Ultra-rapid Orbit Research Articles

The ongoing modernization of the Taiwan semi-dynamic datum based on the surface horizontal deformation model using GNSS data from 2000 to 2016

A semi-dynamic geodetic datum, composed of a static geodetic datum and a surface deformation model, is proposed in this study to maintain the accuracy of geodetic datum in Taiwan. A concept to construct the surface deformation model is also suggested to accommodate the characteristics of temporal variation of the velocity field and coseismic displacements caused by earthquakes in Taiwan. In this study, we proposed a surface deformation model, containing a secular velocity grid model during 2000–2016 and a coseismic displacement grid model of the 2016 ML 6.6 Meinong earthquake, as an example to examine its adaptability in Taiwan. The secular velocity field relative to the station KMNM from 2000 to 2016 was first evaluated in this study using data from 380 continuous GNSS stations in Taiwan. Integrating 672 campaign-mode GNSS velocities from 2002 to 2016, a secular velocity grid model was constructed using the Kriging interpolation method. The high-precision coseismic displacements of the 2016 Meinong earthquake calculated using the IGS ultra-rapid orbit were also evidenced. The coseismic displacement grid model for all Taiwan for this event was built using the kinematic dislocation model to prevent contamination from nontectonic sources. Another 1341 independent GNSS control points surveyed in 2013 and 2016 were adopted to validate the reliability of the surface deformation model. After correction by the deformation model, 1219 points (91%) matched the criterion at the urban region of cadastral surveying in Taiwan (< 6 cm). The Electronic Global Navigation Satellite System (e-GNSS) in Taiwan is suggested to be integrated with the geodetic semi-dynamic datum to improve the precision of e-GNSS and to monitor the accuracy of the surface deformation model in the Taiwan semi-dynamic datum.

Evaluating the impact of higher-order ionospheric corrections on multi-GNSS ultra-rapid orbit determination

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.

Real-time precise orbit determination for BDS satellites using the square root information filter

Though widely used to generate the global navigation satellite system (GNSS) ultra-rapid orbit products for real-time applications, the batch least-squares (LSQ) adjustment and precise orbit determination (POD) prediction is limited for satellites undergoing maneuvers. To generate the truly real-time orbit products, we introduce the square root information filter (SRIF) real-time POD strategy, in which a real-time satellite maneuver handling algorithm that adapts the stochastic model for irregular satellite behaviors is implemented. The performance of the SRIF POD strategy is first evaluated with 1-month of data from multi-GNSS experiment (MGEX) network and BDS experimental tracking stations (BETS). Compared with the MGEX final products provided by GFZ (GBM), the SRIF solutions show higher precision than the ultra-rapid solutions. The averaged 3D RMS of the orbit differences between the SRIF solutions and the GBM final product is about 29.1 cm and 22.5 cm for the BDS IGSO and MEO satellites. The BDS orbits generated by SRIF are continuous over all the time, while the ultra-rapid orbits exhibit obvious jumps and discontinuity at the orbit update time. Validation by satellite laser ranging (SLR) shows that for GEO satellites, the SRIF solutions have better stability and continuity, whereas the GBM final products exhibit obvious accuracy degradation around the day boundary. To evaluate the performance of maneuver handling, the proposed method is further tested on 10 maneuver cases of BDS GEO and IGSO satellites. The start and end time of all maneuver events in different cases are precisely detected, which are consistent with the officially announced ones. Using the proposed strategy, the filter avoids divergence and outputs continuous orbit solutions during the maneuver periods and restores the normal POD within about 7.5 h after the maneuver is finished.

Random Optimization Algorithm on GNSS Monitoring Stations Selection for Ultra-Rapid Orbit Determination and Real-Time Satellite Clock Offset Estimation

Geographical distribution of global navigation satellite system (GNSS) ground monitoring stations affects the accuracy of satellite orbit, earth rotation parameters (ERP), and real-time satellite clock offset determination. The geometric dilution of precision (GDOP) is an important metric used to measure the uniformity of the stations distribution. However, it is difficult to find the optimal configuration with the lowest GDOP when taking the 71% ocean limitation into account, because the ground stations are hardly uniformly distributed on the whole of the Earth surface. The station distribution geometry needs to be optimized and besides the stability and observational quality of the stations should also be taken into account. Based on these considerations, a method of configuring global station tracking networks based on grid control probabilities is proposed to generate optimal configurations that approximately have the minimum GDOP. A random optimization algorithm method is proposed to perform the station selection. It is shown that an optimal subset of the total stations can be obtained in limited iterations by assigning selecting probabilities for the global stations and performing a Monte Carlo sampling. By applying the proposed algorithm for observation data of 201 International GNSS Service (IGS) stations for 3 consecutive days, an experiment of ultra-rapid orbit determination and real-time clock offset estimation is conducted. The distribution effects of stations on the products accuracy are analyzed. It shows that (1) the accuracies of GNSS ultra-rapid observed and predicted orbits and real-time clock offset achieved using the proposed algorithm are higher than those achieved with the traditional method having the drawbacks of lacking evaluation indicators and being time-consuming, corresponding to the improvements 17.15%, 19.30%, and 31.55%, respectively. Only using 30 stations selected by the proposed method, the accuracies achieved reach 2.01 cm (RMS), 4.93 cm (RMS), and 0.20 ns (STD), respectively. Using 60 stations, the accuracies are 1.47 cm, 3.50 cm, and 0.17 ns, respectively. (2) With the increasing number of stations, the accuracies of the Global Positioning System (GPS) orbit and clock offset improve continuously, but more than 60 stations, the improvement on the orbit determination becomes more gradual, while for more than 30 stations, there is no appreciable increase in the accuracy of the real-time clock offset.

Estimation of GPS LNAV based on IGS products for real-time PPP

Precise satellite orbit and clock corrections are essential to precise point positioning (PPP). The standard GPS legacy navigation (LNAV) message disseminated by the satellite is one of the most widely used sources for deriving orbit and clock corrections in real-time using efficient analytical user algorithms. However, the quality of the satellite orbit and clock corrections computed with the standard LNAV is not adequate for real-time PPP mainly due to the low update rate. In this study, we proposed an improved LNAV which is estimated based on the IGS ultra-rapid (IGU) orbit and real-time service (RTS) clock products. Two advantages characterize this improved LNAV message. The first one is that scalable update rates can be used for disseminating satellite orbit and clock corrections. Users can decide to receive and decode the improved LNAV message at the desired update rate considering the availability of correction streams, communication bandwidth, and targeted accuracy. With sufficiently high update rates, the improved LNAV can be applied for high-precision applications such as real-time PPP. The second advantage is that the legacy user algorithms can be maintained for computing real-time satellite orbit and clock corrections. Since the improved LNAV has the same parameter representation as the standard LNAV, no changes are required at the user algorithms. To validate the proposed method, the quality of real-time orbit and clock corrections computed with the improved LNAV, IGU products, Centro Nacional de Estudios Espaciales (CNES) real-time products, and the standard LNAV is compared, while the IGS final products are used as the reference. The numerical results indicate that the improved LNAV can achieve comparable orbit accuracy as CNES real-time products, while the clock accuracy highly depends on the update rate. A globally distributed network of 40 IGS stations is used to assess the kinematic PPP performance. Using the improved LNAV with update intervals of 5 min, an average positioning accuracy of 0.122, 0.100, and 0.242 m at 95% confidence level can be obtained in the east, north, and up directions, respectively. Even when the update intervals extend to 2 h, the positioning accuracy is still about 1.2 times better than that of using IGU products. The proposed method provides a scalable and flexible way to improve the standard LNAV for real-time PPP users.

The Preliminary Results for Five-System Ultra-Rapid Precise Orbit Determination of the One-Step Method Based on the Double-Difference Observation Model

The predicted parts of ultra-rapid orbits are important for (near) real-time Global Navigation Satellite System (GNSS) precise applications; and there is little research on GPS/GLONASS/BDS/Galileo/QZSS five-system ultra-rapid precise orbit determination; based on the one-step method and double-difference observation model. However; the successful development of a software platform for solving five-system ultra-rapid orbits is the basis of determining and analyzing these orbits. Besides this; the different observation models and processing strategies facilitate to validate the reliability of the various ultra-rapid orbits. In this contribution; this paper derives the double-difference observation model of five-system ultra-rapid precise orbit determination; based on a one-step method; and embeds this method and model into Bernese v5.2; thereby forming a new prototype software platform. For validation purposes; 31 days of real tracking data; collected from 130 globally-distributed International GNSS Service (IGS) multi-GNSS Experiment (MGEX) stations; are used to determine a five-system ultra-rapid precise orbit. The performance of the software platform is evaluated by analysis of the orbit discontinuities at day boundaries and by comparing the consistency with the MGEX orbits from the Deutsches GeoForschungsZentrum (GFZ); between the results of this new prototype software platform and the ultra-rapid orbit provided by the International GNSS Monitoring and Assessment System (iGMAS) analysis center (AC) at the Institute of Geodesy and Geophysics (IGG). The test results show that the average standard deviations of orbit discontinuities in the three-dimension direction are 0.022; 0.031; 0.139; 0.064; 0.028; and 0.465 m for GPS; GLONASS; BDS Inclined Geosynchronous Orbit (IGSO); BDS Mid-Earth Orbit (MEO); Galileo; and QZSS satellites; respectively. In addition; the preliminary results of the new prototype software platform show that the consistency of this platform has been significantly improved compared to the software package of the IGGAC.

Predicting orbit and clock corrections during their outage in real-time positioning using GPS, GLONASS and QZSS for natural hazard warning systems

Abstract Real-time Precise Point Positioning (RT PPP) is a primary positioning method used in natural hazard warning systems (NHWS) such as monitoring tsunami and earthquakes. The method relays on precise orbit and clock corrections to eliminate satellite-related errors and its performance can be significantly improved by using measurements from multi-GNSS constellations compared with using only one system, such as GPS. The Japanese Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA) provides these corrections for GPS, GLONASS and QZSS satellites enabling a multi-GNSS RT-PPP. However, the accuracy of RT PPP will suffer a major decline in case of presence of an outage in receiving these corrections, for instance due to a temporary failure of the user modem. For that reason, a method is proposed to maintain RT PPP when such a break takes place. For short outages less than 30 minutes we predict MADOCA orbits using a Holt-Winters’ auto-regressive model, and for longer outages up to 1 hr, the most recent International GNSS Service (IGS) ultra-rapid orbits can be used, but only for GPS. In addition, the clock corrections are predicted as a time series using a linear model with sinusoidal terms. The best regression period to estimate the required model parameters is discussed based on analysis of the autocorrelation of the corrections. The prediction model parameters are estimated using a sliding time window. Evaluation of the proposed method showed that positioning accuracy of 15 cm was maintained during the prediction period, which is twice better than using IGS ultra-rapid predicted products. For NHSW, the displacement errors due to prediction errors were generally within ±6 cm with one min interval and ±10 cm with five min interval.

Correction Method for the Observed Global Navigation Satellite System Ultra-Rapid Orbit Based on Dilution of Precision Values.

For ultra-rapid orbits provided by the Global Navigation Satellite System (GNSS), the key parameters, accuracy and timeliness, must be taken into consideration in real-time and near real-time applications. However, insufficient observations in later epochs appear to generate low accuracy in observed orbits, for which a correlation between the Dilution of Precision (DOP) of the orbit parameters and their accuracy is found. To correct the observed GNSS ultra-rapid orbit, a correction method based on the DOP values is proposed by building the function models between DOP values and the orbit accuracy. With 10-day orbit determination experiments, the results show that the observed ultra-rapid-orbit errors, generated by insufficient observations, can be corrected by 12–22% for the last three hours of the observed orbits. Moreover, considering the timeliness constraints in ultra-rapid-orbit determination, a DOP amplification factor is defined to weight the contribution of each tracking station and optimize the station distribution in the orbit determination procedure. Finally, six schemes are designed to verify the method and strategy in determining the ultra-rapid orbit based on one-month observations. The orbit accuracy is found to decrease by 1.27–6.34 cm with increasing amplification factor from 5–20%. Thus, the observed ultra-orbit correction method proposed is ideal when considering accuracy and timeliness in ultra-rapid orbit determination.

Improving multi-GNSS ultra-rapid orbit determination for real-time precise point positioning

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.

Comparison of Ultra-Rapid Orbit Prediction Strategies for GPS, GLONASS, Galileo and BeiDou.

Currently, ultra-rapid orbits play an important role in the high-speed development of global navigation satellite system (GNSS) real-time applications. This contribution focuses on the impact of the fitting arc length of observed orbits and solar radiation pressure (SRP) on the orbit prediction performance for GPS, GLONASS, Galileo and BeiDou. One full year’s precise ephemerides during 2015 were used as fitted observed orbits and then as references to be compared with predicted orbits, together with known earth rotation parameters. The full nine-parameter Empirical Center for Orbit Determination in Europe (CODE) Orbit Model (ECOM) and its reduced version were chosen in our study. The arc lengths of observed fitted orbits that showed the smallest weighted root mean squares (WRMSs) and medians of the orbit differences after a Helmert transformation fell between 40 and 45 h for GPS and GLONASS and between 42 and 48 h for Galileo, while the WRMS values and medians become flat after a 42 h arc length for BeiDou. The stability of the Helmert transformation and SRP parameters also confirmed the similar optimal arc lengths. The range around 42–45 h is suggested to be the optimal arc length interval of the fitted observed orbits for the multi-GNSS joint solution of ultra-rapid orbits.

Impact of the Initial State on BDS Real-Time Orbit Determination Filter Convergence

High precision real-time orbit of navigation satellites are usually predicted based on batch estimation solutions, which is highly dependent on the accuracy of the dynamic model. However, for the BDS satellites, the accuracy and reliability of the predicted orbit usually decrease due to the inaccurate dynamic model or orbit maneuvers. To improve this situation, the sequential estimation Square Root Information Filtering (SRIF) was applied to determine the real-time BDS orbits. In the filter algorithm, usually a long period is required for the orbit to converge to the final accuracy, due to lake of accurate initial state. This paper focuses on the impact of the initial state with different a priori Standard Deviation (STD) on the BDS orbit convergence performance in both normal and abnormal periods. For the normal period, the Ultra-Rapid (UR) orbit products and the Broadcast Ephemerides (BRDC) used as initial orbits are discussed respectively. For the abnormal period, orbit maneuver is analyzed. Experimental results show that a proper a priori STD of initial state can significantly accelerate the orbit convergence, while a loose a priori STD takes more than 10 h to converge in the radial direction for the BDS GEO/IGSO/MEO satellites. When the UR orbit product is used as the initial orbit, the orbit of the IGSO/MEO satellites can converge to decimeter-level immediately. When the BRDC product is used, the accuracy of meter-level can be obtained for the IGSO/MEO immediately, and converge to decimeter-level in about 6 h. For the period after the orbit maneuver, the real-time orbit accuracy can reach meter-level in about 6 h after the first group of broadcast ephemerides is received.

A method for identification of optimal minimum number of multi-GNSS tracking stations for ultra-rapid orbit and ERP determination

With the rapid increase in the numbers of new generation Global Navigation Satellite Systems (GNSS) satellites, signal frequencies and ground tracking stations, the burden on data processing increases significantly, especially for those real-time or near real-time applications, e.g. generating ultra-rapid satellite orbit and Earth rotation parameters (ERP) products. In order to reduce the number of observations used to estimate the orbit and ERP unknown parameters for better computational efficiency, this study first introduced a parameter called orbit and ERP dilution of precision (OEDOP) factor and a method in “optimally” selecting multi-GNSS tracking stations based on the OEDOP factor is investigated to minimize the data processing burden without significantly sacrificing the accuracy and precision of the satellite orbit and ERP determination. The trade-off between computational efficiency and quality of results is primary focus of this research. The contribution of each tracking station to the precision of the parameter estimates is investigated first, according to the location and multi-GNSS data measurement capacity of the station as well as the length of observations, then those stations that contribute least will be identified and excluded in the estimation system. It aims to use as a fewer number of tracking stations as possible but the degradation in the precision of the solution is still under a desired level. The method was tested using GNSS observations from 409 International GNSS service (IGS) stations over a one-month period. Results showed that when the “degradation” factor of the precision of satellite orbit and ERPs solutions is 5%, 10%, 15% and 20% the accuracy of the satellites orbit and polar motion parameters estimated from an optimal minimum number of stations (in comparison with the results from all stations) reduced about 0.33–9.92 cm and 5.77–41.53 μas respectively, and the accuracy of UT1–UTC reduced 10.63–15.50 μs; while their computational speed was improved by 196%, 332%, 527% and 617% respectively. This suggests that our method is a good trade-off method and an ideal option in cases that rapid solutions are required, e.g. ultra-rapid determination of orbit and ERP using multi-GNSS measurements from global ground tracking stations.

Impact of predicting real-time clock corrections during their outages on precise point positioning

Real-time precise point positioning (RT-PPP) is a popular positioning method for natural hazard warning systems (NHWS) such as for monitoring tsunami and earthquakes. PPP relays on the use of precise orbits and clock corrections. Hence, the positioning accuracy of RT-PPP will significantly deteriorate when experiencing a discontinuity in receiving these corrections, for instance due to a temporary modem failure. The best available approach in this case would be to use the International Global Navigation Satellite Systems Service ultra-rapid (IGU) orbits and clocks that would result in a low positioning accuracy. In this paper, we present a simplified approach to a method that we recently proposed to bridge outages in the corrections and improve the RT-PPP accuracy compared with the use of IGU. In this method, the most recent IGU orbits are used as they are compatible with the RT orbits; however, the clock corrections are predicted as a time series using a linear model with four sinusoidal terms. The prediction errors resulting from this method, age of the model and its validity period are discussed. The impact of using the proposed approach is evaluated at a number of sites of known positions by comparing its performance to using IGU orbits and clocks. Moreover, the impact of using predicted corrections is assessed in different scenarios. The experimental results proved validity of the presented approach where positioning mean RMSE of less than 20 cm was maintained during the outage period.

An approach to GPS clock prediction for real-time PPP during outages of RTS stream

The international GNSS service (IGS) has been providing an open-access real-time service (RTS) since 2013, which allows users to carry out real-time precise point positioning (RT-PPP). As the availability of RTS products is vital for RT-PPP, a disruption in receiving RTS products will be a concern. Currently, the IGS Ultra-rapid (IGU) orbit is accurate enough to be used as an alternative orbit for RTS during RTS outages, while the precision of the IGU predicted clock offsets is far below that of the RTS clock product. The existing clock prediction methods based on received RTS clock data will not work well if the discontinuity arises shortly after the start of the RT-PPP processing due to the lack of RTS clock data to fit the prediction model or to predict clock offsets at a high precision. Even if there is a sufficient amount of RTS clock data available, saving large amounts of RTS clock data would also use processor memory. An alternate approach for GPS clock prediction is proposed. The prediction model, composed of linear polynomial and sinusoidal terms, is similar to those used by the precious methods. The main innovation is the determination of the model coefficients: coefficients of linear and sinusoidal terms are estimated with the epoch-differenced clock offsets from the IGU observed part, while the constant coefficient is computed with the latest RTS clock corrections. There is no need to save the received RTS clock corrections, and clock prediction can be carried out even with only one epoch of RTS data. Evaluation of the proposed method shows that the predicted clock offsets within a short period of prediction time, e.g., 5 min, are slightly worse than RTS clock data. Even when the predicted time reaches up to 1 h, the precision of the predicted clock offsets is still higher than that of IGU predicted clock offsets by about 50%.

Impacts of Earth rotation parameters on GNSS ultra-rapid orbit prediction: Derivation and real-time correction

Analysis centers (ACs) for global navigation satellite systems (GNSSs) cannot accurately obtain real-time Earth rotation parameters (ERPs). Thus, the prediction of ultra-rapid orbits in the international terrestrial reference system (ITRS) has to utilize the predicted ERPs issued by the International Earth Rotation and Reference Systems Service (IERS) or the International GNSS Service (IGS). In this study, the accuracy of ERPs predicted by IERS and IGS is analyzed. The error of the ERPs predicted for one day can reach 0.15mas and 0.053ms in polar motion and UT1-UTC direction, respectively. Then, the impact of ERP errors on ultra-rapid orbit prediction by GNSS is studied. The methods for orbit integration and frame transformation in orbit prediction with introduced ERP errors dominate the accuracy of the predicted orbit. Experimental results show that the transformation from the geocentric celestial references system (GCRS) to ITRS exerts the strongest effect on the accuracy of the predicted ultra-rapid orbit. To obtain the most accurate predicted ultra-rapid orbit, a corresponding real-time orbit correction method is developed. First, orbits without ERP-related errors are predicted on the basis of ITRS observed part of ultra-rapid orbit for use as reference. Then, the corresponding predicted orbit is transformed from GCRS to ITRS to adjust for the predicted ERPs. Finally, the corrected ERPs with error slopes are re-introduced to correct the predicted orbit in ITRS. To validate the proposed method, three experimental schemes are designed: function extrapolation, simulation experiments, and experiments with predicted ultra-rapid orbits and international GNSS Monitoring and Assessment System (iGMAS) products. Experimental results show that using the proposed correction method with IERS products considerably improved the accuracy of ultra-rapid orbit prediction (except the geosynchronous BeiDou orbits). The accuracy of orbit prediction is enhanced by at least 50% (error related to ERP) when a highly accurate observed orbit is used with the correction method. For iGMAS-predicted orbits, the accuracy improvement ranges from 8.5% for the inclined BeiDou orbits to 17.99% for the GPS orbits. This demonstrates that the correction method proposed by this study can optimize the ultra-rapid orbit prediction.

Maintaining real-time precise point positioning during outages of orbit and clock corrections

The precise point positioning (PPP) is a popular positioning technique that is dependent on the use of precise orbits and clock corrections. One serious problem for real-time PPP applications such as natural hazard early warning systems and hydrographic surveying is when a sudden communication break takes place resulting in a discontinuity in receiving these orbit and clock corrections for a period that may extend from a few minutes to hours. A method is presented to maintain real-time PPP with 3D accuracy less than a decimeter when such a break takes place. We focus on the open-access International GNSS Service (IGS) real-time service (RTS) products and propose predicting the precise orbit and clock corrections as time series. For a short corrections outage of a few minutes, we predict the IGS-RTS orbits using a high-order polynomial, and for longer outages up to 3 h, the most recent IGS ultra-rapid orbits are used. The IGS-RTS clock corrections are predicted using a second-order polynomial and sinusoidal terms. The model parameters are estimated sequentially using a sliding time window such that they are available when needed. The prediction model of the clock correction is built based on the analysis of their properties, including their temporal behavior and stability. Evaluation of the proposed method in static and kinematic testing shows that positioning precision of less than 10 cm can be maintained for up to 2 h after the break. When PPP re-initialization is needed during the break, the solution convergence time increases; however, positioning precision remains less than a decimeter after convergence.

Performance of real-time Precise Point Positioning using IGS real-time service

Until recently, the real-time IGS precise orbit and clock corrections were only available for the predicted part of the ultra-rapid solution. Whereas the accuracy of the ultra-rapid orbit is about ...

CODE’s new ultra-rapid orbit and ERP products for the IGS

The International GNSS Service (IGS) issues four sets of so-called ultra-rapid products per day, which are based on the contributions of the IGS Analysis Centers. The traditional (old) ultra-rapid orbit and earth rotation parameters (ERP) solution of the Center for Orbit Determination in Europe (CODE) was based on the output of three consecutive 3-day long-arc rapid solutions. Information from the IERS Bulletin A was required to generate the predicted part of the old CODE ultra-rapid product. The current (new) product, activated in November 2013, is based on the output of exactly one multi-day solution. A priori information from the IERS Bulletin A is no longer required for generating and predicting the orbits and ERPs. This article discusses the transition from the old to the new CODE ultra-rapid orbit and ERP products and the associated improvement in reliability and performance. All solutions used in this article were generated with the development version of the Bernese GNSS Software. The package was slightly extended to meet the needs of the new CODE ultra-rapid generation.

Comparación de la metodología utilizada para el cálculo de los parámetros orbitales en los Centros de Análisis del Servicio GNSS Internacional (IGS)

The orbital information given in the form of Ultra-Rapid Orbits (IGA and IGU), Rapid Orbits (IGR), and Final Orbits (IGS), as well as the Earth rotational parameters and the clock offset provided by the International GNSS Service plays an important role in supporting the Global Navigation Satellite Systems GPS and GLONASS. In this paper, we compare the observables, the force models, the adjustment methods and the numerical integration procedures applied by the different International GNSS Service Analysis Centers for the orbital parameter determination.

A new seismogeodetic approach applied to GPS and accelerometer observations of the 2012 Brawley seismic swarm: Implications for earthquake early warning

The 26 August 2012 Brawley seismic swarm of hundreds of events ranging from M1.4 to M5.5 in the Salton Trough, California provides a unique data set to investigate a new seismogeodetic approach that combines Global Positioning System (GPS) and accelerometer observations to estimate displacement and velocity waveforms. First in simulated real‐time mode, we analyzed 1–5 Hz GPS data collected by 17 stations fully encircling the swarm zone at near‐source distances up to about 40 km using precise point positioning with ambiguity resolution (PPP‐AR). We used a reference network of North American GPS stations well outside the region of deformation to estimate fractional‐cycle biases and satellite clock parameters, which were then combined with ultrarapid orbits from the International GNSS Service to estimate positions during the Brawley seismic swarm. Next, we estimated seismogeodetic displacements and velocities from GPS phase and pseudorange observations and 100–200 Hz accelerations collected at three pairs of GPS and seismic stations in close proximity using a new tightly coupled Kalman filter approach as an extension of the PPP‐AR process. We can clearly discern body waves in the velocity waveforms, including P‐wave arrivals not detectable with the GPS‐only approach for earthquake magnitudes as low as Mw 4.6 and significant static offsets for magnitudes as low as Mw 5.4. Our study shows that GPS networks upgraded with strong motion accelerometers can provide new information for improved understanding of the earthquake rupture process and be of critical value in creating a robust early warning system for any earthquake of societal significance.