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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.

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.

Multipath effect on carrier-phase observation is one of the bottlenecks for mm-level applications when using precise point positioning (PPP). Hence, we extract the multipath directly from raw carrier-phase residuals of GPS, GLONASS, Galileo, and BDS, by using PPP technique. Although the residuals for one frequency assimilate the errors from other frequencies, which is caused by error adjustment by the least squares estimator, the primary component of residuals is multipath. The results indicate that the residuals between frequencies have a significant linear negative correlation and synchronous time lag for each system. Besides BDS Geostationary Earth Orbit satellites, the residuals for other satellites can establish accurate mathematic relationship between the frequencies. For GLONASS, the residuals of R1 frequency recovered from R2 frequency with the mathematical relationship are better than 0.1 mm accuracy, which means the effect of inter-frequency bias can be neglected. These regularities double-reduce the complexity of data processing. Based on the multipath distribution, we propose a modified Multipath Hemispherical Map model (M-MHM), which constructs grids from residuals and is divided into three equal-elevation angle parts with an optimal resolution 0.2° × 0.2° × 1° from numerous experiments. In addition, the multipath manifests great consistency among satellites for GPS, GLONASS, and Galileo systems when elevation angles are higher than 15°, while is more satellite dependent for BDS. Although GPS L1 frequency is identical to Galileo E1, the model still has some systematic bias between GPS and Galileo. Compared with sidereal filtering and original MHM model, the M-MHM brings the highest improvement in both residual variance reduction and positioning accuracy. The positioning accuracy is on average 12% improvement compared to MHM and 29% improvement compared to SF. For four systems combined solutions with the M-MHM model, can reach an accuracy of 0.75, 0.55, and 2.08 cm in the east, north, and up components.

This manuscript reviews recent progress in optical frequency references and optical communication systems and discusses their utilizations in global satellite navigation systems and satellite geodesy. Lasers stabilized with optical cavities or spectroscopy of molecular iodine are analyzed, and a hybrid architecture is proposed to combine both forms of stabilization with the aim of achieving a target frequency stability of 10-15 [s/s] over a wide range of sampling intervals. The synchronization between two optical frequency references in real-time is realized by means of time and frequency transfer on optical carriers. The technologies enabling coherent optical links are reviewed, and the development of an optical communication system for synchronization, ranging and data communication in space is described. An infrastructure exploiting the capabilities of both optical technologies for the realization of a modernized constellation of navigation satellites emitting highly synchronized signals is reviewed. Such infrastructure, named Kepler system, improves satellite navigation in terms intra-system synchronization, orbit determination accuracy, as well as system monitoring and integrity. The potential impact on geodetic key parameters is addressed.

The terrestrial and celestial reference frames are linked by the Earth Orientation Parameters (EOP), which describe the irregularities of the Earth's rotation and are determined by the space geodetic techniques, namely, Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Global Navigation Satellite Systems (GNSS), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS). The satellite geodetic techniques (SLR, GNSS, and DORIS) cannot determine the UT1-UTC or celestial pole offsets (CPO), rendering VLBI the only technique capable of determining full EOP set. On the other hand, the GNSS technique provides precise polar motion estimates due to the continuous observations from a globally distributed network. Integrating VLBI and GNSS provides the full set of EOP and guarantees a superior accuracy than any single-technique solution.In this study we focus on the integrated estimation of the full EOP set from GNSS and VLBI. Using five VLBI continuous observing campaigns (CONT05–CONT17), the GNSS and VLBI observations are processed concurrently in a common least-squares estimator. The impact of applying global ties (EOP), local ties, and tropospheric ties, and combinations thereof is investigated. The polar motion estimates in integrated solution are dominated by the huge GNSS observations, and the accuracy in terms of weighted root mean squares (WRMS) is ~40 μas compared to the IERS 14 C04 product, which is much better than that of the VLBI-only solution. The UT1-UTC and CPO in the integrated solution also show slight improvement compared to the VLBI-only solution. Moreover, the CPO agreement between the two networks in CONT17, i.e., the VLBA and IVS networks, shows an improvement of 20% to 40% in the integrated solution with different types of ties applied.

The precise orbit determination (POD) of Global Navigation Satellite System (GNSS) satellites and low Earth orbiters (LEOs) are usually performed independently. It is a potential way to improve the GNSS orbits by integrating LEOs onboard observations into the processing, especially for the developing GNSS, e.g., Galileo with a sparse sensor station network and Beidou with a regional distributed operating network. In recent years, few studies combined the processing of ground- and space-based GNSS observations. The integrated POD of GPS satellites and seven LEOs, including GRACE-A/B, OSTM/Jason-2, Jason-3 and, Swarm-A/B/C, is discussed in this study. GPS code and phase observations obtained by onboard GPS receivers of LEOs and ground-based receivers of the International GNSS Service (IGS) tracking network are used together in one least-squares adjustment. The POD solutions of the integrated processing with different subsets of LEOs and ground stations are analyzed in detail. The derived GPS satellite orbits are validated by comparing with the official IGS products and internal comparison based on the differences of overlapping orbits and satellite positions at the day-boundary epoch. The differences between the GPS satellite orbits derived based on a 26-station network and the official IGS products decrease from 37.5 to 23.9 mm ($$34\%$$ 34 % improvement) in 1D-mean RMS when adding seven LEOs. Both the number of the space-based observations and the LEO orbit geometry affect the GPS satellite orbits derived in the integrated processing. In this study, the latter one is proved to be more critical. By including three LEOs in three different orbital planes, the GPS satellite orbits improve more than from adding seven well-selected additional stations to the network. Experiments with a ten-station and regional network show an improvement of the GPS satellite orbits from about 25 cm to less than five centimeters in 1D-mean RMS after integrating the seven LEOs.

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 recent years, the precise orbit determination (POD) of the regional Chinese BeiDou Navigation Satellite System (BDS) has been a hot spot because of its special constellation consisting of five geostationary earth orbit (GEO) satellites and five inclined geosynchronous satellite orbit (IGSO) satellites besides four medium earth orbit (MEO) satellites since the end of 2012. GEO and IGSO satellites play an important role in regional BDS applications. However, this brings a great challenge to the POD, especially for the GEO satellites due to their geostationary orbiting. Though a number of studies have been carried out to improve the POD performance of GEO satellites, the result is still much worse than that of IGSO and MEO, particularly in the along-track direction. The major reason is that the geostationary characteristic of a GEO satellite results in a bad geometry with respect to the ground tracking network. In order to improve the tracking geometry of the GEO satellites, a possible strategy is to mount global navigation satellite system (GNSS) receivers on MEO satellites to collect the signals from GEO/IGSO GNSS satellites so as that these observations can be used to improve GEO/IGSO POD. We extended our POD software package to simulate all the related observations and to assimilate the MEO-onboard GNSS observations in orbit determination. Based on GPS and BDS constellations, simulated studies are undertaken for various tracking scenarios. The impact of the onboard GNSS observations is investigated carefully and presented in detail. The results show that MEO-onboard observations can significantly improve the orbit precision of GEO satellites from metres to decimetres, especially in the along-track direction. The POD results of IGSO satellites also benefit from the MEO-onboard data and the precision can be improved by more than 50% in 3D direction.

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.

With the development of China’s BeiDou Navigation Satellite System (BDS) and the operation of the real-time service (RTS) of the International GNSS service, BDS real-time precise point positioning (RTPPP) has become possible. In this contribution, the RTS product CLK93 is employed for BDS RTPPP, and its quality for BDS orbit and clock corrections is first assessed by availability and accuracy over a period of 24 days. Following this, the convergence time and positioning accuracy of BDS-only RTPPP are evaluated by performing a 24-day processing with ten stations from the multi-GNSS experiment (MGEX) network. Finally, a real-time kinematic test is conducted in an urban environment to further investigate the performance of BDS-only RTPPP. Experimental results show that the average availabilities of the CLK93 corrections are approximately 95% for the inclined geosynchronous satellite orbit (IGSO) satellites, 90% for the medium earth orbit (MEO) satellites and 65% for the geostationary earth orbit satellites. The mean accuracy of the real-time corrections, which is represented by the signal-in-space ranging error (SISRE) value, is 10 cm for the IGSO and MEO satellites. Furthermore, the average positioning accuracies in the north, east and up components of the ten MGEX stations are approximately 1.7, 2.2 and 2.6 cm, respectively, for the static mode and 10.3, 15.6 and 29.2 cm, respectively, for the kinematic mode. In addi-tion, the average time required to converge to a 20-cm accuracy in the three-dimensional component is approximately 100 and 136 min for BDS-only RTPPP in the static and kinematic modes, respectively. In addition, the positioning accuracy of BDS-only RTPPP in the real-time kinematic test is 0.86, 0.92 and 1.68 m in the east, north and up components, respectively, for the whole solutions during the test, which is obviously worse than that obtained by GPS-only RTPPP.

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.

The correction of higher-order ionospheric (HOI) delays remaining in the dual-frequency ionosphere-free combined observations is suggested after the confirmation of its impact on precise Global Navigation Satellite System (GNSS) data processing. However, in the precise orbit determination (POD) for generating ultra-rapid orbits, the higher-order corrections are not always considered most likely because a RT ionospheric model needed for calculating the higher-order corrections is hardly available or the HOI impact is believed rather small compared to the accuracy of the predicted orbit. With the increasing requirement on the positioning performances from various applications, providing more accurate and reliable ultra-rapid orbits becomes an essential task of the real-time GNSS precise positioning services. In this contribution, the temporal–spatial characteristics of HOI effects on GNSS observables are investigated thoroughly using data collected from International GNSS Service (IGS) global ground stations and fluctuations of the higher-order delays up to several centimeters are detected during periods of high ionospheric activity. Hereafter, we evaluate the HOI effects on the multi-GNSS POD based on a network with globally distributed IGS stations. Results show that owing to the applied HOI corrections, the agreement of overlapping orbits can be improved significantly for all satellites and especially in radial direction. The three-dimensional RMS values of the overlapping differences are reduced from 1.6, 2.0, 4.6 and 1.7 to 1.0, 1.1, 3.4, and 1.5 cm for GPS, GALILEO, BDS, and GLONASS, respectively. Furthermore, the orbit improvement is also confirmed by the satellite laser ranging (SLR) observations over a 2-month time period where the STD of SLR residuals is reduced by HOI corrections from 6.4 to 5.3 cm for the BDS-IGSO satellites.

The rapid development of the BeiDou Satellite Navigation System (BDS) and other Global Navigation Satellite System (multi-GNSS) constellations provides a great opportunity to contribute to earthquake early warning systems in terms of capturing displacement and velocity waveforms for the estimation of magnitude and fault slip inversion. In this study, we demonstrate the capability of BDS and the benefit of multi-GNSS for real-time capturing seismic waveforms using the combined high-rate BDS + GPS + GLONASS data collected during the 2017 Mw 6.5 Jiuzhaigou earthquake. For this event, we found that the displacements, derived from BDS precise point positioning (PPP) are better than that of Global Positioning System-only (GPS) results, especially in the east and vertical components with improvements of 43% and 23%. While the velocity waveforms from BDS present a comparable performance with GPS. the multi-GNSS fusion can significantly improve the accuracy by 47%, 55%, and 28% in the east, north, and vertical components compared with GPS-only results. The BDS and multi-GNSS derived displacement waveforms agree quite well with those obtained from integrating the acceleration, with accuracy at the millimeter level. In addition, the theoretical permanent displacement field calculated from a finite-fault slip model is selected as an independent reference, and the differences between GNSS derived permanent displacements and theoretical permanent displacements are mostly less than 1 mm. Therefore, we conclude that the BDS and multi-GNSS fusion can significantly contribute to the real-time capture of accurate seismic waveforms and that it has the potential to benefit for earthquake early warning and rapid geohazard assessment.

The tropospheric horizontal gradients with high spatiotemporal resolutions provide important information to describe the azimuthally asymmetric delays and significantly increase the ability of ground-based GNSS (Global Navigation Satellite Systems) within the field of meteorological studies, like the nowcasting of severe rainfall events. The recent rapid development of multi-GNSS constellations has potential to provide such high-resolution gradients with a significant degree of accuracy. In this study, we develop a multi-GNSS process for the precise retrieval of high-resolution tropospheric gradients. The tropospheric gradients with different temporal resolutions, retrieved from both single-system and multi-GNSS solutions, are validated using independent numerical weather models (NWM) data and water vapor radiometer (WVR) observations. The benefits of multi-GNSS processing for the retrieval of tropospheric gradients, as well as for the improvement of precise positioning, are demonstrated. The multi-GNSS high-resolution gradients agree well with those derived from the NWM and WVR, especially for the fast-changing peaks, which are mostly associated with synoptic fronts. The multi-GNSS gradients behave in a much more stable manner than the single-system estimates, especially in cases of high temporal resolution, benefiting from the increased number of observed satellites and improved observation geometry. The high-resolution multi-GNSS gradients show higher correlation with the NWM and WVR gradients than the low-resolution gradients. Furthermore, the precision of station positions can also be noticeably improved by multi-GNSS fusion, and enhanced results can be achieved if the high-resolution gradient estimation is performed, instead of the commonly used daily gradient estimation in the multi-GNSS data processing.

This paper investigates the effect of 06-09-2017 X9.3 solar flare on Global Navigation Satellite System (GNSS) signal and positioning performance. To conduct the study we select 60 IGS stations and collect the observations and ephemeris from August 30 to September 13, 2017. The Solar activity Indexes of Ap, Kp, Dst are evaluated and the global ROTI maps are constructed to indicate and define the magnitude of the storm. As for the GNSS signal, signal-in-space-ranging-errors (SISRE) is used to assess the solar flare’s effect on the accuracy of broadcast ephemeris, and the cycle slip occurrence is used to assess it’s impact on observation quality, especially phase observation. Furthermore, the kinematic GNSS PPP solution is used to evaluate the GNSS positioning performance during the storm. After processing, root mean square errors (RMS) of north, east and up component were calculated for each station on each day. The results indicate that at eight of all the selected IGS stations three-dimensional (3D) accuracy of PPP has degraded significantly and the GNSS are unreliable during the storm.

GLONASS precise point positioning (PPP) performance is affected by the inter-frequency biases (IFBs) due to the application of frequency division multiple access technique. In this contribution, the impact of GLONASS pseudorange IFBs on convergence performance and positioning accuracy of GLONASS-only and GPS + GLONASS PPP based on undifferenced and uncombined observation models is investigated. Through a re-parameterization process, the following four pseudorange IFB handling schemes were proposed: neglecting IFBs, modeling IFBs as a linear or quadratic polynomial function of frequency number, and estimating IFBs for each GLONASS satellite. One week of GNSS observation data from 132 International GNSS Service stations was selected to investigate the contribution of simultaneous estimation of GLONASS pseudorange IFBs on GLONASS-only and combined GPS + GLONASS PPP in both static and kinematic modes. The results show that considering IFBs can speed up the convergence of PPP using GLONASS observations by more than 20%. Apart from GLONASS-only kinematic PPP, the positioning accuracy of GLONASS-only and GPS + GLONASS PPP is comparable among the four schemes. Overall, the scheme of estimating IFBs for each GLONASS satellite outperforms the other schemes in both convergence time reduction and positioning accuracy improvement, which indicates that the GLONASS IFBs may not strictly obey a linear or quadratic function relationship with the frequency number.

The distinctive high orbits, regional coverage and stationary characteristics of BeiDou Geostationary Earth Orbit (GEO) satellites result in the poor geometric diversity with respect to ground stations and the difficulty for Precise Orbit Determination (POD). Considering that BeiDou is a regional system currently, the global ground stations cannot effectively ameliorate POD geometry, especially for GEO and IGSO satellites. Integrating the LEO-onboard GNSS data would be an effective way to improve the estimation of BeiDou orbits since LEO’s faster motion can significantly enhance geometric diversity. In this paper, we study the POD of combined GNSS and LEO constellation with regional ground stations in China, where the LEO constellation plays the role of moving tracking stations to ameliorate the poor POD geometry resulting from regional ground stations. The Iridium system is used as the LEO constellation and the LEO-onboard and ground tracking GNSS data are all simulated. The POD of combined GPS, BeiDou and LEO constellation is conducted with 8 ground stations in mainland of China. To balance the computation burden and POD accuracy, the different LEO satellites are selected for combined POD while the orbits of remained LEO satellites are computed with solved GPS and BeiDou orbits. With the LEO satellites increasing, the orbits of all GPS and BeiDou satellites are significantly improved, especially for along-track direction of GEO satellites. With the regional ground stations, the sub-decimeter-level orbit accuracies are achievable for BeiDou GEO and IGSO satellites, and centimeter accuracies for BeiDou MEO and GPS satellites. Furthermore, the impact of code precision on combined POD is numerically analyzed.

The revitalized Russian GLONASS system provides new potential for real-time retrieval of zenith tropospheric delays (ZTD) and precipitable water vapor (PWV) in order to support time-critical meteorological applications such as nowcasting or severe weather event monitoring. In this study, we develop a method of real-time ZTD/PWV retrieval based on GLONASS and/or GPS observations. The performance of ZTD and PWV derived from GLONASS data using real-time precise point positioning (PPP) technique is carefully investigated and evaluated. The potential of combining GLONASS and GPS data for ZTD/PWV retrieving is assessed as well. The GLONASS and GPS observations of about half a year for 80 globally distributed stations from the IGS (International GNSS Service) network are processed. The results show that the real-time GLONASS ZTD series agree quite well with the GPS ZTD series in general: the RMS of ZTD differences is about 8 mm (about 1.2 mm in PWV). Furthermore, for an inter-technique validation, the real-time ZTD estimated from GLONASS-only, GPS-only, and the GPS/GLONASS combined solutions are compared with those derived from very long baseline interferometry (VLBI) at colocated GNSS/VLBI stations. The comparison shows that GLONASS can contribute to real-time meteorological applications, with almost the same accuracy as GPS. More accurate and reliable water vapor values, about 1.5---2.3 mm in PWV, can be achieved when GLONASS observations are combined with the GPS ones in the real-time PPP data processing. The comparison with radiosonde data further confirms the performance of GLONASS-derived real-time PWV and the benefit of adding GLONASS to stand-alone GPS processing.

The bottleneck of Precise Point Positioning (PPP) is the long convergence time for achieving the centimeter accuracy. Some researchers put forward to improve the diversity of available satellites’ geometric distribution and reduce the correlation of observation data by deploying the Low Earth Orbit (LEO) constellations in addition to the medium and high-orbit satellites. The prerequisite is to get the precise orbit products of all these orbiting satellites. This paper studies the combined precise orbit determination for high-, medium-, and low-orbit navigation satellite systems. In order to investigate the theory and algorithms of the high–medium–low POD and to study the effect of LEO to the POD of high-orbit satellites and the influence of ground data from LEO to its own POD, we simulate all the data, including high orbit to low orbit, medium orbit to low orbit, high orbit to ground stations, medium orbit to ground stations, and low orbit to ground stations. The results show that the combined POD can improve the precision of high-orbit satellites significantly, especially for the along-track component, which can reach to sub-decimeter even centimeter level. Also, the precision of LEO POD can be improved with the data from ground stations.

Precise positioning with the current Chinese BeiDou Navigation Satellite System is proven to be of comparable accuracy to the Global Positioning System, which is at centimeter level for the horizontal components and sub-decimeter level for the vertical component. But the BeiDou precise point positioning (PPP) shows its limitation in requiring a relatively long convergence time. In this study, we develop a numerical weather model (NWM) augmented PPP processing algorithm to improve BeiDou precise positioning. Tropospheric delay parameters, i.e., zenith delays, mapping functions, and horizontal delay gradients, derived from short-range forecasts from the Global Forecast System of the National Centers for Environmental Prediction (NCEP) are applied into BeiDou real-time PPP. Observational data from stations that are capable of tracking the BeiDou constellation from the International GNSS Service (IGS) Multi-GNSS Experiments network are processed, with the introduced NWM-augmented PPP and the standard PPP processing. The accuracy of tropospheric delays derived from NCEP is assessed against with the IGS final tropospheric delay products. The positioning results show that an improvement in convergence time up to 60.0 and 66.7% for the east and vertical components, respectively, can be achieved with the NWM-augmented PPP solution compared to the standard PPP solutions, while only slight improvement in the solution convergence can be found for the north component. A positioning accuracy of 5.7 and 5.9 cm for the east component is achieved with the standard PPP that estimates gradients and the one that estimates no gradients, respectively, in comparison to 3.5 cm of the NWM-augmented PPP, showing an improvement of 38.6 and 40.1%. Compared to the accuracy of 3.7 and 4.1 cm for the north component derived from the two standard PPP solutions, the one of the NWM-augmented PPP solution is improved to 2.0 cm, by about 45.9 and 51.2%. The positioning accuracy for the up component improves from 11.4 and 13.2 cm with the two standard PPP solutions to 8.0 cm with the NWM-augmented PPP solution, an improvement of 29.8 and 39.4%, respectively.

Single-frequency precise point positioning (SF-PPP) is a potential precise positioning technique due to the advantages of the high accuracy in positioning after convergence and the low cost in operation. However, there are still challenges limiting its applications at present, such as the long convergence time, the low reliability, and the poor satellite availability and continuity in kinematic applications. In recent years, the achievements in the dual-frequency PPP have confirmed that its performance can be significantly enhanced by employing the slant ionospheric delay and receiver differential code bias (DCB) constraint model, and the multi-constellation Global Navigation Satellite Systems (GNSS) data. Accordingly, we introduce the slant ionospheric delay and receiver DCB constraint model, and the multi-GNSS data in SF-PPP modular together. In order to further overcome the drawbacks of SF-PPP in terms of reliability, continuity, and accuracy in the signal easily blocking environments, the inertial measurements are also adopted in this paper. Finally, we form a new approach to tightly integrate the multi-GNSS single-frequency observations and inertial measurements together to ameliorate the performance of the ionospheric delay and receiver DCB-constrained SF-PPP. In such model, the inter-system bias between each two GNSS systems, the inter-frequency bias between each two GLONASS frequencies, the hardware errors of the inertial sensors, the slant ionospheric delays of each user-satellite pair, and the receiver DCB are estimated together with other parameters in a unique Kalman filter. To demonstrate its performance, the multi-GNSS and low-cost inertial data from a land-borne experiment are analyzed. The results indicate that visible positioning improvements in terms of accuracy, continuity, and reliability can be achieved in both open-sky and complex conditions while using the proposed model in this study compared to the conventional GPS SF-PPP.

SUMMARY High-rate GNSS has attracted increasing attention and numerous applications in geohazard monitoring and early warning. In this paper, we investigate three current existing singlereceiver approaches for real-time GNSS seismology, comparing their observation models for equivalence andassessingtheimpactofmainerrorcomponents. Weproposesomerefinements to the variometric approach and especially consider compensating the geometry error component by using the accurate initial coordinates before the earthquake to eliminate the drift trend in the integrated coseismic displacements. After careful corrections of satellite ephemeris, ionospheric delay, tropospheric delay and geometry errors, the refined variometric approach andthetemporalpointpositioning(TPP)methodhaveequivalentmathematicalmodelwiththe converged precise point positioning (PPP). We evaluated the precision of the variometric and TPP approaches with various error correction schemes and duration time using numerous data sets and demonstrated that few centimetres accuracy of coseismic displacements is achievable even for 20 min interval. We applied these single-receiver approaches to process 1 Hz GPS data collected from the Tohoku-Oki earthquake (Mw 9.0, 2011 March 11) in Japan to capture coseismic displacement, and further, inverted the obtained displacement fields for fault slip distribution and moment magnitude. Comparisons of the results obtained using the refined variometric approach and TPP, as well as the converged PPP, displayed very good consistence both in coseismic displacements within few centimetres and in the slip distribution patterns and moment magnitudes.

[1] High-rate Global Navigation Satellite Systems (GNSS) has an increasing number of applications in geohazard monitoring. GNSS-derived displacements can provide important information for magnitude estimation and fault slip inversion, which is critical for seismic and tsunamigenic hazard mitigation. In this paper, we propose a new approach to quickly capture coseismic displacements with a single GNSS receiver in real time. The new approach can overcome the convergence problem of precise point positioning, and also avoids the integration process of the variometric approach. Using the results of the 2011 Tohoku-Oki earthquake, it is demonstrated that the proposed method can provide accurate displacement waveforms and permanent coseismic offsets at an accuracy of few centimeters, and can also reliably recover the moment magnitude and fault slip distribution.

[1] This paper describes an altimetric method based on data recorded during experimental zeppelin flights over Lake Constance. Interferometric observations for this method are obtained using a Master-Slave receiver configuration. These observations contain the relative phasing of direct and reflected signals and are used for altimetry. Separated antennas are attached to the receiver to record direct and reflected signals at slant elevation angles. Filtering is required to remove direct contributions in this slant geometry. Filtered observations are corrected using an altimetric model, and thus Doppler residuals are retrieved. This correction reduces the width of the spectral reflection peak from 3 mHz to less than 10 mHz. Doppler residuals are sensitive to surface height. Lake level is estimated inversely for the residuals at different trial heights. A case study of reflection events is presented. Lake level is estimated using data from antennas with right-handed and left-handed circular polarization. Reference level is determined from tide gauge data for stations around the lake. Mean deviation of estimates from reference level is 50 cm. Doppler shifts of different model corrections are compared. The altimetric correction is the most important, with mean Doppler shifts between 316 and 560 mHz. Mean Doppler shifts are much smaller for baseline correction (less than 0.2 mHz) and water-vapor correction (0.1–1.0 mHz). In addition, the geoid undulation effect (up to 25 cm amplitude) is predicted with mean Doppler shifts between 0.1 and 0.9 mHz. Precision of Doppler residuals (0.5–0.6 mHz) is insufficient to resolve the geoid undulation effect. The resolution from phase residuals is better. The effect of geoid undulation, however, is not dominant in phase residuals.

The frequency division multiple access adopted in present GLONASS introduces inter-frequency bias (IFB) at the receiver-end both in code and phase observables, which makes GLONASS ambiguity resolution rather difficult or even not available, especially for long baselines up to several thousand kilometers. This is one of the major reasons that GLONASS could hardly reach the orbit precision of GPS, both in terms of consistency among individual International GNSS Service (IGS) analysis centers and discontinuity at the overlapping day boundaries. Based on the fact that the GLONASS phase IFB is similar on L1 and L2 bands in unit of length and is a linear function of the frequency number, several approaches have been developed to estimate and calibrate the IFB for integer ambiguity resolution. However, they are only for short and medium baselines. In this study, a new ambiguity resolution approach is developed for GLONASS global networks. In the approach, the phase ambiguities in the ionosphere-free linear combination are directly transformed with a wavelength of about 5.3 cm, according to the special frequency relationship of GLONASS L1 and L2 signals. After such transformation, the phase IFB rate can be estimated and corrected precisely and then the corresponding double-differenced ambiguities can be directly fixed to integers even for baselines up to several thousand kilometers. To evaluate this approach, experimental validations using one-month data of a global network with 140 IGS stations was carried out for GLONASS precise orbit determination. The results show that the GLONASS double-difference ambiguity resolution for long baselines could be achieved with an average fixing-rate of 91.4 %. Applying the fixed ambiguities as constraints, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 37.2 % in ideal cases and with an averaged reduction of about 21.4 %, which is comparable with that by the GPS ambiguity resolution. The orbit improvement is also confirmed by the better agreement with the independent satellite laser ranging observations.

When formation flying spacecrafts are used as platform to gain earth oriented observation, precise baselines between these spacecrafts are always essential. Gravity recovery and climate experiment (GRACE) mission is aimed at mapping the global gravity field and its variation. Accurate baseline of GRACE satellites is necessary for the gravity field modeling. The determination of kinematic and reduced dynamic relative orbits of twin satellites has been studied in this paper, and an accuracy of 2 mm for dynamic relative orbits and 5 mm for kinematic ones can be obtained, whereby most of the double difference onboard GPS ambiguities are resolved.

The rapid development of the Chinese BeiDou Navigation Satellite System (BDS) brings a promising prospect for the real-time retrieval of zenith tropospheric delays (ZTD) and precipitable water vapor (PWV), which is of great benefit for supporting the time-critical meteorological applications such as nowcasting or severe weather event monitoring. In this study, we develop a real-time ZTD/PWV processing method based on Global Positioning System (GPS) and BDS observations. The performance of ZTD and PWV derived from BDS observations using real-time precise point positioning (PPP) technique is carefully investigated. The contribution of combining BDS and GPS for ZTD/PWV retrieving is evaluated as well. GPS and BDS observations of a half-year period for 40 globally distributed stations from the International GNSS Service Multi-GNSS Experiment and BeiDou Experiment Tracking Network are processed. The results show that the real-time BDS-only ZTD series agree well with the GPS-only ZTD series in general: the RMS values are about 11–16 mm (about 2–3 mm in PWV). Furthermore, the real-time ZTD derived from GPS-only, BDS-only, and GPS/BDS combined solutions are compared with those derived from the Very Long Baseline Interferometry. The comparisons show that the BDS can contribute to real-time meteorological applications, slightly less accurately than GPS. More accurate and reliable water vapor estimates, about 1.3–1.8 mm in PWV, can be obtained if the BDS observations are combined with the GPS observations in the real-time PPP data processing. The PWV comparisons with radiosondes further confirm the performance of BDS-derived real-time PWV and the benefit of adding BDS to standard GPS processing.

GLONASS could hardly reach the positioning performance of GPS, especially for fast and real-time precise positioning. One of the reasons is the phase inter-frequency bias (IFB) at the receiver end prevents its integer ambiguity resolution. A number of studies were carried out to achieve the integer ambiguity resolution for GLONASS. Based on some of the revealed IFB characteristics, for instance IFB is a linear function of the received carrier frequency and L1 and L2 have the same IFB in unit of length, most of recent methods recommend estimating the IFB rate together with ambiguities. However, since the two sets of parameters are highly correlated, as demonstrated in previous studies, observations over several hours up to 1 day are needed even with simultaneous GPS observations to obtain a reasonable solution. Obviously, these approaches cannot be applied for real-time positioning. Actually, it can be demonstrated that GLONASS ambiguity resolution should also be available even for a single epoch if the IFB rate is precisely known. In addition, the closer the IFB rate value is to its true value, the larger the fixing RATIO will be. Based on this fact, in this paper, a new approach is developed to estimate the IFB rate by means of particle filtering with the likelihood function derived from RATIO. This approach is evaluated with several sets of experimental data. For both static and kinematic cases, the results show that IFB rates could be estimated precisely just with GLONASS data of a few epochs depending on the baseline length. The time cost with a normal PC can be controlled around 1 s and can be further reduced. With the estimated IFB rate, integer ambiguity resolution is available immediately and as a consequence, the positioning accuracy is improved significantly to the level of GPS fixed solution. Thus the new approach enables real-time precise applications of GLONASS.

Precise knowledge and consistent modeling of the yaw-attitude of GNSS satellites are essential for high-precision data processing and applications. As the exact attitude control mechanism for the satellites of the BeiDou Satellite Navigation System (BDS) is not yet released, the reverse kinematic precise point positioning (PPP) method was applied in our study. However, we confirm that the recent precise orbit determination (POD) processing for GPS satellites could not provide suitable products for estimating BDS attitude using the reverse PPP because of the special attitude control switching between the nominal and the orbit-normal mode. In our study, we propose a modified processing schema for studying the attitude behavior of the BDS satellites. In this approach, the observations of the satellites during and after attitude switch are excluded in the POD processing, so that the estimates, which are needed in the reverse PPP, are not contaminated by the inaccurate initial attitude mode. The modified process is validated by experimental data sets and the attitude yaw-angles of the BDS IGSO and MEO satellites are estimated with an accuracy of better than $$9^{\circ }$$ . Furthermore, the results confirm that the switch is executed when the Sun elevation is about $$4^{\circ }$$ and the actual orientation is very close to its target one. Based on the estimated yaw-angles, a preliminary attitude switch model was established and reintroduced into the POD, yielding to a substantial improvement in the orbit overlap RMS.

In this contribution, we present a GPS+GLONASS+BeiDou+Galileo four-system model to fully exploit the observations of all these four navigation satellite systems for real-time precise orbit determination, clock estimation and positioning. A rigorous multi-GNSS analysis is performed to achieve the best possible consistency by processing the observations from different GNSS together in one common parameter estimation procedure. Meanwhile, an efficient multi-GNSS real-time precise positioning service system is designed and demonstrated by using the multi-GNSS Experiment, BeiDou Experimental Tracking Network, and International GNSS Service networks including stations all over the world. The statistical analysis of the 6-h predicted orbits show that the radial and cross root mean square (RMS) values are smaller than 10 cm for BeiDou and Galileo, and smaller than 5 cm for both GLONASS and GPS satellites, respectively. The RMS values of the clock differences between real-time and batch-processed solutions for GPS satellites are about 0.10 ns, while the RMS values for BeiDou, Galileo and GLONASS are 0.13, 0.13 and 0.14 ns, respectively. The addition of the BeiDou, Galileo and GLONASS systems to the standard GPS-only processing, reduces the convergence time almost by 70 %, while the positioning accuracy is improved by about 25 %. Some outliers in the GPS-only solutions vanish when multi-GNSS observations are processed simultaneous. The availability and reliability of GPS precise positioning decrease dramatically as the elevation cutoff increases. However, the accuracy of multi-GNSS precise point positioning (PPP) is hardly decreased and few centimeter are still achievable in the horizontal components even with 40 $$^{\circ }$$ elevation cutoff. At 30 $$^{\circ }$$ and 40 $$^{\circ }$$ elevation cutoffs, the availability rates of GPS-only solution drop significantly to only around 70 and 40 %, respectively. However, multi-GNSS PPP can provide precise position estimates continuously (availability rate is more than 99.5 %) even up to 40 $$^{\circ }$$ elevation cutoff (e.g., in urban canyons).

Integer carrier-phase ambiguity resolution is one of the critical issues for precise GPS applications in geodesy and geodynamics. To resolve as many integer ambiguities as possible, the ‘most-easy-to-fix’ double-difference ambiguities have to be defined. For this purpose, several strategies are implemented in existing GPS software packages, such as choosing the ambiguities according to the baseline length or the variances of the estimated real-valued ambiguities. Although their efficiencies are demonstrated in practice, it is proven in this paper that they do not reflect all effects of varying data quality, because they are based on theoretical considerations of GPS data processing. Therefore, a new approach is presented, which selects the double-difference ambiguities according to their probability of being fixed to the nearest integer. The probability is computed from estimates and variances of wide-lane and narrow-lane ambiguities. Together with an optimized ambiguity fixing procedure, the new approach is implemented in the routine data processing for the International GPS Service (IGS) at GeoForschungsZentrum (GFZ) Potsdam. Within a sub-network of about 90 IGS stations, it is demonstrated that more than 97% of the independent ambiguities are fixed correctly compared to 75% by a commonly used method, and that the additionally fixed ambiguities improve the repeatability of the station coordinates by 10–26% in regions with sparse site distribution.

GNSS reflectometry (GNSS-R) measurements were conducted in Sep 2012 over Lake Constance between Austria, Germany and Switzerland. A Zeppelin NT (New Technology) type airship equipped with a GORS (GNSS Occultation Reflectometry Scatterometry) receiver setup conducted flight transects (up to 64 km long) at about 500 m altitude above the lake surface. The setup uses two downwards tilted antennas with right-handed and left-handed circular polarisation (RHCP and LHCP) to acquire the reflected signal. An up-looking RHCP antenna acquires the signal on the direct link. The GORS receiver uses a Master-Slave sampling to process direct and reflected signals. An additional geodetic GNSS receiver provides direct link observations to calculate an airship trajectory with centimeter precision. A phase altimetric method is applied to the GORS samples in postprocessing. The height retrieval is initialised with an apriori height of the lake surface. Ancillary water gauge data provides reference at crossover points to adapt the apriori height. This height referencing allows to mitigate the phase-ambiguity induced bias. In this demonstration study interpolated water gauge data serve as reference. Height retrievals of an example event agree with lake surface undulations predicted by the GCG-05 (German Combined QuasiGeoid 2005) model. For RHCP (LHCP) observations a mean difference of 7 cm (5 cm) and a corresponding standard deviation of 3 cm (4 cm) is reported that confirm the phase altimetric performance.

With the availability of real-time high-rate GPS observations and precise satellite orbit and clock products, the interest in the real-time precise point positioning (PPP) technique has greatly increased to construct displacement waveforms and to invert for source parameters of earthquakes in real time. Furthermore, PPP ambiguity resolution approaches, developed in the recent years, overcome the accuracy limitation of the standard PPP float solution and achieve comparable accuracy with relative positioning. In this paper, we introduce the real-time PPP service system and the key techniques for real-time PPP ambiguity resolution. We assess the performance of the ambiguity-fixed PPP in real-time scenarios and confirm that positioning accuracy in terms of root mean square of 1.0–1.5 cm can be achieved in horizontal components. For the 2011 Tohoku-Oki (Japan) and the 2010 El Mayor–Cucapah (Mexico) earthquakes, the displacement waveforms estimated from ambiguity-fixed PPP and those provided by the accelerometer instrumentation are consistent in the dynamic component within few centimeters. The PPP fixed solution not only can improve the accuracy of coseismic displacements but also provides a reliable recovery of earthquake magnitude and of the fault slip distribution in real time.

The recent development of the International Global Navigation Satellite Systems Service Real-Time Pilot Project and the enormous progress in precise point positioning (PPP) techniques provide a promising opportunity for real-time determination of Integrated Water Vapor (IWV) using GPS ground networks for various geodetic and meteorological applications. In this study, we develop a new real-time GPS water vapor processing system based on the PPP ambiguity fixing technique with real-time satellite orbit, clock, and phase delay corrections. We demonstrate the performance of the new real-time water vapor estimates using the currently operationally used near-real-time GPS atmospheric data and collocated microwave radiometer measurements as an independent reference. The results show that an accuracy of 1.0 ~ 2.0 mm is achievable for the new real-time GPS based IWV value. Data of such accuracy might be highly valuable for time-critical geodetic (positioning) and meteorological applications.

The complementary advantages of GPS and seismic measurements are well recognized in seismotectonic monitoring studies. Therefore, integrated processing of the two data streams has been proposed recently in an attempt to obtain accurate and reliable information of surface displacements associated with earthquakes. A hitherto still critical issue in the integrated processing is real-time detection and precise estimation of the transient baseline error in the seismic records. Here, we report on a new approach by introducing the seismic acceleration corrected by baseline errors into the state equation system. The correction is performed and regularly updated in short epochs (with increments which may be as short as seconds), so that station position, velocity, and acceleration can be constrained very tightly and baseline error can be estimated as a random-walk process. With the adapted state equation system, our study highlights the use of a new approach developed for integrated processing of GPS and seismic data by means of sequential least-squares adjustment. The efficiency of our approach is demonstrated and validated using simulated, experimental, and real datasets. The latter were collected at collocated GPS and seismic stations around the 4 April 2010, E1 Mayor-Cucapah earthquake (Mw, 7.2). The results have shown that baseline errors of the strong-motion sensors are corrected precisely and high-precision seismic displacements are real-timely obtained by the new approach.

Although the computational burden of global navigation satellite systems (GNSS) data processing is nowadays already a big challenge, especially for huge networks, integrated processing of denser networks with data of multi-GNSS and multi-frequency is desired in the expectation of more accurate and reliable products. Based on the concept of carrier range, in this study, the precise point positioning with integer ambiguity resolution is engaged to obtain the integer ambiguities for converting carrier phases to carrier ranges. With such carrier ranges and pseudo-ranges, rigorous integrated processing is realized computational efficiently for the orbit and clock estimation using massive networks. The strategy is validated in terms of computational efficiency and product quality using data of the IGS network with about 460 stations. The experimental validation shows that the computation time of the new strategy increases gradually with the number of stations. It takes about 14 min for precise orbit and clock determination with 460 stations, while the current strategy needs about 82 min. The overlapping orbit RMS is reduced from 27.6 mm with 100 stations to 24.8 mm using the proposed strategy, and the RMS could be further reduced to 23.2 mm by including all 460 stations. Therefore, the new strategy could be applied to massive networks of multi-GNSS and multi-frequency receivers and possibly to achieve GNSS data products of higher quality.

We implement an automatic orbit quality control procedure in order to reduce the effect of satellite orbit error for near real-time estimating of zenith total delay (ZTD). We estimate the three Keplerian parameters of the GPS orbits that represent the main error sources (semi-major axis, inclination, and argument of perigee). We start with an a priori constraint corresponding to the typical orbit accuracy for each parameter and adjust it iteratively according to its estimated value and variance. This data analysis procedure shows an improvement of 20% in ZTD rms compared to a strategy based only on the quality index provided with the IGS predicted orbits. A real-time test with IGS ultra-rapid orbits also shows significant improvement compared to fixing IGS ultra-rapid orbits. This strategy allows for a totally automated estimation of orbital parameters directly from the real-time GPS data, without altering the accuracy of the ZTD estimates.

High-rate GPS and seismic sensors are mutually contributing to seismological applications for capturing earthquake-induced coseismic displacements. In this study, we propose an approach for tightly integrating GPS and strong motion data on raw observation level to increase the quality of the derived displacements. The performance of the proposed approach is demonstrated using 5 Hz high-rate GPS and 200 Hz strong motion data collected during the El Mayor–Cucapah earthquake (M w 7.2, 2010 April 4) in Baja California, Mexico. The new approach not only takes advantages of both GPS and strong motion sensors, but also improves the reliability of the displacement by enhancing GPS integer-cycle phase ambiguity resolution, which is very critical for deriving displacements with highest quality.

Currently, ground-based Global Navigation Satellite System (GNSS) stations of the International GNSS Service (IGS) are distributed unevenly around the world. Most of them are located on the mainland, while only a small part of them are scattered on some islands in the oceans. As a consequence, many unreasonable zero values (in fact negative values) appear in Vertical Total Electron Content (VTEC) of European Space Agency (ESA) and Center for Orbit Determination in Europe (CODE) IONEX products, especially in 2008 and 2009 when the solar activities were rather quiet. To improve this situation, we directly implement non-negative physical constraints of ionosphere for global ionosphere maps (GIM) with spherical harmonic functions. Mathematically, we propose an inequality-constrained least squares method by imposing non-negative inequality constraints in the areas where negative VTEC values may occur to reconstruct GIM models. We then apply the new method to process the IGS data in 2008. The results have shown that the new algorithm efficiently eliminates the unwanted behavior of negative VTEC values, which could otherwise often be seen in the current CODE and ESA GIM products in both middle and high latitude areas of the Southern Hemisphere (45°S∼90°S) and the Northern Hemisphere (50°N∼90°N). About 64% of GPS receivers’ DCBs have been significantly improved. Finally, we compare the GIM results between with and without the inequality constraints, which has clearly shown that the GIM result with inequality constraints is significantly better than that without the inequality constraints. The inequality-constrained GIM result is also highly consistent with the final IGS products in terms of root mean squared (RMS) and mean VTEC.

[1] Nowadays more and more high-rate real-time GPS data become available that provide a great opportunity to contribute to earthquake early warning (EEW) system in terms of capturing regional surface displacements, as an independent information source, useful for promptly estimating the magnitude of large destructive earthquake. In our study, we demonstrate the performance of the real-time ambiguity-fixed precise point positioning (PPP) approach using 5 Hz GPS data collected during El Mayor-Cucapah earthquake (Mw 7.2, 4 April 2010). The PPP-based displacements show to agree with accelerometer-based displacement at centimeter level. The key for successfully obtaining high precision displacements is the efficient ambiguity resolution. PPP with ambiguity fixing can result in correct permanent co-seismic offsets and correct recovery of moment magnitude and fault slip inversion at levels comparable to post-processing.

High-rate GNSS is commonly used in seismology, as the impacts of orbit error, clock error, atmosphere error and multipath effect, the coseismic velocity and displacement which are estimated by the broadcast ephemeris usually exists drifts, and serious distort by the pollution of high-rate noise. This paper proposes a new method with the low pass filter and linear correction are used to de-trending low frequency drifts and de-noising high frequency noise by S transform, then the coseismic velocity and displacement are real-time recovered. The validations show that, the recovered velocity is very consistent with the waveforms recorded by strong-motion, the precision of coseismic displacement is better than 2 and 5 cm in horizontal and vertical respectively, the inversion results which gained by real time recovered displacements is closed to the post processed results.

Ambiguity resolution dedicated to a single global positioning system (GPS) station can improve the accuracy of precise point positioning. In this process, the estimation accuracy of the narrow-lane fractional-cycle biases (FCBs), which destroy the integer nature of undifferenced ambiguities, is crucial to the ambiguity-fixed positioning accuracy. In this study, we hence propose the improved narrow-lane FCBs derived from an ambiguity-fixed GPS network solution, rather than the original (i.e. previously proposed) FCBs derived from an ambiguity-float network solution. The improved FCBs outperform the original FCBs by ensuring that the resulting ambiguity-fixed daily positions coincide in nature with the state-of-the-art positions generated by the International GNSS Service (IGS). To verify this improvement, 1 year of GPS measurements from about 350 globally distributed stations were processed. We find that the original FCBs differ more from the improved FCBs when fewer stations are involved in the FCB estimation, especially when the number of stations is less than 20. Moreover, when comparing the ambiguity-fixed daily positions with the IGS weekly positions for 248 stations through a Helmert transformation, for the East component, we find that on 359 days of the year the daily RMS of the transformed residuals based on the improved FCBs is smaller by up to 0.8 mm than those based on the original FCBs, and the mean RMS over the year falls evidently from 2.6 to 2.2 mm. Meanwhile, when using the improved rather than the original FCBs, the RMS of the transformed residuals for the East component of 239 stations (i.e. 96.4% of all 248 stations) is clearly reduced by up to 1.6 mm, especially for stations located within a sparse GPS network. Therefore, we suggest that narrow-lane FCBs should be determined with ambiguity-fixed, rather than ambiguity-float, GPS network solutions.

Integer ambiguity resolution at a single receiver can be achieved if the fractional-cycle biases are separated from the ambiguity estimates in precise point positioning (PPP). Despite the improved positioning accuracy by such integer resolution, the convergence to an ambiguity-fixed solution normally requires a few tens of minutes. Even worse, these convergences can repeatedly occur on the occasion of loss of tracking locks for many satellites if an open sky-view is not constantly available, consequently totally destroying the practicability of real-time PPP. In this study, in case of such re-convergences, we develop a method in which ionospheric delays are precisely predicted to significantly accelerate the integer ambiguity resolution. The effectiveness of this method consists in two aspects: first, wide-lane ambiguities can be rapidly resolved using the ionosphere-corrected wide-lane measurements, instead of the noisy Melbourne–Wubbena combination measurements; second, narrow-lane ambiguity resolution can be accelerated under the tight constraints derived from the ionosphere-corrected unambiguous wide-lane measurements. In the test at 90 static stations suffering from simulated total loss of tracking locks, 93.3 and 95.0% of re-convergences to wide-lane and narrow-lane ambiguity resolutions can be achieved within five epochs of 1-Hz measurements, respectively, even though the time latency for the predicted ionospheric delays is up to 180 s. In the test at a mobile van moving in a GPS-adverse environment where satellite number significantly decreases and cycle slips frequently occur, only when the predicted ionospheric delays are applied can the rate of ambiguity-fixed epochs be dramatically improved from 7.7 to 93.6% of all epochs. Therefore, this method can potentially relieve the unrealistic requirement of a continuous open sky-view by most PPP applications and improve the practicability of real-time PPP.

At present, usually only the ground stations are used for the precise orbit determination (POD) of GPS satellites. The precise orbits of Low Earth Orbiters (LEO) are determined with GPS orbits and clocks fixed. The integrated adjustment of LEO and GPS for POD that is first reported in (Zhu et al., 2004),which means the orbits of GPS satellites and LEOs are determined simultaneously, is introduced here. At first, the contribution of LEOs to GPS POD is illuminated. On the one hand, the data from 43, 32 and 21 ground stations besides three LEOs are used. In the case of 21 ground stations plus three LEOs, about 5.0 cmaccuracy from IGS final orbit can be achieved with only one day’s data. On the other hand, the data from one, two and three LEOs besides 43 stations are employed. It is shown that the improvement can reach 31% when only one LEO is added to 43 ground stations. These achievements are mainly attributed to the strengthened geometry afterLEOsare included. Then, the improvement of LEO orbits in the integrated adjustment is presented. When 43 ground stations are used, the improvement can get to 17% and 32% without accelerometer data for CHAMPand GRACE, respectively. So it is demonstrated that the LEO orbit accuracy is improved simultaneously with the GPS orbits in the integrated adjustment.

Precise Point Positioning (PPP) has been demonstrated to be a powerful tool in geodetic and geodynamic applications. Although its accuracy is almost comparable with network solutions, the east component of the PPP results is still to be improved by integer ambiguity fixing, which is, up to now, prevented by the presence of the uncalibrated phase delays (UPD) originating in the receivers and satellites. In this paper, it is shown that UPDs are rather stable in time and space, and can be estimated with high accuracy and reliability through a statistical analysis of the ambiguities estimated from a reference network. An approach is implemented to estimate the fractional parts of the single-difference (SD) UPDs between satellites in wide- and narrow-lane from a global reference network. By applying the obtained SD-UPDs as corrections to the SD-ambiguities at a single station, the corrected SD-ambiguities have a naturally integer feature and can therefore be fixed to integer values as usually done for the double-difference ones in the network mode. With data collected at 450 stations of the International GNSS Service (IGS) through days 106 to 119 in 2006, the efficiency of the presented ambiguity-fixing strategy is validated using IGS Final products. On average, more than 80% of the independent ambiguities could be fixed reliably, which leads to an improvement of about 27% in the repeatability and 30% in the agreement with the IGS weekly solutions for the east component of station coordinates, compared with the real-valued solutions.