it is negligibly present in BDS-3 satellite observations. The traditional method of mitigating BDS code bias involves two steps, first addressing multipath delay and then code bias, and does not obtain optimal results. A one-step strategy is therefore proposed to model and eliminate code bias and multipath delay considering BDS-2 and BDS-3 integrated processing. A combined least-square and autoregressive strategy is selected to estimate the model coefficients of code bias and construct the multipath delay with one solution. Moreover, inter-satellite correlations of BDS-2 and BDS-3 are extracted to improve the weight matrix in the estimation of model coefficients. To verify the proposed strategy, experiments are designed for eight schemes to analyze the coefficients and residuals of modelling code bias. Experimental results indicate that a more stable and accurate code bias model is acquired by introducing inter-satellite correlation; with the one-step strategy, the model residuals are reduced and a more optimal code bias model is output. Meanwhile, the single-frequency precise point positioning (PPP) and real-time PPP of BDS-2 and BDS-3 combined estimations are tested for different stations, frequencies, and code bias models. The results of final positions reveal that accuracy in the Up (U) direction is improved compared with that in the East (E) and North (N) directions; improvements are greater for B1I than for B3I. In general, the one-step strategy enhances the precision of single-frequency (B1I/B3I) PPP, especially in the U direction. However, the effects on BDS ultra-rapid orbit determination are negligible. Equally, the double-frequency real-time PPP solution is improved, compared with adopting the traditional method, by 10.6–64.9%, 0.0–59.1%, and 12.6–67.2% for E, N, and U directions, respectively, through BDS-2/BDS-3 integrated processing. The proposed one-step strategy therefore outperforms the two-step strategy in terms of rapidly processing high-precision BDS observations.

Improved Ultra-Rapid UT1-UTC Determination and Its Preliminary Impact on GNSS Satellite Ultra-Rapid Orbit Determination

Errors in ultra-rapid UT1-UTC primarily affect the overall rotation of spatial datum expressed by GNSS (Global Navigation Satellite System) satellite ultra-rapid orbit. In terms of existing errors of traditional strategy, e.g., piecewise linear functions, for ultra-rapid UT1-UTC determination, and the requirement to improve the accuracy and consistency of ultra-rapid UT1-UTC, the potential to improve the performance of ultra-rapid UT1-UTC determination based on an LS (Least Square) + AR (Autoregressive) combination model is explored. In this contribution, based on the LS+AR combination model and by making joint post-processing/rapid UT1-UTC observation data, we propose a new strategy for ultra-rapid UT1-UTC determination. The performance of the new strategy is subsequently evaluated using data provided by IGS (International GNSS Services), iGMAS (international GNSS Monitoring and Assessment System), and IERS (International Earth Rotation and Reference Systems Service). Compared to the traditional strategy, the numerical results over more than 1 month show that the new strategy improved ultra-rapid UT1-UTC determination by 29–43%. The new strategy can provide a reference for GNSS data processing to improve the performance of ultra-rapid products.

Impact analysis of arc length in multi-GNSS ultra-rapid orbit determination based on the one-step method

With the development of near real-time and real-time high-precision global navigation satellite system (GNSS) applications, users’ requirements for the accuracy and stability of ultra-rapid orbits have increased, especially for multi-constellation orbits. Generally, several factors affect the accuracy and stability of multi-GNSS ultra-rapid orbit determination; however, this study is focused only on analyzing the orbit arc length of ultra-rapid orbits of the GPS, GLONASS, BeiDou-2, and Galileo satellites based on the one-step method. To realize nearly ideal conditions in the process of analysis, one full year’s rapid orbit products during 2018 provided by the GeoForschungsZentrum multi-GNSS experiment analysis center were used as fitted observed orbits and also as a reference orbit for comparison to the predicted orbit. In terms of residual analysis of orbit difference and stability analysis of Helmert transformation parameters, the numerical results showed that the optimal orbit arc lengths of quad-constellation medium earth orbit (MEO) satellites for 6 h and 3 h predicted ultra-rapid orbits based on the one-step method were in the range of 44–45 h and 41–44 h, respectively. Overall, for both 6 h and 3 h predictions, when only considering the impact of the orbit arc length on the accuracy and stability of the orbit itself, 44 h can be considered as the overlapping optimal orbit arc length of quad-constellation MEO satellitesʼ ultra-rapid orbits generated by the one-step method. In addition, these ranges of orbit arc length can contribute to the multi-GNSS ultra-rapid orbit determination.

Investigating the effects of ultra-rapid, rapid vs. final precise orbit and clock products on high-rate GNSS-PPP for capturing dynamic displacements

The use of final IGS precise orbit and clock products for high-rate GNSS-PPP proved its effectiveness in capturing dynamic displacement of engineering structures caused by earthquakes. However, the main drawback of using the final products is that they are available after approximately two weeks of data collection, which is not suitable for timely measures after an event. In this study, the use of ultra-rapid products (observed part), which are available after a few hours of data collection, and rapid products, which are available in less than 24 hrs, are investigated and their results are compared to the more precise final products. The tests are designed such that harmonic oscillations with different frequencies and amplitudes and ground motion of a simulated real earthquake are generated using a single axis shake table and the PPP was used to capture these movements by monitoring timechange of the table positions. To evaluate the accuracy of PPP using ultra-rapid, rapid and final products, their results were compared with relative GNSS positioning and LVDT (Linear Variable Differential Transformer) data, treated as reference. The results show that the high-rate GNSS-PPP solutions based on the three products can capture frequencies of harmonic oscillations and dynamic displacement with good accuracy. There were slight differences between ultra-rapid, rapid and final products, where some of the tested events indicated that the latter two produced are more accurate and provide better results compared to the ultrarapid product for monitoring short-term dynamic displacements.

Impact of ECOM Solar Radiation Pressure Models on Multi-GNSS Ultra-Rapid Orbit Determination

The Global Navigation Satellite System (GNSS) ultra-rapid precise orbits are crucial for global and wide-area real-time high-precision applications. The solar radiation pressure (SRP) model is an important factor in precise orbit determination. The real-time orbit determination is generally less accurate than the post-processed one and may amplify the instability and mismodeling of SRP models. Also, the impact of different SRP models on multi-GNSS real-time predicted orbits demands investigations. We analyzed the impact of the ECOM 1 and ECOM 2 models on multi-GNSS ultra-rapid orbit determination in terms of ambiguity resolution performance, real-time predicted orbit overlap precision, and satellite laser ranging (SLR) validation. The multi-GNSS observed orbital arc and predicted orbital arcs of 1, 3, 6, and 24 h are compared. The simulated real-time experiment shows that for GLONASS and Galileo ultra-rapid orbits, compared to ECOM 1, ECOM 2 increased the ambiguity fixing rate to 89.3% and 83.1%, respectively, and improves the predicted orbit accuracy by 9.2% and 27.7%, respectively. For GPS ultra-rapid orbits, ECOM 2 obtains a similar ambiguity fixing rate as ECOM 1 but slightly better orbit overlap precision. For BDS GEO ultra-rapid orbits, ECOM 2 obtains better overlap precision and SLR residuals, while for BDS IGSO and MEO ultra-rapid orbits, ECOM 1 obtains better orbit overlap precision and SLR residuals.

Performance Assessment for Combined GPS and BDS Real-time Precise Point Positioning in the Coastal Region of Bohai Gulf, China

Qu, L.; Huang, H.; Du, M., and Acharya, T.D., 2019. Performance assessment for combined GPS and BDS real-time precise point positioning in the coastal region of Bohai Gulf, China. In: Lee, J.L.; Yoon, J.-S.; Cho, W.C.; Muin, M., and Lee, J. (eds.), The 3rd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 91, pp. 271-275. Coconut Creek (Florida), ISSN 0749-0208.In this study, we focus on the performance assessment of combined Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) real-time Precise Point Positioning (PPP) in the coastal region of Bohai Gulf, China. Firstly, 120 Global Navigation Satellite System (GNSS) stations from Multi-GNSS Experiment (MGEX) network of the International GNSS Service (IGS) were processed to generate ultra-rapid precise orbit of both GPS and BDS satellites, updated with the interval of three hours. Secondly, real-time precise satellite clock errors were estimated to compensate the orbit error with 24 regional stations from Crustal Monitor of Network of China (CMONOC) and MGEX networks. Finally, with those products, the performances of GPS-only, BDS-only and combined GPS and BDS real-time PPP were compared and evaluated. The experimental result illustrated that the ultra-rapid orbit accuracy of BDS-2 satellites was still worse than that of GPS satellites which was sub-decimeter level. Among three types of orbital satellites of BDS-2, the orbital accuracy of medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites were at decimeter level while for geostationary Earth orbit (GEO) satellites was at meter-level. The MEO satellites had the best accuracy while the GEO satellites performed the worst. In addition, the 3D accuracy of BDS-only real-time PPP was 10 cm better. Although the accuracy of BDS-2 real-time PPP was still worse than that of GPS and more time was taken for convergence. By adding BDS on top of GPS, the accuracy in the east, north and up components improved 40.0%, 33.3% and 18.5%, respectively, and the convergence time reduced 36.3%, 15.4% and 58.3%, respectively compared to the GPS only.

High-resolution vertical total electron content maps based on multi-scale B-spline representations

Abstract. For more than 2 decades the IGS (International GNSS Service) ionosphere associated analysis centers (IAACs) have provided global maps of the vertical total electron content (VTEC). In general, the representation of a 2-D or 3-D function can be performed by means of a series expansion or by using a discretization technique. While in the latter case, pixels or voxels are usually chosen for a spherical function such as VTEC, for a series expansion spherical harmonics (SH) are primarily used as basis functions. The selection of the best suited approach for ionosphere modeling means a trade-off between the distribution of available data and their possibility of representing ionospheric variations with high resolution and high accuracy. Most of the IAACs generate global ionosphere maps (GIMs) based on SH expansions up to the spectral degree n=15 and provide them with a spatial resolution of 2.5∘×5∘ with respect to the latitudinal and longitudinal directions, respectively, and a temporal sampling interval of 2 h. In recent years, it has frequently been claimed that the spatial resolution of the VTEC GIMs has to be increased to a spatial resolution of 1∘×1∘ and to a temporal sampling interval of about 15 min. Enhancing the grid resolution means an interpolation of VTEC values for intermediate points but with no further information about variations in the signal. n=15 in the SH case, for instance, corresponds to a spatial sampling of 12∘×12∘. Consequently, increasing the grid resolution concurrently requires an extension of the spectral content, i.e., to choose a higher SH degree value than 15. Unlike most of the IAACs, the VTEC modeling approach at Deutsches Geodätisches Forschungsinstitut der Technischen Universität München (DGFI-TUM) is based on localizing basis functions, namely tensor products of polynomial and trigonometric B-splines. In this way, not only can data gaps be handled appropriately and sparse normal equation systems be established for the parameter estimation procedure, a multi-scale representation (MSR) can also be set up to determine GIMs of different spectral content directly, by applying the so-called pyramid algorithm, and to perform highly effective data compression techniques. The estimation of the MSR model parameters is finally performed by a Kalman filter driven by near real-time (NRT) GNSS data. Within this paper, we realize the MSR and create multi-scale products based on B-spline scaling, wavelet coefficients and VTEC grid values. We compare these products with different final and rapid products from the IAACs, e.g., the SH model from CODE (Berne) and the voxel solution from UPC (Barcelona). In contrast to the abovementioned products, DGFI-TUM's products are based solely on NRT GNSS observations and ultra-rapid orbits. Nevertheless, we can conclude that the DGFI-TUM's high-resolution product (“othg”) outperforms all products used within the selected time span of investigation, namely September 2017.

A BDS-2/BDS-3 Integrated Method for Ultra-Rapid Orbit Determination with the Aid of Precise Satellite Clock Offsets

The accuracy of ultra-rapid orbits is a key parameter for the performance of GNSS (Global Navigation Satellite System) real-time or near real-time precise positioning applications. The quality of the current BeiDou demonstration system (BDS) ultra-rapid orbits is lower than that of GPS, especially for the new generational BDS-3 satellites due to the fact that the availability of the number of ground tracking stations is limited, the geographic distribution of these stations is poor, and the data processing strategies adopted are not optimal. In this study, improved data processing strategies for the generation of ultra-rapid orbits of BDS-2/BDS-3 satellites are investigated. This includes both observed and predicted parts of the orbit. First, the predicted clock offsets are taken as constraints in the estimation process to reduce the number of the unknown parameters and improve the accuracy of the parameter estimates of the orbit. To obtain more accurate predicted clock offsets for the BDS’ orbit determination, a denoising method (also called the Tikhonov regularization algorithm), inter-satellite correlation, and the partial least squares method are all incorporated into the clock offsets prediction model. Then, the Akaike information criterion (AIC) is used to determine the arc length in the estimation models by taking the optimal arc length in the estimation of the initial orbit states into consideration. Finally, a number of experiments were conducted to evaluate the performance of the ultra-rapid orbits resulting from the proposed methods. Results showed that: (1) Compared with traditional models, the accuracy improvement of the predicted clock offsets from the proposed methods were 40.5% and 26.1% for BDS-2 and BDS-3, respectively; (2) the observed part of the orbits can be improved 9.2% and 5.0% for BDS-2 and BDS-3, respectively, by using the predicted clock offsets as constraints; (3) the accuracy of the predicted part of the orbits showed a high correlation with the AIC value, and the accuracy of the predicted orbits could be improved up to 82.2%. These results suggest that the approaches proposed in this study can significantly enhance the accuracy of the ultra-rapid orbits of BDS-2/BDS-3 satellites.

Implementation of quasi-real-time estimation of BDS clock

To obtain high reliability and accuracy of the zenith tropospheric delay more quickly, this study describes a parameter estimation method that uses an epoch-differenced and undifferenced function model to estimate the clock of the BeiDou navigation satellite system (BDS)/global positioning system (GPS) satellites using a quasi-real-time process. Forty-five MGEX tracking stations distributed globally were selected for study. The initial orbit information of the clock estimation used the ultra-rapid orbit products released by the German Research Center for Geosciences and post-products as reference values. The experimental results showed that the accuracy of the GPS satellite clock was better than 0.06 ns. The precision of clock for three kinds of BDS satellites was between 0.04 and 0.08 ns, slightly worse than the GPS. The estimated BDS clock appears to meet the demands for computing the quasi-real-time zenith tropospheric delay.