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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.

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.

In multi-GNSS integration, fixing inter-system double-difference ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first; then, the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterward, a two-dimensional particle filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown. The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity-fixed solutions having positioning errors larger than 3 cm. However, when our approach is adopted, the number of integer ambiguity parameters increases to five. The integer ambiguity fixing rate increases to 99.7% with 100% of ambiguity-fixed solutions having positioning errors smaller than 3 cm.

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.

Real-time satellite orbit and clock product is a key prerequisite for real-time precise positioning service based on precise point positioning (PPP). With the rapid development of the multiple global navigation satellite systems (Multi-GNSS), about 120 satellites will be processed for Multi-GNSS real-time clock estimation. Unfortunately, the computation is very time-consuming, especially for quality control since problematic observations are inevitable. Taking advantage of computer technology, sequential least square adjustment with an adapted online quality control procedure is developed to rapidly estimate Multi-GNSS real-time clocks, although various filtering estimators are commonly used now. A globally distributed network including 70 stations tracking mostly satellites of GPS, GLONASS, BDS, and Galileo is employed for experimental validation. The results show that the computation time per epoch is less than 3 s in average and can meet the 5 s update rate of the IGS real-time clock product. Compared to the GeoForschungsZentrum MGEX (GBM) final clock product, the averaged STD values of the estimated clocks of the four GNSS systems are 0.089 ns and 0.153 ns, respectively, for the clock solutions with and without the online quality control, which also confirms the importance of the quality control procedure. The Multi-GNSS kinematic PPP experiment using the estimated clocks with quality control shows that the positioning RMS is about 4 cm and generally 2 cm in vertical and horizontal components, respectively, and the corresponding convergence time is about 15 min.

Accuracy of dynamic precise point positioning (PPP) degrades significantly under users’ challenging environments because of the limited or unavailable GPS observations. To overcome such weakness, a tight-integration system of micro-electromechanical systems (MEMS) inertial measurement unit (IMU), odometer, and GPS ionospheric delay constrained PPP is investigated to provide users positions and attitudes with higher accuracy, reliability, and continuity under the weak GPS observability environments. In this approach, the data from different sensors are integrated in two joint extend Kalman filters (EKF). One is for PPP/INS tight-integration and the other one is for odometer aiding the solutions from INS or PPP/INS tight-integration modes. Here, the advantages of slow time-varying ionospheric delay, high-accuracy in short time of inertial navigation system (INS), and hardly-disturbed odometer are utilized effectively to enhance PPP solutions. The corresponding mathematical models are provided and are evaluated by a set of one-hour real land-borne test data collected from a MEMS IMU, an odometer, and a dual-frequency GPS receiver in suburbs of Wuhan city, China, and also a set of simulated weak satellites availability data which is to imitate the GPS availability under unban canyons. Results indicate that the fusion system can improve navigation accuracy of GPS or GPS/INS significantly. That are, more than fifty percentages position enhancements in north-east-down components, and about forty percentages attitude enhancements in roll-pitch-yaw direction under the weak GPS availability.

Currently, with the rapid development of multi-constellation Global Navigation Satellite Systems (GNSS), the real-time positioning and navigation are undergoing dramatic changes with potential for a better performance. To provide more precise and reliable ultra-rapid orbits is critical for multi-GNSS real-time positioning, especially for the three merging constellations Beidou, Galileo and QZSS which are still under construction. In this contribution, we present a five-system precise orbit determination (POD) strategy to fully exploit the GPS $$+$$ GLONASS $$+$$ BDS $$+$$ Galileo $$+$$ QZSS observations from CDDIS $$+$$ IGN $$+$$ BKG archives for the realization of hourly five-constellation ultra-rapid orbit update. After adopting the optimized 2-day POD solution (updated every hour), the predicted orbit accuracy can be obviously improved for all the five satellite systems in comparison to the conventional 1-day POD solution (updated every 3 h). The orbit accuracy for the BDS IGSO satellites can be improved by about 80, 45 and 50% in the radial, cross and along directions, respectively, while the corresponding accuracy improvement for the BDS MEO satellites reaches about 50, 20 and 50% in the three directions, respectively. Furthermore, the multi-GNSS real-time precise point positioning (PPP) ambiguity resolution has been performed by using the improved precise satellite orbits. Numerous results indicate that combined GPS $$+$$ BDS $$+$$ GLONASS $$+$$ Galileo (GCRE) kinematic PPP ambiguity resolution (AR) solutions can achieve the shortest time to first fix (TTFF) and highest positioning accuracy in all coordinate components. With the addition of the BDS, GLONASS and Galileo observations to the GPS-only processing, the GCRE PPP AR solution achieves the shortest average TTFF of 11 min with $$7{^{\circ }}$$ cutoff elevation, while the TTFF of GPS-only, GR, GE and GC PPP AR solution is 28, 15, 20 and 17 min, respectively. As the cutoff elevation increases, the reliability and accuracy of GPS-only PPP AR solutions decrease dramatically, but there is no evident decrease for the accuracy of GCRE fixed solutions which can still achieve an accuracy of a few centimeters in the east and north components.

Global navigation satellite systems (GNSS) are acting as an indispensable tool for geodetic research and global monitoring of the Earth, and they have been rapidly developed over the past few years with abundant GNSS networks, modern constellations, and significant improvement in mathematic models of data processing. However, due to the increasing number of satellites and stations, the computational efficiency becomes a key issue and it could hamper the further development of GNSS applications. In this contribution, this problem is overcome from the aspects of both dense linear algebra algorithms and GNSS processing strategy. First, in order to fully explore the power of modern microprocessors, the square root information filter solution based on the blocked QR factorization employing as many matrix–matrix operations as possible is introduced. In addition, the algorithm complexity of GNSS data processing is further decreased by centralizing the carrier-phase observations and ambiguity parameters, as well as performing the real-time ambiguity resolution and elimination. Based on the QR factorization of the simulated matrix, we can conclude that compared to unblocked QR factorization, the blocked QR factorization can greatly improve processing efficiency with a magnitude of nearly two orders on a personal computer with four 3.30 GHz cores. Then, with 82 globally distributed stations, the processing efficiency is further validated in multi-GNSS (GPS/BDS/Galileo) satellite clock estimation. The results suggest that it will take about 31.38 s per epoch for the unblocked method. While, without any loss of accuracy, it only takes 0.50 and 0.31 s for our new algorithm per epoch for float and fixed clock solutions, respectively.

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.

Global navigation satellite system (GNSS) precise point positioning (PPP) requires continuous carrier-phase observations to achieve a solution of high precision. Precisely correcting cycle slips caused by signal interruptions is crucial for recovering the data continuity. Most of the existing approaches usually employ only data of one epoch after the interruption for real-time cycle slip processing. In this study, we propose to introduce and estimate cycle slip parameters together with standard PPP parameters, such as position, ionospheric delay, and ambiguities in the case that possible cycle slips are detected, using a Kalman-filter-based procedure with the undifferenced and uncombined PPP model. The integer search strategy is used to fix cycle slips. To reduce the probability of wrong integer fixing, a strict integer validation threshold is suggested. As a result, it is not easy to fix all cycle slips with only one epoch of data. Our approach can be easily extended to use multi-epoch observations to enhance the cycle slip estimation. Once the cycle slips are correctly determined, continuous PPP can be achieved instantaneously. This new approach is tested and validated with three groups of experiments using GPS and GLONASS stations operated by the International GNSS Service from DOY 1–10, 2017, and a real vehicle kinematic data. Numerous experimental results showed that the proposed method can correctly fix the cycle slips for more than 99.5% of epochs suffering from re-convergence. On average, this method takes observation information from about 1.5–2.5 epochs to fix cycle slips and realize rapid re-convergence. Consequently, positioning performance is significantly improved.

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.

During the past years, real-time precise point positioning has been proven to be an efficient tool in the applications of navigation, precise orbit determination of LEO as well as earthquake and tsunami early warning, etc. One of the most crucial issues of these applications is the high-precision real-time GNSS satellite clock. Though the performance and character of the GNSS onboard atomic frequency standard have been widely studied, the white noise model is still the most popular hypothesis that employed in the real-time GNSS satellite clock estimation. However, concerning the real-time applications, significant data discontinuity may arise either due to the fact that only regional stations involved, or the failure in the stations, satellites and network connections. These data discontinuity would result in an arbitrary clock jump between adjacent arcs when the clock offsets are modeled as white noise. In addition, it is also expected that the detection and identification of outliers would be benefited from the constrains of the satellite oscillator noise model. Thus in this contribution, based on the statistic analysis of almost 2-year multi-GNSS precise clock products, we developed the oscillator noise model for the satellites of GPS, GLONASS, BDS and Galileo according to the oscillator type as well as the block type. Then, the efficiency of this oscillator noise model in multi-GNSS satellite clock estimation is demonstrated with 2-months data for both regional and global networks in simultaneous real-time mode. For the regional network, the results suggest that compared with the traditional solution based on white noise model, the improvement is 44.4 and 12.1% on average for STD and RMS, respectively, and the improvement is mainly attributed to the efficiency of the oscillator noise model during the convergence period and the gross error resistance. Concerning the global experiment, since the stations guarantee the continuous tracking of the satellites with redundant observable, the improvement is not as evident as that of regional experiment for GPS, GLONASS and BDS. The STD of Galileo clock improves from 0.28 to 0.19 ns due to that, the satellites E14 and E18 still suffer significant data discontinuity during our experimental period.

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.

Global Navigation Satellite System (GNSS) has been widely used in many geosciences areas with its Positioning, Navigation and Timing (PNT) service. However, GNSS still has its own bottleneck, such as the long initialization period of Precise Point Positioning (PPP) without dense reference network. Recently, the concept of PNTRC (Positioning, Navigation, Timing, Remote sensing and Communication) has been put forward, where Low Earth Orbit (LEO) satellite constellations are recruited to fulfill diverse missions. In navigation aspect, a number of selected LEO satellites can be equipped with a transmitter to transmit similar navigation signals to ground users, so that they can serve as GNSS satellites but with much faster geometric change to enhance GNSS capability, which is named as LEO constellation enhanced GNSS (LeGNSS). As a result, the initialization time of PPP is expected to be shortened to the level of a few minutes or even seconds depending on the number of the LEO satellites involved. In this article, we simulate all the relevant data from June 8th to 14th, 2014 and investigate the feasibility of LeGNSS with the concentration on the key issues in the whole data processing for providing real-time PPP service based on a system configuration with fourteen satellites of BeiDou Navigation Satellite System (BDS), twenty-four satellites of the Global Positioning System (GPS), and sixty-six satellites of the Iridium satellite constellations. At the server-end, Precise Orbit Determination (POD) and Precise Clock Estimation (PCE) with various operational modes are investigated using simulated observations. It is found out that GNSS POD with partial LEO satellites is the most practical mode of LeGNSS operation. At the user-end, the Geometry Dilution Of Precision (GDOP) and Signal-In-Space Ranging Error (SISRE) are calculated and assessed for different positioning schemes in order to demonstrate the performance of LeGNSS. Centimeter level SISRE can be achieved for LeGNSS.

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.

Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities.

To upgrade the positioning accuracy, re-initialization speed, and attitude determination performance of precise point positioning (PPP) in dynamic applications, we proposed a multi-sensor fusion system consisting of four global navigation satellite systems (GNSSs), namely GPS, BDS, Galileo, and GLONASS, several low-cost inertial sensors, and an odometer. The study shows that the performance of PPP in terms of continuity, reliability, stability, and re-initialization speed improves by such a multi-sensor fusion system. This manifests itself in a significantly increased accuracy. For position solutions, compared to un-aided PPP solutions, the improvements achieved using low-cost inertial navigation system (INS) are about 36.4, 38.7, and 31.3% in the north, east, and vertical components, respectively, and the improvement using odometer are about 1.58, 0.35, and 4.32% relative to the INS-aided PPP solutions. Moreover, using the odometer can provide more than 2.1, 1.4, and 50.6% attitude improvements for roll, pitch, and heading angles compared to the attitude solutions obtained from the INS-aided PPP system. Under GNSS outage conditions, the mean position improvements using the odometer are about 2.3, 1.8, and 8.7%, with maximum increases of 74.6, 74.7, and 28.3%, and the average attitude improvements are about 4.7, 5.4, and 3.3%, with maximum increases of 36.4, 31.7, and 28.9%, respectively. This means that the odometer can enhance the performance of PPP and PPP/INS integration in challenging dynamic conditions.

Precise track irregularity measuring is a pivotal technique to protect dynamic safety for railway transportation applications, especially those on high-speed railways. Current methods, such as the total station-based automatic inspection systems, commonly have a high cost and are inefficient. To reduce the costs and improve the measuring efficiency, a multi-sensors fusion system consisting of multi-constellation global navigation satellite systems (GNSS)-based precise point positioning, inertial navigation system, odometer, and track gauge is proposed and is further enhanced by using the Rauch–Tung–Striebel smoother. By using this system, one not only obtains high measuring accuracy, but also obtains increased efficiency of track irregularity measuring tens of times than achieved by conventional methods. After the principle investigations, a set of high-speed railway track measuring data containing quad-GNSS (GPS, BDS, GLONASS, and Galileo) observations, laser inertial measurement unit data, odometer measurements, and track gauge data are processed and analyzed to evaluate the capability of the proposed system. The results illustrate that the proposed system, which provided approximately 0.25, 0.59, 0.65, and 0.48 mm measuring accuracy in the super elevation, horizontal, vertical, and gauge components, respectively, can be used for high-accuracy track irregularity measuring.

Lots of ambiguities in un-differenced (UD) model lead to lower calculation efficiency, which isn’t appropriate for the high-frequency real-time GNSS clock estimation, like 1 Hz. Mixed differenced model fusing UD pseudo-range and epoch-differenced (ED) phase observations has been introduced into real-time clock estimation. In this contribution, we extend the mixed differenced model for realizing multi-GNSS real-time clock high-frequency updating and a rigorous comparison and analysis on same conditions are performed to achieve the best real-time clock estimation performance taking the efficiency, accuracy, consistency and reliability into consideration. Based on the multi-GNSS real-time data streams provided by multi-GNSS Experiment (MGEX) and Wuhan University, GPS + BeiDou + Galileo global real-time augmentation positioning prototype system is designed and constructed, including real-time precise orbit determination, real-time precise clock estimation, real-time Precise Point Positioning (RT-PPP) and real-time Standard Point Positioning (RT-SPP). The statistical analysis of the 6 h-predicted real-time orbits shows that the root mean square (RMS) in radial direction is about 1–5 cm for GPS, Beidou MEO and Galileo satellites and about 10 cm for Beidou GEO and IGSO satellites. Using the mixed differenced estimation model, the prototype system can realize high-efficient real-time satellite absolute clock estimation with no constant clock-bias and can be used for high-frequency augmentation message updating (such as 1 Hz). The real-time augmentation message signal-in-space ranging error (SISRE), a comprehensive accuracy of orbit and clock and effecting the users’ actual positioning performance, is introduced to evaluate and analyze the performance of GPS + BeiDou + Galileo global real-time augmentation positioning system. The statistical analysis of real-time augmentation message SISRE is about 4–7 cm for GPS, whlile 10 cm for Beidou IGSO/MEO, Galileo and about 30 cm for BeiDou GEO satellites. The real-time positioning results prove that the GPS + BeiDou + Galileo RT-PPP comparing to GPS-only can effectively accelerate convergence time by about 60%, improve the positioning accuracy by about 30% and obtain averaged RMS 4 cm in horizontal and 6 cm in vertical; additionally RT-SPP accuracy in the prototype system can realize positioning accuracy with about averaged RMS 1 m in horizontal and 1.5–2 m in vertical, which are improved by 60% and 70% to SPP based on broadcast ephemeris, respectively.

The main objective of this research was to examine the feasibility of Multi-GNSS precise point positioning (PPP) in precision agriculture (PA) through a series of experiments with different working modes (i.e. stationary and moving) under different observation conditions (e.g. open sky, with buildings or with canopy). For the stationary test carried out in open space in the UK, the positioning accuracy achieved was 13.9 mm in one dimension by a PPP approach, and the repeatability of positioning results was improved from 19.0 to 6.0 mm by using Multi-GNSS with respect to GPS only. For the moving test carried out in similar location in the UK, almost the same performance was achieved by GPS-only and by Multi-GNSS PPP. However, for a moving experiment carried out in China with obstruction conditions, Multi-GNSS improved the accuracy of baseline length from 126.0 to 35.0 mm and the repeatability from 110.0 mm to 49.0 mm, The results suggested that the addition of the BeiDou, Galileo and GLONASS systems to the standard GPS-only processing improved the positioning repeatability, while a positioning accuracy was achieved at about 20 mm level in the horizontal direction with an improvement against the GPS-only PPP results. In space-constrained and harsh environments (e.g. farms surrounded with dense trees), the availability and reliability of precise positioning decreased dramatically for the GPS-only PPP results, but limited impacts were observed for Multi-GNSS PPP. In addition, compared to real time kinematic (RTK) GNSS, which is currently most commonly used for high precision PA applications, similar accuracy has been achieved by PPP. In contrast to RTK GNSS, PPP can provide high accuracy positioning with higher flexibility and potentially lower capital and running costs. Hence, PPP might be a great opportunity for agriculture to meet the high accuracy requirements of PA in the near future.

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 multiconstellation Global Navigation Satellite Systems (GNSS) (e.g., GPS, GLObal NAvigation Satellite System (GLONASS), Galileo, and BeiDou) offers great opportunities for real-time retrieval of atmospheric parameters for supporting numerical weather prediction nowcasting or severe weather event monitoring. In this study, the observations from different GNSS are combined to retrieve atmospheric parameters based on the real-time precise point positioning technique. The atmospheric parameters, retrieved from multi-GNSS observations of a 180 day period from about 100 globally distributed stations, including zenith total delay, integrated water vapor, horizontal gradient, and slant total delay (STD), are analyzed and evaluated. The water vapor radiometer data and a numerical weather model, the operational analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF), are used to independently validate the performance of individual GNSS and also demonstrate the benefits of multiconstellation GNSS for real-time atmospheric monitoring. Our results show that the GLONASS and BeiDou have the potential capability for real-time atmospheric parameter retrieval for time-critical meteorological applications as GPS does, and the combination of multi-GNSS observations can improve the performance of a single-system solution in meteorological applications with higher accuracy and robustness. The multi-GNSS processing greatly increases the number of STDs. The mean and standard deviation of STDs between each GNSS and ECMWF exhibit a good stability as function of the elevation angle, the azimuth angle, and time, in general. An obvious latitude dependence is confirmed by a map of station specific mean and standard deviations. Such real-time atmospheric products, provided by multi-GNSS processing with higher accuracy, stronger reliability, and better distribution, might be highly valuable for atmospheric sounding systems, especially for nowcasting of extreme weather.

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.

Precise point positioning (PPP) using the Global Positioning System (GPS) is widely recognized as an efficient approach for providing precise positioning services. However, its accuracy and reliability could be significantly degraded by unexpected observation discontinuities and unfavorable tracking geometry which are unavoidable, especially in severe environments such as city canyons. Therefore, in the last decades inertial navigation system (INS) has been integrated to overcome such drawbacks. Recently, multi-Global Navigation Satellite Systems (GNSS) were applied to enhance the PPP performance by appropriate usage of the increased number of satellites. We present a new approach to tightly integrate the multi-GNSS PPP and INS together in the observation level. The inter-system bias and inter-frequency bias of multi-GNSS and the hardware errors of INS sensors are estimated to improve the position accuracy and to shorten the convergence time of PPP. In order to demonstrate the impact of multi-GNSS observations and INS data on the derived position, velocity, attitude, and the convergence time of PPP, the new approach is validated through an experimental test with a set of land vehicle data. The results show that the position accuracy can be improved by multi-GNSS and INS significantly, but very little improvement in velocity and attitude is achieved. The position root-mean-square improves from 23.3, 19.8, and 14.9 cm of the GPS PPP/INS tightly coupled integration (TCI) solution to 7.9, 3.3, and 5.1 cm of multi-GNSS PPP/INS TCI in north, east, and up components, respectively. Furthermore, GNSS outages are simulated and their effect on the performance of multi-GNSS PPP/INS TCI is investigated to demonstrate the contribution of the multi-GNSS PPP/INS TCI during GNSS outages. In addition, the convergence test also shows that both multi-GNSS and INS can improve the PPP convergence performance noticeably.

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.

The unexpected observing environments in dynamic applications may lead to partial and/or complete satellite signal outages frequently, which can definitely impact on the positioning performance of the Precise Point Positioning (PPP) in terms of decreasing available satellite numbers, breaking the continuity of observations, and degrading PPP’s positioning accuracy. Generally, both the Inertial Navigation System (INS) and the multi-constellation Global Navigation Satellite System (GNSS) can be used to enhance the performance of PPP. This paper introduces the mathematical models of the multi-GNSS PPP/INS Tightly Coupled Integration (TCI), and investigates its performance from several aspects. Specifically, it covers (1) the use of the BDS/GPS PPP, PPP/INS, and their combination; (2) three positioning modes including PPP, PPP/INS TCI, and PPP/INS Loosely Coupled Integration (LCI); (3) the use of four various INS systems named navigation grade, tactical grade, auto grade, and Micro-Electro-Mechanical-Sensors (MEMS) one; (4) three PPP observation scenarios including PPP available, partially available, and fully outage. According to the statistics results, (1) the positioning performance of the PPP/INS (either TCI or LCI) mode is insignificantly depended on the grade of inertial sensor, when there are enough available satellites; (2) after the complete GNSS outages, the TCI mode expresses both higher convergence speed and more accurate positioning solutions than the LCI mode. Furthermore, in the TCI mode, using a higher grade inertial sensor is beneficial for the PPP convergence; (3) under the partial GNSS outage situations, the PPP/INS TCI mode position divergence speed is also restrained significantly; and (4) the attitude determination accuracy of the PPP/INS integration is highly correlated with the grade of inertial sensor.

The satellite network of Chinese Beidou system and the European Galileo System are on-contraction recently, which promotes the development of Multi-GNSS high-precision fusion applications. In this paper, the algorithm of multi-GNSS real-time clock fusion estimation is studied deeply, the real-time augmentation message processing strategy is also discussed and real-time orbit data processing and analysis are carried out based on PANDA software. Then the multi-GNSS real-time augmentation system prototype is constructed based on the GNSS real-time stream which could be obtained currently and real-time augmentation messages including GPS, BeiDou and Galileo are broadcasting on the Internet. The experiment results show that the real-time augmentation message signal-in-space ranging error(RTAM-SISRE), effecting the user’s actual positioning performance, of GPS is about 4–7 cm, that of Beidou IGSO/MEO and Galileo is about 10 cm and BeiDou GEO satellites’ is about 33 cm, respectively. The real-time Precise Point Positioning (PPP) results prove that 5–7 cm horizontal RMS and better-than 10 cm vertical RMS based on carrier-phase observation can be obtained.

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.

[1] Real-time detection and precise estimation of strong ground motion are crucial for rapid assessment and early warning of geohazards such as earthquakes, landslides, and volcanic activity. This challenging task can be accomplished by combining GPS and accelerometer measurements because of their complementary capabilities to resolve broadband ground motion signals. However, for implementing an operational monitoring network of such joint measurement systems, cost-effective techniques need to be developed and rigorously tested. We propose a new approach for joint processing of single-frequency GPS and MEMS (microelectromechanical systems) accelerometer data in real time. To demonstrate the performance of our method, we describe results from outdoor experiments under controlled conditions. For validation, we analyzed dual-frequency GPS data and images recorded by a video camera. The results of the different sensors agree very well, suggesting that real-time broadband information of ground motion can be provided by using single-frequency GPS and MEMS accelerometers.

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.

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.

In order to obtain crustal deformations of higher spatial resolution, existing GPS networks must be densified. This densification can be carried out using single-frequency receivers at moderate costs. However, ionospheric delay handling is required in the data processing. We adapt the Satellite-specific Epoch-differenced Ionospheric Delay model (SEID) for GPS networks with mixed single- and dual-frequency receivers. The SEID model is modified to utilize the observations from the three nearest dual-frequency reference stations in order to avoid contaminations from more remote stations. As data of only three stations are used, an efficient missing data constructing approach with polynomial fitting is implemented to minimize data losses. Data from large scale reference networks extended with single-frequency receivers can now be processed, based on the adapted SEID model. A new data processing scheme is developed in order to make use of existing GPS data processing software packages without any modifications. This processing scheme is evaluated using a sub-network of the German SAPOS network. The results verify that the new scheme provides an efficient way to densify existing GPS networks with single-frequency receivers.

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.

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.

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.

Currently, China is strengthening infrastructure construction in South China Sea (SCS) area, it is believed that in the near future, SCS territory will play an increasingly important role in political and economic exploitation as well as international cooperation issues. However, political and economical development plans must also consider possible impact of various natural hazards as well as strategies for damage minimization. In particular, the Manila subduction zone has been identified as a zone of potential tsunami hazard in the SCS region. Despite the fact, that no earthquake higher than Mw7.6 has occurred in this region during last years, events of higher magnitudes cannot be excluded which could expose SCS to the tsunami risk. Recently, development of a region-wide Tsunami Early Warning System (TEWS) was proposed. Traditional TEWS incorporates seismic network for detection of earthquakes and estimating their tsunamigenic potential combined with ocean-based observations for monitoring of wave propagation. After the striking Great Sumatra 2004 earthquake and tsunami, new technologies were introduced into the tsunami early warning. In particular, continuous GPS-arrays able to measure earthquake source parameters in almost real-time. Around the end of 2012, China has completed the constellation of the regional Beidou Navigation Satellite System (BDS), and this system is running operationally since that time. Nowadays, China government is reinforcing the application of BDS in scientific and engineering fields. Numerous studies have demonstrated that the precise positioning performance of BDS is equal in match against GPS in the Asian-Pacific region, which promisingly suggests BDS can be implemented to facilitate tsunami early warning in the South China Sea. In present study, we use numerical simulation technique to assess the potential of the BDS for the tsunami early warning in SCS. We suggest deployment of a real-time BDS coastal network at the Luzon Island. Such a network, if established, will effectively contribute to fast source inversion at the Manila trench and, hence, to more rapid and reliable tsunami early warning in the whole SCS region.

The rapid development of multi-Global Navigation Satellite Systems (GNSSs, e.g., BeiDou, Galileo, GLONASS, and GPS) and the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) brings great opportunities and challenges for real-time determination of tropospheric zenith total delays (ZTDs) and integrated water vapor (IWV) to improve numerical weather prediction, particularly for nowcasting or severe weather event monitoring. In this paper, we develop a multi-GNSS model to fully exploit the potential of observations from all currently available GNSSs for enhancing real-time ZTD/IWV processing. A prototype multi-GNSS real-time ZTD/IWV monitoring system is also designed and realized at the Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences (GFZ) based on the precise point positioning technique. The ZTD and IWV derived from multi-GNSS stations are carefully analyzed and compared with those from collocated Very Long Baseline Interferometry and radiosonde stations. The performance of individual GNSS is assessed, and the significant benefit of multi-GNSS for real-time water vapor retrieval is also evaluated. The statistical results show that accuracy of several millimeters with high reliability is achievable for the multi-GNSS-based real-time ZTD estimates, which corresponds to about 1- to 1.5-mm accuracy for the IWV. The ZTD/IWV with improved accuracy and reliability would be beneficial for atmospheric sounding systems, particularly for time-critical geodetic and meteorological applications.

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).

Nowadays, Global Positioning System (GPS) plays an increasingly important role in retrieving real-time precise co-seismic displacements for geo-hazard monitoring and early warning. Several real-time positioning approaches have been demonstrated for such purpose, such as real-time kinematic relative positioning, precise point positioning, etc., where dual-frequency geodetic receivers are applied for the removal of ionosphere delays by inter-frequency combination. At the same time, it would be also useful to develop efficient algorithms for estimating precise displacements with low-cost GPS receivers since they can make a denser network or multi-sensors combination without putting too much financial burden. In this contribution, we present a new method to retrieve precise co-seismic displacements in real-time using a standalone single-frequency receiver. In the new method, observations prior to an earthquake are utilized to establish a precise ionospheric delay prediction model, so that precise co-seismic displacements can be obtained without any convergence process. Our method was validated with an outdoor experiment as well as by re-processing of 1-Hz GPS data collected by the GEONET network during the 2011 Tohoku Mw 9.0 earthquake. For the latter, RMS against dual-frequency receivers constituted 2 cm for horizontal components and 3 cm for the vertical component. We specially address the observation biases and their impact on the accuracy of single frequency positioning. Our approach makes real-time GPS displacement monitoring with dense network much more affordable in terms of financial costs.

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.

As a preliminary step for assessing the impact of global positioning system (GPS) refractive delay data in numerical weather prediction (NWP) models, the GPS zenith tropospheric delays (ZTDs) are analyzed from 51 permanent GPS sites in the western Mediterranean. The objectives are to estimate the error statistics necessary for future assimilation of GPS ZTD data in numerical models and to investigate the variability of the data in this area. The time series, which were derived continuously from November 1998 to June 2001, are compared with independent equivalent values derived from radiosonde profiles and the High-Resolution Limited-Area Model (HIRLAM) NWP model. Based on over two years of data, the difference between radiosonde and GPS ZTD has a standard deviation of 12 mm of delay and a bias of 7 mm of delay. Some sites have biases as high as 14 mm of delay. The bimodal distribution of residuals, with a higher bias for daytime launches, indicates these biases may be due to radiosonde day–night ...

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.

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.

Coexistence and development of four kinds of Global Satellite Navigation System, GPS, GLONASS, BDS, and GALILEO have initially established. In order to benefit from multi-GNSS applications, including increase in usable SVs, signals and frequencies, increase in availability and coverage, more robust and reliable services, and so on, firstly we need to obtain the precise multi-GNSS orbit and clock in a unified space and time frame. Based on the knowledge of the EPOS and EPOS-RT (Earth Parameter and Orbit determination System in Real-Time) software package, Beijing Aerospace Control Center (BACC) has been working on his own software package for multi-GNSS data processing. This paper firstly introduces the multi-GNSS processing strategies in detail, and adopts additional inter system biases parameter (ISB) except the normal IGS and GFZ observation model and dynamic model. On the basis of above strategies and the observation data from a network of multi-GNSS capable receivers from the IGS Multi-GNSS EXperiment (MGEX) and a regional BDS station network operated by China, the experiments and simulation are carried out. The results are validated against products from other institutes and by overlap comparison. The impact on orbit and clock precision by combined processing against single system processing is investigated and the improvement on precise point positioning (PPP) is also evaluated.