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ABSTRACTThe Real-Time Global Navigation Satellite System (GNSS) Precise Positioning Service (RTPPS) is recognized as the most promising system by providing precise satellite orbit and clock corrections for users to achieve centimeter-level positioning with a stand-alone receiver in real-time. Although the products are available with high accuracy almost all the time, they may occasionally suffer from unexpected significant biases, which consequently degrades the positioning performance. Therefore, quality monitoring at the system-level has become more and more crucial for providing a reliable GNSS service. In this paper, we propose a method for the monitoring of real-time satellite orbit and clock products using a monitoring station network based on the Quality Control (QC) theory. The satellites with possible biases are first detected based on the outliers identified by Precise Point Positioning (PPP) in the monitoring station network. Then, the corresponding orbit and clock parameters with temporal constraints are introduced and estimated through the sequential Least Square (LS) estimator and the corresponding Instantaneous User Range Errors (IUREs) can be determined. A quality indicator is calculated based on the IUREs in the monitoring network and compared with a pre-defined threshold. The quality monitoring method is experimentally evaluated by monitoring the real-time orbit and clock products generated by GeoForschungsZentrum (GFZ), Potsdam. The results confirm that the problematic satellites can be detected accurately and effectively with missed detection rate [Formula: see text] and false alarm rate [Formula: see text]. Considering the quality alarms, the PPP results in terms of RMS of positioning differences with respect to the International GNSS Service (IGS) weekly solution in the north, east and up directions can be improved by 12%, 10% and 27%, respectively.

Abstract With the high-precision products of satellite orbit and clock, uncalibrated phase delay, and the atmosphere delay corrections, Precise Point Positioning (PPP) based on a Real-Time Kinematic (RTK) network is possible to rapidly achieve centimeter-level positioning accuracy. In the ionosphere-weighted PPP–RTK model, not only the a priori value of ionosphere but also its precision affect the convergence and accuracy of positioning. This study proposes a method to determine the precision of the interpolated slant ionospheric delay by cross-validation. The new method takes the high temporal and spatial variation into consideration. A distance-dependent function is built to represent the stochastic model of the slant ionospheric delay derived from each reference station, and an error model is built for each reference station on a five-minute piecewise basis. The user can interpolate ionospheric delay correction and the corresponding precision with an error function related to the distance and time of each reference station. With the European Reference Frame (EUREF) Permanent GNSS (Global Navigation Satellite Systems) network (EPN), and SONEL (Système d'Observation du Niveau des Eaux Littorales) GNSS stations covering most of Europe, the effectiveness of our wide-area ionosphere constraint method for PPP-RTK is validated, compared with the method with a fixed ionosphere precision threshold. It is shown that although the Root Mean Square (RMS) of the interpolated ionosphere error is within 5 cm in most of the areas, it exceeds 10 cm for some areas with sparse reference stations during some periods of time. The convergence time of the 90th percentile is 4.0 and 20.5 min for horizontal and vertical directions using Global Positioning System (GPS) kinematic solution, respectively, with the proposed method. This convergence is faster than those with the fixed ionosphere precision values of 1, 8, and 30 cm. The improvement with respect to the latter three solutions ranges from 10 to 60%. After integrating the Galileo navigation satellite system (Galileo), the convergence time of the 90th percentile for combined kinematic solutions is 2.0 and 9.0 min, with an improvement of 50.0% and 56.1% for horizontal and vertical directions, respectively, compared with the GPS-only solution. The average convergence time of GPS PPP-RTK for horizontal and vertical directions are 2.0 and 5.0 min, and those of GPS + Galileo PPP-RTK are 1.4 and 3.0 min, respectively.

Abstract Real-time satellite orbit and clock estimations are the prerequisite for Global Navigation Satellite System (GNSS) real-time precise positioning services. To meet the high-rate update requirement of satellite clock corrections, the computational efficiency is a key factor and a challenge due to the rapid development of multi-GNSS constellations. The Square Root Information Filter (SRIF) is widely used in real-time GNSS data processing thanks to its high numerical stability and computational efficiency. In real-time clock estimation, the outlier detection and elimination are critical to guarantee the precision and stability of the product but could be time-consuming. In this study, we developed a new quality control procedure including the three standard steps: i.e., detection, identification, and adaption, for real-time data processing of huge GNSS networks. Effort is made to improve the computational efficiency by optimizing the algorithm to provide only the essential information required in the processing, so that it can be applied in real-time and high-rate estimation of satellite clocks. The processing procedure is implemented in the PANDA (Positioning and Navigation Data Analyst) software package and evaluated in the operational generation of real-time GNSS orbit and clock products. We demonstrated that the new algorithm can efficiently eliminate outliers, and a clock precision of 0.06 ns, 0.24 ns, 0.06 ns, and 0.11 ns can be achieved for the GPS, GLONASS, Galileo, and BDS-2 IGSO/MEO satellites, respectively. The computation time per epoch is about 2 to 3 s depending on the number of existing outliers. Overall, the algorithm can satisfy the IGS real-time clock estimation in terms of both the computational efficiency and product quality.

With the completion of Chinese BeiDou Navigation Satellite System (BDS), the world has begun to enjoy the Positioning, Navigation, and Timing (PNT) services of four Global Navigation Satellite Systems (GNSS). In order to improve the GNSS performance and expand its applications, Low Earth Orbit (LEO) Enhanced Global Navigation Satellite System (LeGNSS) is being vigorously advocated. Combined with high-, medium-, and low- earth orbit satellites, it can improve GNSS performance in terms of orbit determination, Precise Point Positioning (PPP) convergence time, etc. This paper comprehensively reviews the current status of LeGNSS, focusing on analyzing its advantages and challenges for precise orbit and clock determination, PPP convergence, earth rotation parameter estimation, and global ionosphere modeling. Thanks to the fast geometric change brought by LEO satellites, LeGNSS is expected to fundamentally solve the problem of the long convergence time of PPP without any augmentation. The convergence time can be shortened within 1 minute if appropriate LEO constellations are deployed. However, there are still some issues to overcome, such as the optimization of LEO constellation as well as the real time LEO precise orbit and clock determination.

In the absence of detailed surface information, empirical solar radiation pressure (SRP) models, such as the five-parameter Empirical CODE Orbit Model (ECOM1) and its extended version-ECOM2, are widely used for modeling SRP forces acting on GNSS satellites. This study shows that the orbits of BeiDou-3 Inclined Geosynchronous Orbit satellites (IGSOs) determined with the ECOM1 model suffer from systematic once-per-revolution radial orbit errors, which can be partly reduced by the ECOM2 model. To eliminate such orbit errors, the BeiDou-3 IGSO optical coefficients are solved by using an adjustable box-wing (ABW) model and then introduced into an a priori box-wing SRP model to enhance the ECOM1 model (ECOM1 + BW). In the ABW solution, in addition to satellite body and solar panels, the contributions of the communication payloads installed on BeiDou-3 IGSO ±X panels on the SRP are also considered, which markedly improves the stability of the optical coefficient estimates. The efficiency of the developed a priori box-wing model is demonstrated through eliminated once-per-revolution radial orbit errors and decreased day boundary discontinuities. However, the orbit solutions still show significant degradations during eclipse seasons. The results of the first yaw-attitude analysis for eclipsing BeiDou-3 IGSOs show that their yaw behaviors are the same as those of BeiDou-3 CAST (China Academy of Space Technology) MEOs (Medium Earth Orbit satellites), and have been well considered in the study. This rules out the possibility that attitude errors are the potential reason for the orbit deterioration. By introducing a once-per-revolution sine term in the Sun direction (Ds term) and keeping Ds active during the Earth’s shadow transitions to the ECOM1 + BW model, the orbit performance inside the eclipse seasons is significantly improved and can be comparable to that outside the eclipse seasons.

The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou Navigation Satellite System (BDS-2), for which apparent deficiencies of non-conservative models are identified and evidenced in the Satellite Laser Ranging (SLR) residuals. The orbit errors derived from the empirical 5-parameter Extended CODE Orbit Model (ECOM) as well as a semi-analytical adjustable box-wing model show prominent dependency on the Sun elongation angle, even in the yaw-steering attitude mode. Hence, a periodic acceleration in the normal direction of the +X surface, presumably generated by the mismodeled thermal radiation pressure, is introduced. The SLR validations reveal that the Sun elongation angle-dependent systematic errors were significantly reduced, and the orbit accuracy was improved by 10–30% to approximately 4.5 cm and 3.0 cm for the BDS-2 IGSO and MEO satellites, respectively.

For Global Positioning System (GPS) precise orbit determination (POD), the solar radiation pressure (SRP) is the dominant nongravitational perturbation force. Among the current SRP models, the ECOM and box-wing models are widely used in the International GNSS Service (IGS) community. However, the performance of different models varies over different GPS satellites. In this study, we investigate the performances of different SRP models, including the box-wing and adjustable box-wing as a priori models, and ECOM1 and ECOM2 as parameterization models, in the GPS POD solution from 2017 to 2019. Moreover, we pay special attention to the handling of the shadow factor in the SRP modeling for eclipsing satellites, which is critical to achieve high-precision POD solutions but has not yet been fully investigated. We demonstrate that, as an a priori SRP model, the adjustable box-wing has better performance than the box-wing model by up to 5 mm in the orbit day boundary discontinuity (DBD) statistics, with the largest improvement observed on the BLOCK IIR satellites using the ECOM1 as a parameterization SRP model. The box-wing model shows an insignificant orbit improvement serving as the a priori SRP model. For the eclipsing satellites, the three-dimensional (3D) root mean square (RMS) values of orbit DBD are improved when the shadow factor is applied only in the D direction (pointing toward to Sun) than that in the three directions (D, Y, and B) in the satellite frame. Different SRP models have comparable performance in terms of the Earth rotation parameter (ERP) agreement with the IERS EOP 14C04 product, whereas the magnitude of the length of day (LoD) annual signal is reduced when the shadow factor is applied in the D direction than in the three directions. This study clarifies how the shadow factor should be applied in the GPS POD solution and demonstrates that the a priori adjustable box-wing model combined with ECOM1 is more suitable for high-precision GPS POD solutions, which is useful for the further GNSS data analysis.

Although ionosphere-free (IF) combination is usually employed in long-range precise positioning, in order to employ the knowledge of the spatiotemporal ionospheric delays variations and avoid the difficulty in choosing the IF combinations in case of triple-frequency data processing, using uncombined observations with proper ionospheric constraints is more beneficial. Yet, determining the appropriate power spectral density (PSD) of ionospheric delays is one of the most important issues in the uncombined processing, as the empirical methods cannot consider the actual ionosphere activities. The ionospheric delays derived from actual dual-frequency phase observations contain not only the real-time ionospheric delays variations, but also the observation noise which could be much larger than ionospheric delays changes over a very short time interval, so that the statistics of the ionospheric delays cannot be retrieved properly. Fortunately, the ionospheric delays variations and the observation noise behave in different ways, i.e., can be represented by random-walk and white noise process, respectively, so that they can be separated statistically. In this paper, we proposed an approach to determine the PSD of ionospheric delays for each satellite in real-time by denoising the ionospheric delay observations. Based on the relationship between the PSD, observation noise and the ionospheric observations, several aspects impacting the PSD calculation are investigated numerically and the optimal values are suggested. The proposed approach with the suggested optimal parameters is applied to the processing of three long-range baselines of 103 km, 175 km and 200 km with triple-frequency BDS data in both static and kinematic mode. The improvement in the first ambiguity fixing time (FAFT), the positioning accuracy and the estimated ionospheric delays are analysed and compared with that using empirical PSD. The results show that the FAFT can be shortened by at least 8% compared with using a unique empirical PSD for all satellites although it is even fine-tuned according to the actual observations and improved by 34% compared with that using PSD derived from ionospheric delay observations without denoising. Finally, the positioning performance of BDS three-frequency observations shows that the averaged FAFT is 226 s and 270 s, and the positioning accuracies after ambiguity fixing are 1 cm, 1 cm and 3 cm in the East, North and Up directions for static and 3 cm, 3 cm and 6 cm for kinematic mode, respectively.

Concerning the triple-frequency ambiguity resolution, in principle there are three different realizations. The first one is to fix all the ambiguities of the original frequencies together. However, it is also believed that fixing the combined integer ambiguities with longer wavelength, such as extra-wide-lane (EWL), wide-lane (WL), should be advantageous. Also, it is demonstrated that fixing sequentially EWL, WL and one type of original ambiguities provides better results, as the previously fixed ambiguities increase parameters’ precision for later fixings. In this paper, we undertake a comparative study of the three fixing approaches by means of experimental validation. In order to realize the three fixing approaches from the same information in terms of adjustment, we developed a processing strategy to provide fully consistent normal equations. We first generate the normal equation with the original undifferentiated carrier phase ambiguities, then map it into that with the combined and double-differenced ambiguities required by the individual approach for fixing. Four baselines of 258 m, 22 km, 47 km and 53 km are selected and processed in both static and kinematic mode using the three ambiguity-fixing approaches. Indicators including time of first fixed solution (TFFS), the correct fixing rate, positioning accuracy and RATIO are used to evaluate and investigate results. We also made a preliminary theoretical explanation of the results by looking into the decorrelation procedure of the ambiguity searching algorithm and the intermediate results. As conclusions, integrated searching of original ambiguities or combined ambiguities has almost the same fixing performance, whereas the sequential fixing of EWL, WL and B1 ambiguities overperforms the integrated searching. By the way, the third-frequency data can shorten the TFFS significantly but can hardly improve the positioning.

The Korean government has a plan to build a new regional satellite navigation system called the Korean Positioning System (KPS). The initial KPS constellation is designed to consist of seven satellites, which include three geostationary Earth orbit (GEO) satellites and four inclined geosynchronous orbit (IGSO) satellites. KPS will provide an independent positioning, navigation, and timing (PNT) service in the Asia-Oceania region and can also be compatible with GPS. In the simulation for KPS, we employ 24 GPS as designed initially and 7 KPS satellites. Compared to the true orbit that we simulated, the averaged root mean square (RMS) values of orbit-only signal-in-space ranging errors (SISRE) are approximately 4.3 and 3.9 cm for KPS GEO and IGSO. Two different positioning solutions are analyzed to demonstrate the KPS performance. KPS standard point positioning (SPP) errors in the service area are about 4.7, 3.9, and 7.1 m for east (E), north (N), and up (U) components, respectively. The combined KPS+GPS SPP accuracy can be improved by 25.0%, 31.8%, and 35.0% compared to GPS in E, N, and U components. The averaged position errors for KPS kinematic precise point positioning (KPPP) are less than 10 cm. In the fringe of the KPS service area, however, the position RMS errors can reach about 40 cm. Unlike KPS, GPS solutions show high positioning accuracy in the KPS service area. The combined KPS+GPS can be improved by 28.7%, 27.1%, and 30.5% compared to GPS in E, N, and U components, respectively. It is noted that KPS can provide better performance with GPS in the Asia-Oceania region.

In order to improve the precision of GLONASS orbits, this paper presents a method to connect the data segments of a single station-satellite pair to increase the observation continuity and, consequently, the strength of the precise orbit determination (POD) solution. In this method, for each GLONASS station-satellite pair, the wide-lane ambiguities derived from the Melbourne–Wübbena combination are statistically tested and corrected for phase integer offsets and then the same is carried out for the narrow-lane ambiguities calculated from the POD solution. An experimental validation was carried out using one-month GNSS data of a global network with 175 IGS stations. The result shows that, on average, 27.1% of the GLONASS station-satellite pairs with multiple data segments could be connected to a single long observation arc and, thus, only one ambiguity parameter was estimated. Using the connected data, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 19.2% in ideal cases with an averaged reduction of about 6.3%.

Global Positioning System (GPS) has been proved to be a powerful tool for measuring co-seismic ground displacements with an application to seismic source inversion. Whereas most of the tsunamis are triggered by large earthquakes, GPS can contribute to the tsunami early warning system (TEWS) by helping to obtain tsunami source parameters in near real-time. Toward the end of 2012, the second phase of the BeiDou Navigation Satellite System (BDS) constellation was accomplished, and BDS has been providing regional positioning service since then. Numerical results indicate that precision of BDS nowadays is equivalent to that of the GPS. Compared with a single Global Satellite Navigation System (GNSS), combined BDS/GPS real-time processing can improve accuracy and especially reliability of retrieved co-seismic displacements. In the present study, we investigate the potential of BDS to serve for the early warning system of tsunamis in the South China Sea region. To facilitate early warnings of tsunamis and forecasting capabilities in this region, we propose to distribute an array of BDS-stations along the Luzon Island (Philippines). By simulating an earthquake with Mw = 8 at the Manila trench as an example, we demonstrate that such an array will be able to detect earthquake parameters in real time with a high degree of accuracy and, hence, contribute to the fast and reliable tsunami early warning system in this region.

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 Expectation-Maximization algorithm is adapted to the extended Kalman filter to multiple GNSS Precise Point Positioning (PPP), named EM-PPP. EM-PPP considers better the compatibility of multiple GNSS data processing and characteristics of receiver motion, targeting to calibrate the process noise matrix Qt and observation matrix Rt, having influence on PPP convergence time and precision, with other parameters. It is possibly a feasible way to estimate a large number of parameters to a certain extent for its simplicity and easy implementation. We also compare EM-algorithm with other methods like least-squares (co)variance component estimation (LS-VCE), maximum likelihood estimation (MLE), showing that EM-algorithm from restricted maximum likelihood (REML) will be identical to LS-VCE if certain weight matrix is chosen for LS-VCE. To assess the performance of the approach, daily observations from a network of 14 globally distributed International GNSS Service (IGS) multi-GNSS stations were processed using ionosphere-free combinations. The stations were assumed to be in kinematic motion with initial random walk noise of 1 mm every 30 s. The initial standard deviations for ionosphere-free code and carrier phase measurements are set to 3 m and 0.03 m, respectively, independent of the satellite elevation angle. It is shown that the calibrated Rt agrees well with observation residuals, reflecting effects of the accuracy of different satellite precise product and receiver-satellite geometry variations, and effectively resisting outliers. The calibrated Qt converges to its true value after about 50 iterations in our case. A kinematic test was also performed to derive 1 Hz GPS displacements, showing the RMSs and STDs w.r.t. real-time kinematic (RTK) are improved and the proper Qt is found out at the same time. According to our analysis despite the criticism that EM-PPP is very time-consuming because a large number of parameters are calculated and the first-order convergence of EM-algorithm, it is a numerically stable and simple approach to consider the temporal nature of state-space model of PPP, in particular when Qt and Rt are not known well, its performance without fixing ambiguities can even parallel to traditional PPP-RTK.

Global navigation satellite systems (GNSS) are an important tool for positioning, navigation, and timing (PNT) services. The fast and high-precision GNSS data processing relies on reliable integer ambiguity fixing, whose performance depends on phase bias estimation. However, the mathematic model of GNSS phase bias estimation encounters the rank-deficiency problem, making bias estimation a difficult task. Combining the Monte-Carlo-based methods and GNSS data processing procedure can overcome the problem and provide fast-converging bias estimates. The variance reduction of the estimation algorithm has the potential to improve the accuracy of the estimates and is meaningful for precise and efficient PNT services. In this paper, firstly, we present the difficulty in phase bias estimation and introduce the sequential quasi-Monte Carlo (SQMC) method, then develop the SQMC-based GNSS phase bias estimation algorithm, and investigate the effects of the low-discrepancy sequence on variance reduction. Experiments with practical data show that the low-discrepancy sequence in the algorithm can significantly reduce the standard deviation of the estimates and shorten the convergence time of the filtering.

Real-time multi-GNSS precise point positioning (PPP) requires the support of high-rate satellite clock corrections. Due to the large number of ambiguity parameters, it is difficult to update clocks at high frequency in real-time for a large reference network. With the increasing number of satellites of multi-GNSS constellations and the number of stations, real-time high-rate clock estimation becomes a big challenge. In this contribution, we propose a decentralized clock estimation (DECE) strategy, in which both undifferenced (UD) and epoch-differenced (ED) mode are implemented but run separately in different computers, and their output clocks are combined in another process to generate a unique product. While redundant UD and/or ED processing lines can be run in offsite computers to improve the robustness, processing lines for different networks can also be included to improve the clock quality. The new strategy is realized based on the Position and Navigation Data Analyst (PANDA) software package and is experimentally validated with about 110 real-time stations for clock estimation by comparison of the estimated clocks and the PPP performance applying estimated clocks. The results of the real-time PPP experiment using 12 global stations show that with the greatly improved computational efficiency, 3.14 cm in horizontal and 5.51 cm in vertical can be achieved using the estimated DECE clock.

The continuity and reliability of precise GNSS positioning can be seriously limited by severe user observation environments. The Inertial Navigation System (INS) can overcome such drawbacks, but its performance is clearly restricted by INS sensor errors over time. Accordingly, the tightly coupled integration of GPS and INS can overcome the disadvantages of each individual system and together form a new navigation system with a higher accuracy, reliability and availability. Recently, ionosphere-constrained (IC) precise point positioning (PPP) utilizing raw GPS observations was proven able to improve both the convergence and positioning accuracy of the conventional PPP using ionosphere-free combined observations (LC-PPP). In this paper, a new mode of tightly coupled integration, in which the IC-PPP instead of LC-PPP is employed, is implemented to further improve the performance of the coupled system. We present the detailed mathematical model and the related algorithm of the new integration of IC-PPP and INS. To evaluate the performance of the new tightly coupled integration, data of both airborne and vehicle experiments with a geodetic GPS receiver and tactical grade inertial measurement unit are processed and the results are analyzed. The statistics show that the new approach can further improve the positioning accuracy compared with both IC-PPP and the tightly coupled integration of the conventional PPP and INS.

In order to catch up the short-term clock variation of GNSS satellites, clock corrections must be estimated and updated at a high-rate for Precise Point Positioning (PPP). This estimation is already very time-consuming for the GPS constellation only as a great number of ambiguities need to be simultaneously estimated. However, on the one hand better estimates are expected by including more stations, and on the other hand satellites from different GNSS systems must be processed integratively for a reliable multi-GNSS positioning service. To alleviate the heavy computational burden, epoch-differenced observations are always employed where ambiguities are eliminated. As the epoch-differenced method can only derive temporal clock changes which have to be aligned to the absolute clocks but always in a rather complicated way, in this paper, an efficient method for high-rate clock estimation is proposed using the concept of “carrier-range” realized by means of PPP with integer ambiguity resolution. Processing procedures for both post- and real-time processing are developed, respectively. The experimental validation shows that the computation time could be reduced to about one sixth of that of the existing methods for post-processing and less than 1 s for processing a single epoch of a network with about 200 stations in real-time mode after all ambiguities are fixed. This confirms that the proposed processing strategy will enable the high-rate clock estimation for future multi-GNSS networks in post-processing and possibly also in real-time mode.

High-rate multi-constellation global navigation satellite system (GNSS) precise point positioning (PPP) has been recognized as an efficient and reliable technique for large earthquake monitoring. However, the displacements derived from PPP are often overwhelmed by the centimeter-level noise, therefore they are usually unable to detect slight deformations which could provide new findings for geophysics. In this paper, Global Positioning System (GPS), GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS), and BeiDou navigation satellite system (BDS) data collected during the 2017 Mw 6.5 Jiuzhaigou earthquake were used to further exploit the capability of BDS-only and multi-GNSS PPP in deformation monitoring by applying sidereal filtering (SF) in the observation domain. The equation that unifies the residuals for the uncombined and undifferenced (UCUD) PPP solution on different frequencies was derived, which could greatly reduce the complexity of data processing. An unanticipated long-term periodic error term of up to ± 3 cm was found in the phase residuals associated with BDS satellites in geostationary Earth orbit (GEO), which is not due to multipath originated from the ground but is in fact satellite dependent. The period of this error is mainly longer than 2000 s and cannot be alleviated by using multi-GNSS. Compared with solutions without sidereal filtering, the application of the SF approach dramatically improves the positioning precision with respect to the weekly averaged positioning solution, by 75.2%, 42.8%, and 56.7% to 2.00, 2.23, and 5.58 cm in the case of BDS-only PPP in the east, north, and up components, respectively, and 71.2%, 27.7%, and 37.9% to 1.25, 0.81, and 3.79 cm in the case of GPS/GLONASS/BDS combined PPP, respectively. The GPS/GLONASS/BDS combined solutions augmented by the SF successfully suppress the GNSS noise, which contributes to the detection of the true seismic signal and is beneficial to the pre- and post-seismic signal analysis.

The low-cost single-frequency GNSS receiver is one of the most economical and affordable tools for the onboard real-time navigation of numerous remote sensing small/micro satellites. We concentrate on the algorithm and experiments of onboard real-time orbit determination (RTOD) based on a single-frequency GPS/BDS receiver. Through various experiments of processing the real single-frequency GPS/BDS measurements from the Yaogan-30 (YG30) series and FengYun-3C (FY3C) satellites of China, some critical aspects of the onboard RTOD are investigated, such as the optimal force models setting, the effect of different measurements, and the impact of GPS/BDS fusion. The results demonstrate that a gravity model truncated to 55 × 55 order/degree for YG30 and 45 × 45 for FY3C and compensated with an optimal stochastic modeling of empirical accelerations, which minimize the onboard computational load and only result in a slight loss of orbit accuracy, is sufficient to obtain high-precision real-time orbit results. Under the optimal force models, the real-time orbit accuracy of 0.4−0.7 m for position and 0.4−0.7 mm/s for velocity is achievable with the carrier-phase-based solution, while an inferior real-time orbit accuracy of 0.8−1.6 m for position and 0.9−1.7 mm/s for velocity is achieved with the pseudo-range-based solution. Furthermore, although the GPS/BDS fusion only makes little change to the orbit accuracy, it increases the number of visible GNSS satellites significantly, and thus enhances the geometric distribution of GNSS satellites that help suppress the local orbit errors and improves the reliability and availability of the onboard RTOD, especially in some anomalous arcs where only a few GPS satellites are trackable.

The emergence of multiple global navigation satellite systems (multi-GNSS), including global positioning system (GPS), global navigation satellite system (GLONASS), Beidou navigation satellite system (BDS), and Galileo, brings not only great opportunities for real-time precise point positioning (PPP), but also challenges in quality control because of inevitable data anomalies. This research aims at achieving the real-time quality control of the multi-GNSS combined PPP using additional observations with opposite weight. A robust multiple-system combined PPP estimation is developed to simultaneously process observations from all the four GNSS systems as well as single, dual, or triple systems. The experiment indicates that the proposed quality control can effectively eliminate the influence of outliers on the single GPS and the multiple-system combined PPP. The analysis on the positioning accuracy and the convergence time of the proposed robust PPP is conducted based on one week’s data from 32 globally distributed stations. The positioning root mean square (RMS) error of the quad-system combined PPP is 1.2 cm, 1.0 cm, and 3.0 cm in the east, north, and upward components, respectively, with the improvements of 62.5%, 63.0%, and 55.2% compared to those of single GPS. The average convergence time of the quad-system combined PPP in the horizontal and vertical components is 12.8 min and 12.2 min, respectively, while it is 26.5 min and 23.7 min when only using single-GPS PPP. The positioning performance of the GPS, GLONASS, and BDS (GRC) combination and the GPS, GLONASS, and Galileo (GRE) combination is comparable to the GPS, GLONASS, BDS and Galileo (GRCE) combination and it is better than that of the GPS, BDS, and Galileo (GCE) combination. Compared to GPS, the improvements of the positioning accuracy of the GPS and GLONASS (GR) combination, the GPS and Galileo (GE) combination, the GPS and BDS (GC) combination in the east component are 53.1%, 43.8%, and 40.6%, respectively, while they are 55.6%, 48.1%, and 40.7% in the north component, and 47.8%, 40.3%, and 34.3% in the upward component.

Precise Point Positioning (PPP) has become a very hot topic in GNSS research and applications. However, it usually takes about several tens of minutes in order to obtain positions with better than 10 cm accuracy. This prevents PPP from being widely used in real-time kinematic positioning services, therefore, a large effort has been made to tackle the convergence problem. One of the recent approaches is the ionospheric delay constrained precise point positioning (IC-PPP) that uses the spatial and temporal characteristics of ionospheric delays and also delays from an a priori model. In this paper, the impact of the quality of ionospheric models on the convergence of IC-PPP is evaluated using the IGS global ionospheric map (GIM) updated every two hours and a regional satellite-specific correction model. Furthermore, the effect of the receiver differential code bias (DCB) is investigated by comparing the convergence time for IC-PPP with and without estimation of the DCB parameter. From the result of processing a large amount of data, on the one hand, the quality of the a priori ionosphere delays plays a very important role in IC-PPP convergence. Generally, regional dense GNSS networks can provide more precise ionosphere delays than GIM and can consequently reduce the convergence time. On the other hand, ignoring the receiver DCB may considerably extend its convergence, and the larger the DCB, the longer the convergence time. Estimating receiver DCB in IC-PPP is a proper way to overcome this problem. Therefore, current IC-PPP should be enhanced by estimating receiver DCB and employing regional satellite-specific ionospheric correction models in order to speed up its convergence for more practical applications.

This is a great era of significant changes and innovations in the field of geodesy and navigation with the emerging multi-constellation Global Navigation Satellite Systems (GNSS) [...]

The GNSS derived Zenith Tropospheric Delay (ZTD) plays today a very critical role in meteorological study and weather forecasts, as ZTDs of thousands of GNSS stations are operationally assimilated into numerical weather prediction models. Recently, the Chinese BeiDou Navigation Satellite System (BDS) was officially announced to provide operational services around China and its neighborhood and it was demonstrated to be very promising for precise navigation and positioning. In this contribution, we concentrate on estimating ZTD using BDS observations to assess its capacity for troposphere remote sensing. A local network which is about 250 km from Beijing and comprised of six stations equipped with GPS- and BDS-capable receivers is utilized. Data from 5 to 8 November 2012 collected on the network is processed in network mode using precise orbits and in Precise Point Positioning mode using precise orbits and clocks. The precise orbits and clocks are generated from a tracking network with most of the stations in China and several stations around the world. The derived ZTDs are compared with that estimated from GPS data using the final products of the International GNSS Service (IGS). The comparison shows that the bias and the standard deviation of the ZTD differences are about 2 mm and 5 mm, respectively, which are very close to the differences of GPS ZTD estimated using different software packages.

The regional service of the Chinese BeiDou satellite navigation system is now in operation with a constellation including five Geostationary Earth Orbit satellites (GEO), five Inclined Geosynchronous Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. Besides the standard positioning service with positioning accuracy of about 10 m, both precise relative positioning and precise point positioning are already demonstrated. As is well known, precise orbit and clock determination is essential in enhancing precise positioning services. To improve the satellite orbits of the BeiDou regional system, we concentrate on the impact of the tracking geometry and the involvement of MEOs, and on the effect of integer ambiguity resolution as well. About seven weeks of data collected at the BeiDou Experimental Test Service (BETS) network is employed in this experimental study. Several tracking scenarios are defined, various processing schemata are designed and carried out; and then, the estimates are compared and analyzed in detail. The results show that GEO orbits, especially the along-track component, can be significantly improved by extending the tracking network in China along longitude direction, whereas IGSOs gain more improvement if the tracking network extends in latitude. The involvement of MEOs and ambiguity-fixing also make the orbits better.

The main challenge of precise point positioning (PPP) applications is the long convergence time of typically a half hour, or even more, to achieve centimeter accuracy. Even when the multi-constellation is involved and ambiguity resolution is implemented, it still requires about ten minutes. It is becoming a hot spot to incorporate the low Earth orbit (LEO) satellite constellation for enhancing the Global Navigation Satellite System (GNSS), named here as LEO-enhanced GNSS (LeGNSS). In this system, the LEO satellites cannot only receive GNSS signals, but also serve as GNSS satellites by transmitting similar navigation signals to the ground users, but with higher signal strength and much faster geometric change due to their low altitude. As a result, the convergence time of PPP is expected to be shortened to a few minutes, or even seconds. Simulation software is developed to simulate GNSS and LEO observations for ground stations taking into account tropospheric delay, satellite clock errors, observation noises, as well as other error sources. Then the number of visible satellites, the geometry dilution of precision (GDOP), and the convergence time of the kinematic mode of PPP are evaluated on a global scale compared to those of GNSS systems. The simulation results show that LeGNSS can decrease the PPP convergence to 5 min. If there are more LEO satellites included in the LeGNSS, it is expected that the initialization of PPP can be further shortened.

The multiple global navigation satellite systems (multi-GNSS) bring great opportunity for the real-time retrieval of high-quality zenith tropospheric delay (ZTD), which is a critical quality for atmospheric science and geodetic applications. In this contribution, a multi-GNSS precise point positioning (PPP) ambiguity resolution (AR) analysis approach is developed for real-time tropospheric delay retrieval. To validate the proposed multi-GNSS ZTD estimates, we collected and processed data from 30 Multi-GNSS Experiment (MGEX) stations; the resulting real-time tropospheric products are evaluated by using standard post-processed troposphere products and European Centre for Medium-Range Weather Forecasts analysis (ECMWF) data. An accuracy of 4.5 mm and 7.1 mm relative to the Center for Orbit Determination in Europe (CODE) and U.S. Naval Observatory (USNO) products is achievable for real-time tropospheric delays from multi-GNSS PPP ambiguity resolution after an initialization process of approximately 5 min. Compared to Global Positioning System (GPS) results, the accuracy of retrieved zenith tropospheric delay from multi-GNSS PPP-AR is improved by 16.7% and 31.7% with respect to USNO and CODE final products. The GNSS-derived ZTD time-series exhibits a great agreement with the ECMWF data for a long period of 30 days. The average root mean square (RMS) of the real-time zenith tropospheric delay retrieved from multi-GNSS PPP-AR is 12.5 mm with respect to ECMWF data while the accuracy of GPS-only results is 13.3 mm. Significant improvement is also achieved in terms of the initialization time of the multi-GNSS tropospheric delays, with an improvement of 50.7% compared to GPS-only fixed solutions. All these improvements demonstrate the promising prospects of the multi-GNSS PPP-AR method for time-critical meteorological applications.

Precise Point Positioning (PPP) is a popular technology for precise applications based on the Global Navigation Satellite System (GNSS). Multi-GNSS combined PPP has become a hot topic in recent years with the development of multiple GNSSs. Meanwhile, with the operation of the real-time service (RTS) of the International GNSS Service (IGS) agency that provides satellite orbit and clock corrections to broadcast ephemeris, it is possible to obtain the real-time precise products of satellite orbits and clocks and to conduct real-time PPP. In this contribution, the real-time multi-GNSS orbit and clock corrections of the CLK93 product are applied for real-time multi-GNSS PPP processing, and its orbit and clock qualities are investigated, first with a seven-day experiment by comparing them with the final multi-GNSS precise product ‘GBM’ from GFZ. Then, an experiment involving real-time PPP processing for three stations in the Multi-GNSS Experiment (MGEX) network with a testing period of two weeks is conducted in order to evaluate the convergence performance of real-time PPP in a simulated kinematic mode. The experimental result shows that real-time PPP can achieve a convergence performance of less than 15 min for an accuracy level of 20 cm. Finally, the real-time data streams from 12 globally distributed IGS/MGEX stations for one month are used to assess and validate the positioning accuracy of real-time multi-GNSS PPP. The results show that the simulated kinematic positioning accuracy achieved by real-time PPP on different stations is about 3.0 to 4.0 cm for the horizontal direction and 5.0 to 7.0 cm for the three-dimensional (3D) direction.

Slant delay data obtained from global positioning system (GPS) observations carry valuable meteorological information. The spatial distribution of the water vapour can be reconstructed from such slant delays. To estimate the quality of the GPS slant delays two validation studies were carried out. One study was based on the observations of a water vapour radiometer, a second on the analysis fields of a numerical weather model which were used to compute the corresponding GPS delays. Both studies yielded a high correlation between the available slant delays at higher elevation angles but showed deficiencies at low elevations. The mean bias between the GPS zenith delays and the radiometer data is 1.18 mm with a RMS of 6.0 mm. The corresponding bias and RMS of the GPS vs. model comparison are 3.3 mm and 2.9 mm.

The integration of the Global Positioning System (GPS) and the Inertial Navigation System (INS) based on Real-time Kinematic (RTK) and Single Point Positioning (SPP) technology have been applied as a powerful approach in kinematic positioning and attitude determination. However, the accuracy of RTK and SPP based GPS/INS integration mode will degrade visibly along with the increasing user-base distance and the quality of pseudo-range. In order to overcome such weaknesses, the tightly coupled integration between GPS Precise Point Positioning (PPP) and INS was proposed recently. Because of the rapid development of the multi-constellation Global Navigation Satellite System (multi-GNSS), we introduce the multi-GNSS into the tightly coupled integration of PPP and INS in this paper. Meanwhile, in order to weaken the impacts of the GNSS observations with low quality and the inaccurate state model on the performance of the multi-GNSS PPP/INS tightly coupled integration, the Helmert variance component estimation based adaptive Kalman filter is employed in the algorithm implementation. Finally, a set of vehicle-borne GPS + BeiDou + GLONASS and Micro-Electro-Mechanical-Systems (MEMS) INS data is analyzed to evaluate the performance of such algorithm. The statistics indicate that the performance of the multi-GNSS PPP/INS tightly coupled integration can be enhanced significantly in terms of both position accuracy and convergence time.